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+Influence of illumination on the quantum lifetime in selectively doped single GaAs 
+quantum wells with short-period AlAs/GaAs superlattice barriers
+A. A. Bykov, D. V. Nomokonov, A. V. Goran, I. S. Strygin, I. V. Marchishin, A. K. Bakarov
+Rzhanov Institute of Semiconductor Physics, Russian Academy of Sciences, Siberian Branch, 
+Novosibirsk, 630090, Russia
+The influence  of illumination  on a high mobility  two-dimensional  electron  gas  with high 
+concentration of charge carriers is studied in selectively doped single GaAs quantum wells with 
+short-period  AlAs/GaAs  superlattice  barriers  at a temperature  T = 4.2 K  in  magnetic  fields 
+B < 2 T. It is shown that illumination at low temperatures in the studied heterostructures leads to 
+an increase in the concentration, mobility, and quantum lifetime of electrons. An increase in the 
+quantum lifetime due to illumination of single GaAs quantum wells with modulated superlattice 
+doping is explained by a decrease in the effective concentration of remote ionized donors.
+Introduction
+Persistent  photoconductivity  (PPC),  which  occurs  in  selectively  doped  GaAs/AlGaAs 
+heterostructures at low temperatures (T) as the result of visible light illumination, is widely used 
+as a method for changing the concentration (ne), mobility () and quantum lifetime (q) of 
+electrons in such two-dimensional (2D) systems [1-5]. PPC is also used in one-dimensional 
+lateral superlattices  based on high mobility selectively doped  GaAs/AlGaAs  heterostructures 
+[6, 7]. One of the causes of PPC is the change in the charge state of DX centers in doped AlGaAs 
+layers under illumination [8, 9]. PPC is undesirable in high mobility heterostructures intended for 
+the manufacturing of field-effect transistors, as it introduces instability into their performance. 
+One of the ways to suppress PPC is to use short-period AlAs/GaAs superlattices as barriers to 
+single GaAs quantum wells [10]. In this case, the sources of free charge carriers are thin -doped 
+GaAs layers located in short-period superlattice barriers in which DX centers do not appear.
+Another motivation for remote superlattice doping of single GaAs quantum wells is the 
+fabrication of 2D electronic systems with simultaneously high  ne and  . In selectively doped 
+GaAs/AlGaAs heterostructures, to suppress the scattering of 2D electron gas on a random 
+potential of ionized donors, the charge transfer region is separated from the doping region by an 
+undoped AlGaAs layer (spacer) [4]. High  in such a system is achieved due to a “thick” spacer 
+(dS > 50 nm) with a relatively low concentration ne ~ 31015 m-2. To implement high mobility 2D 
+electron systems with a “thin” spacer (dS < 50 nm) and high ne, it was proposed in [11] to use 
+short-period AlAs/GaAs superlattices as barriers to single GaAs quantum wells (Fig. 1). In this 
+case, the suppression of scattering by ionized Si donors is achieved not only by separation of the 
+regions of doping and transport, but also by the screening effect of X-electrons localized in AlAs 
+layers [11-13].
+1
+
+0.6
+口1
+2
+0.4
+(sd)
+0.2
+(a)
+0.0
+(b)
+1.2
+0.8
+d
+口
+1
+0.4
+0
+2
+0.0
+1.0
+1.2
+1.4
+1.6
+ne (1016 m*2)(a)
+AlAs/GaAs
+Si-S-doping
+SPSL
+dsi
+GaAs SQW
+SQW
+AlAs/GaAs
+↓ Si-8-doping
+SPSL
+(b)
+AlAs
+GaAs
+Si-
++
++
++
+AIAs18
+Pyy
+12
+1
+3
+2
+6
+4
+(a)
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+B (T)
+6
+(b)
+3
+5
+4
+4
+3
+1
+口
+1
+A
+2
+2
+2
+△
+3
+4
+0.0
+0.4
+0.8
+1.2
+1.6
+2.0
+1/B (1/T)60
+1
+40
+2
+3
+20
+4
+(a)
+0
+0.0
+0.6
+1.2
+1.8
+B (T)
+12
+(b)
+2
+0
+0
+8
+口
+(sd)
+1
+口
+4.
+口
+1
+2
+0
+1.1
+1.2
+1.3
+1.4
+1.5
+ne (1016 m*2)Fig. 1. (a) Schematic view of a single GaAs quantum well with side barriers of short-period 
+AlAs/GaAs superlattices. (b) An enlarged view of a portion of the -doped layer in a narrow 
+GaAs quantum well with adjacent AlAs layers. Ellipses show compact dipoles formed by 
+positively charged Si donors in the -doped layer and X-electrons in AlAs layers [13].
+Superlattice doping of single GaAs quantum wells is used not only to implement high 
+mobility 2D electronic systems with a thin spacer [11, 12], but also to achieve ultrahigh  in 2D 
+electronic systems with a thick spacer [14-16]. In GaAs/AlAs heterostructures with modulated 
+superlattice doping, PPC due to a change in the charge states of DX centers should not arise [10]. 
+However, it has been found that in selectively doped single GaAs quantum wells with short-
+period AlAs/GaAs superlattice barriers and a thin spacer, illumination increases ne and  [17-19], 
+and with a thick spacer, it increases q [20]. The increase in q was explained by the redistribution 
+of X-electrons in AlAs layers adjacent to thin  -doped GaAs layers. However, the effect of 
+illumination on  q in single GaAs quantum wells with a thin spacer and superlattice doping 
+remains unexplored.
+2
+
+0.6
+口1
+2
+0.4
+(sd)
+0.2
+(a)
+0.0
+(b)
+1.2
+0.8
+d
+口
+1
+0.4
+0
+2
+0.0
+1.0
+1.2
+1.4
+1.6
+ne (1016 m*2)(a)
+AlAs/GaAs
+Si-S-doping
+SPSL
+dsi
+GaAs SQW
+SQW
+AlAs/GaAs
+↓ Si-8-doping
+SPSL
+(b)
+AlAs
+GaAs
+Si-
++
++
++
+AIAs18
+Pyy
+12
+1
+3
+2
+6
+4
+(a)
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+B (T)
+6
+(b)
+3
+5
+4
+4
+3
+1
+口
+1
+A
+2
+2
+2
+△
+3
+4
+0.0
+0.4
+0.8
+1.2
+1.6
+2.0
+1/B (1/T)60
+1
+40
+2
+3
+20
+4
+(a)
+0
+0.0
+0.6
+1.2
+1.8
+B (T)
+12
+(b)
+2
+0
+0
+8
+口
+(sd)
+1
+口
+4.
+口
+1
+2
+0
+1.1
+1.2
+1.3
+1.4
+1.5
+ne (1016 m*2)One of the features of GaAs/AlAs heterostructures with a thin spacer and superlattice doping 
+grown by molecular beam epitaxy on (001) GaAs substrates is the anisotropy of  [21]. In such 
+structures,  y in the [-110] crystallographic direction can exceed  x in the [110] direction by 
+several times [22]. The anisotropy of   is due to scattering on the heterointerface roughness 
+oriented along the [-110] direction and arising during the growth of heterostructures [23, 24]. 
+This work is devoted to studying the effect of illumination on a 2D electron gas with an 
+anisotropic  in single GaAs quantum wells with a thin spacer and superlattice doping. It has 
+been established that illumination increases ne, , and q in the heterostructures under study. It is 
+shown that the increase in q after illumination is due to a decrease in the effective concentration 
+of remote ionized donors.
+Quantum lifetime
+The traditional method of measuring  q in a 2D electron gas is based on studying the 
+dependence of the amplitude of the Shubnikov – de Haas (SdH) oscillations on the magnetic 
+field (B) [25-30]. In 2D electron systems with isotropic   low field SdH oscillations  are 
+described by the following relation [28]:
+SdH = 4 0 X(T) exp(-/cq) cos(2F/ħc - ),                                    (1)
+where SdH is the oscillating component of the dependence xx(B), 0 = xx(B = 0) is the Drude 
+resistance, X(T) = (22kBT/ħc)/sinh(22kBT/ħc), c = eB/m*, F is the Fermi energy. Using the 
+results of [26], it is easy to generalize (1) for a 2D system with anisotropic mobility d. In this 
+case,  the  normalized  amplitude  of  SdH  oscillations  will  be  determined  by  the  following 
+expression [31]:
+Ad
+SdH = d
+SdH/0d X(T) = A0d
+SdH exp(-/cqd),                                     (2)
+where the index  d  corresponds to the main mutually perpendicular directions x and y,  and A0d
+SdH 
+= 4.
+The value of  q in single GaAs quantum wells with short-period AlAs/GaAs superlattice 
+barriers is determined mainly by small-angle scattering [11, 12]. In this case, q can be expressed 
+by the relation [32-34]:
+q  qR = (2m*/) (kFdR)/nR
+eff,                                                 (3)
+where  qR  is the quantum lifetime upon scattering on a random potential of a remote impurity, kF 
+= (2ne)0.5, dR = (dS + dSQW/2), dSQW is the thickness of a single GaAs quantum well, and neff
+R is 
+the effective concentration of remote ionized donors. The value of neff
+R takes into account the 
+change in the scattering potential of remote donors when they are bound to X-electrons (Fig. 1b) 
+[13]. The dependence of  neff
+R on  ne in the heterostructures under study is described by the 
+following phenomenological relation [35]:
+neff
+R = neff
+R0/{exp[(ne - a)/b] + 1}  neff
+R0 fab(ne),                                   (4)
+where  neff
+R0,  a and  b are fitting parameters.  fab is the fraction of ionized remote donors not 
+associated with X-electrons into compact dipoles.
+3
+
+0.6
+口1
+2
+0.4
+(sd)
+0.2
+(a)
+0.0
+(b)
+1.2
+0.8
+d
+口
+1
+0.4
+0
+2
+0.0
+1.0
+1.2
+1.4
+1.6
+ne (1016 m*2)(a)
+AlAs/GaAs
+Si-S-doping
+SPSL
+dsi
+GaAs SQW
+SQW
+AlAs/GaAs
+↓ Si-8-doping
+SPSL
+(b)
+AlAs
+GaAs
+Si-
++
++
++
+AIAs18
+Pyy
+12
+1
+3
+2
+6
+4
+(a)
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+B (T)
+6
+(b)
+3
+5
+4
+4
+3
+1
+口
+1
+A
+2
+2
+2
+△
+3
+4
+0.0
+0.4
+0.8
+1.2
+1.6
+2.0
+1/B (1/T)60
+1
+40
+2
+3
+20
+4
+(a)
+0
+0.0
+0.6
+1.2
+1.8
+B (T)
+12
+(b)
+2
+0
+0
+8
+口
+(sd)
+1
+口
+4.
+口
+1
+2
+0
+1.1
+1.2
+1.3
+1.4
+1.5
+ne (1016 m*2)Samples under study and details of the experiment
+The GaAs/AlAs heterostructures under study were grown using molecular beam epitaxy on 
+semi-insulating GaAs (100) substrates. They were single GaAs quantum wells with short-period 
+AlAs/GaAs superlattice barriers [11, 12]. Two Si -doping layers located at distances dS1 and dS2 
+from the upper and lower heterointerfaces of the GaAs quantum well served as the sources of 
+electrons. L-shaped bridges oriented along the [110] and [-110] directions were fabricated based 
+on  the heterostructures grown  by optical lithography  and liquid etching.  The  bridges  were 
+100 µm long  and 50 µm wide.  The bridge resistance  was  measured at an alternating  current Iac 
+< 1 μA with a frequency fac ~ 0.5 kHz at a temperature  T = 4.2 K in magnetic fields B < 2 T. A 
+red LED was used for illumination.
+Table 1. Heterostructure parameters: dSQW is the quantum well thickness; dS = (dS1 + dS2)/2 is 
+the spacer average thickness; nSi is the total concentration of remote Si donors in -doped thin 
+GaAs layers; ne is the electron concentration; x is the mobility in the [110] direction; y is the 
+mobility in the direction [-110];  y/x is the mobility ratio. The asterisk marks the values 
+obtained after illumination.
+Structure
+number
+dSQW
+(nm)
+dS
+(nm)
+nSi
+(1016 m-2)
+ne
+(1015 m-2)
+y
+(m2/V s)
+x
+(m2/V s)
+y/x
+1
+13
+29.4
+3.2
+7.48
+8.42*
+124
+206*
+80.5
+103*
+1.54
+2*
+2
+10
+10.8
+5
+11.5
+14.5*
+14.7
+27.2*
+9.33
+18.6*
+1.58
+1.46*
+Experimental results and discussion
+Fig. 2a shows the experimental dependences of d(B) at T = 4.2 K for heterostructure no. 1 
+before  illumination  (curves 1 and 2)  and after illumination  (curves 3 and 4).  In  the region of 
+B > 0.5 T, SdH oscillations are observed, the period of which in the reverse magnetic field 
+decreased after illumination, which indicates an increase in ne. After illumination, the values of 
+0d also decreased, which is due not only to an increase in ne, but also to an increase in d. The 
+illumination also led to an increase in the positive magnetoresistance (MR) of the 2D electron 
+gas, which indicates an increase in the quantum lifetime [36, 37]. The dependences of Ad
+SdH on 
+1/B for structure no. 1 are shown in Fig. 2b. In accordance with formula (2), the slope of the 
+dependences Ad
+SdH(1/B) on a semilogarithmic scale is determined by the value qd. A decrease in 
+slope after illumination indicates an increase in qd. At the same time, the values of qd measured 
+in the directions [110] and [-110] are equal with an accuracy of 5%.
+4
+
+0.6
+口1
+2
+0.4
+(sd)
+0.2
+(a)
+0.0
+(b)
+1.2
+0.8
+d
+口
+1
+0.4
+0
+2
+0.0
+1.0
+1.2
+1.4
+1.6
+ne (1016 m*2)(a)
+AlAs/GaAs
+Si-S-doping
+SPSL
+dsi
+GaAs SQW
+SQW
+AlAs/GaAs
+↓ Si-8-doping
+SPSL
+(b)
+AlAs
+GaAs
+Si-
++
++
++
+AIAs18
+Pyy
+12
+1
+3
+2
+6
+4
+(a)
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+B (T)
+6
+(b)
+3
+5
+4
+4
+3
+1
+口
+1
+A
+2
+2
+2
+△
+3
+4
+0.0
+0.4
+0.8
+1.2
+1.6
+2.0
+1/B (1/T)60
+1
+40
+2
+3
+20
+4
+(a)
+0
+0.0
+0.6
+1.2
+1.8
+B (T)
+12
+(b)
+2
+0
+0
+8
+口
+(sd)
+1
+口
+4.
+口
+1
+2
+0
+1.1
+1.2
+1.3
+1.4
+1.5
+ne (1016 m*2)Fig. 2. (a) Experimental dependences of d on B measured on an L-shaped bridge at T = 4.2 K 
+before illumination (1, 2) and after illumination (3, 4) (no. 1). 1, 3 – xx(B). 2, 4 – yy(B). The 
+inset shows the geometry of the L-shaped bridge. (b) Dependences of  Ad
+SdH on 1/B before 
+illumination (1, 2) and after illumination (3, 4). Symbols are experimental data. Solid lines – 
+calculation by formula (2): 1 – A0x
+SdH = 5.02; qx = 1.44 ps; 2 – A0y
+SdH = 4.57; qy = 1.38 ps; 3 – 
+A0x
+SdH = 6.29; qx = 2.72 ps; 4 – A0y
+SdH = 4.66; qy = 3.01 ps.
+Fig. 3a shows the experimental dependences of d(B) at T = 4.2 K for heterostructure no. 2 
+before illumination (curves 1 and 2) and after illumination (curves 3 and 4). For this structure, as 
+well as for structure no. 1, short-term illumination at low temperature leads to an increase in ne 
+and d. However, for structure no. 2, in contrast to no. 1, the dependences xx(B) do not show 
+quantum  positive  MR,  while  a  classical  negative  MR  is  observed  [38],  which  decreases 
+significantly after illumination. Dependences td(ne) are presented in Fig. 3b. These dependences 
+are not described by the theory [32], which takes into account only the change in  kF with 
+increasing ne, which is due to the change in neff
+R after illumination. A similar behavior of td on ne 
+is also observed when the concentration of the 2D electron gas is changed using a Schottky gate 
+[12, 35].
+5
+
+0.6
+口1
+2
+0.4
+(sd)
+0.2
+(a)
+0.0
+(b)
+1.2
+0.8
+d
+口
+1
+0.4
+0
+2
+0.0
+1.0
+1.2
+1.4
+1.6
+ne (1016 m*2)(a)
+AlAs/GaAs
+Si-S-doping
+SPSL
+dsi
+GaAs SQW
+SQW
+AlAs/GaAs
+↓ Si-8-doping
+SPSL
+(b)
+AlAs
+GaAs
+Si-
++
++
++
+AIAs18
+Pyy
+12
+1
+3
+2
+6
+4
+(a)
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+B (T)
+6
+(b)
+3
+5
+4
+4
+3
+1
+口
+1
+A
+2
+2
+2
+△
+3
+4
+0.0
+0.4
+0.8
+1.2
+1.6
+2.0
+1/B (1/T)60
+1
+40
+2
+3
+20
+4
+(a)
+0
+0.0
+0.6
+1.2
+1.8
+B (T)
+12
+(b)
+2
+0
+0
+8
+口
+(sd)
+1
+口
+4.
+口
+1
+2
+0
+1.1
+1.2
+1.3
+1.4
+1.5
+ne (1016 m*2)Fig. 3. (a)  Dependences  of  xx(B)  and  yy(B)  measured  on the L-shaped bridge  at T = 4.2 K 
+(no. 2):  1,  2 – before illumination;  3,  4 - after short-term illumination by a red LED. (b) 
+Dependencies of tx(ne) and ty(ne). Squares and circles - experimental data: 1 - tx; 2 - ty. Solid 
+lines – calculation according to the formula: td  ne
+1.5: 1 – tx; 2 – ty.
+The experimental dependences qd(ne) for structure no. 2 (Fig. 4a) show that qd for different 
+crystallographic directions are equal with an accuracy of 5%, which agrees with [31]. The 
+experimental data are well described by formula (3) for the effective concentration of positively 
+charged  Si  donors  calculated  by  formula  (4).  The  agreement  between  the  experimental 
+dependences qd(ne) and the calculated one indicates that the increase in the quantum lifetime of 
+electrons in a single GaAs quantum well after low-temperature illumination is due to a decrease 
+in neff
+R.
+6
+
+0.6
+口1
+2
+0.4
+(sd)
+0.2
+(a)
+0.0
+(b)
+1.2
+0.8
+d
+口
+1
+0.4
+0
+2
+0.0
+1.0
+1.2
+1.4
+1.6
+ne (1016 m*2)(a)
+AlAs/GaAs
+Si-S-doping
+SPSL
+dsi
+GaAs SQW
+SQW
+AlAs/GaAs
+↓ Si-8-doping
+SPSL
+(b)
+AlAs
+GaAs
+Si-
++
++
++
+AIAs18
+Pyy
+12
+1
+3
+2
+6
+4
+(a)
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+B (T)
+6
+(b)
+3
+5
+4
+4
+3
+1
+口
+1
+A
+2
+2
+2
+△
+3
+4
+0.0
+0.4
+0.8
+1.2
+1.6
+2.0
+1/B (1/T)60
+1
+40
+2
+3
+20
+4
+(a)
+0
+0.0
+0.6
+1.2
+1.8
+B (T)
+12
+(b)
+2
+0
+0
+8
+口
+(sd)
+1
+口
+4.
+口
+1
+2
+0
+1.1
+1.2
+1.3
+1.4
+1.5
+ne (1016 m*2)Fig.  4.  (a)  Dependences  of  qd(ne):  squares  are  the  experimental  values  of  qy;  circles  – 
+experimental values of qx; the solid line is the calculation for neff
+R = neff
+R0fab. (b) Dependences of 
+neff
+R and neff
+R0fab on ne: squares and circles are the values of neff
+R calculated from the experimental 
+values of qx and qy; solid line – neff
+R0fab for neff
+R0 = 1.261016 m-2, a = 1.371016 m-2 and b = 
+0.0821016 m-2.
+Conclusion
+The influence of illumination on the low-temperature transport in a 2D electron gas with 
+anisotropic  mobility  in  selectively  doped  single  GaAs  quantum  wells  with  short-period 
+AlAs/GaAs superlattice barriers in classically strong magnetic fields was studied. It has been 
+shown that, in the heterostructures under study, illumination by a red LED at low temperatures 
+leads to an increase in the concentration, mobility, and quantum lifetime of electrons. An 
+increase in the quantum lifetime of electrons in single GaAs quantum wells with modulated 
+superlattice doping after illumination is explained by a decrease in the effective concentration of 
+remote ionized donors.
+7
+
+0.6
+口1
+2
+0.4
+(sd)
+0.2
+(a)
+0.0
+(b)
+1.2
+0.8
+d
+口
+1
+0.4
+0
+2
+0.0
+1.0
+1.2
+1.4
+1.6
+ne (1016 m*2)(a)
+AlAs/GaAs
+Si-S-doping
+SPSL
+dsi
+GaAs SQW
+SQW
+AlAs/GaAs
+↓ Si-8-doping
+SPSL
+(b)
+AlAs
+GaAs
+Si-
++
++
++
+AIAs18
+Pyy
+12
+1
+3
+2
+6
+4
+(a)
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+B (T)
+6
+(b)
+3
+5
+4
+4
+3
+1
+口
+1
+A
+2
+2
+2
+△
+3
+4
+0.0
+0.4
+0.8
+1.2
+1.6
+2.0
+1/B (1/T)60
+1
+40
+2
+3
+20
+4
+(a)
+0
+0.0
+0.6
+1.2
+1.8
+B (T)
+12
+(b)
+2
+0
+0
+8
+口
+(sd)
+1
+口
+4.
+口
+1
+2
+0
+1.1
+1.2
+1.3
+1.4
+1.5
+ne (1016 m*2)Funding
+This work was supported by the Russian Foundation for Basic Research (project no. 20-02-
+00309).
+References
+[1] H. Stormer, R. Dingle, A. Gossard, W. Wiegmann, and M. Sturge, Solid State Commun. 29, 
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+703 (2015).
+[20] X. Fu, A. Riedl, M. Borisov, M. A. Zudov, J. D. Watson, G. Gardner, M. J. Manfra, K. W. 
+Baldwin, L. N. Pfeiffer, and K. W. West, Phys. Rev. B 98, 195403 (2018).
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+164 (2001).
+8
+
+0.6
+口1
+2
+0.4
+(sd)
+0.2
+(a)
+0.0
+(b)
+1.2
+0.8
+d
+口
+1
+0.4
+0
+2
+0.0
+1.0
+1.2
+1.4
+1.6
+ne (1016 m*2)(a)
+AlAs/GaAs
+Si-S-doping
+SPSL
+dsi
+GaAs SQW
+SQW
+AlAs/GaAs
+↓ Si-8-doping
+SPSL
+(b)
+AlAs
+GaAs
+Si-
++
++
++
+AIAs18
+Pyy
+12
+1
+3
+2
+6
+4
+(a)
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+B (T)
+6
+(b)
+3
+5
+4
+4
+3
+1
+口
+1
+A
+2
+2
+2
+△
+3
+4
+0.0
+0.4
+0.8
+1.2
+1.6
+2.0
+1/B (1/T)60
+1
+40
+2
+3
+20
+4
+(a)
+0
+0.0
+0.6
+1.2
+1.8
+B (T)
+12
+(b)
+2
+0
+0
+8
+口
+(sd)
+1
+口
+4.
+口
+1
+2
+0
+1.1
+1.2
+1.3
+1.4
+1.5
+ne (1016 m*2)[22] K.-J. Friedland, R. Hey, O. Bierwagen, H. Kostial, Y. Hirayama, and K. H. Ploog, Physica 
+E 13, 642 (2002).
+[23] Y. Tokura, T. Saku, S. Tarucha, and Y. Horikoshi, Phys. Rev. B 46 15558 (1992).
+[24] M. D. Johnson, C. Orme, A. W. Hunt, D. Graff, J. Sudijono, L. M. Sander, and B. G. Orr, 
+Phys. Rev. Lett. 72, 116 (1994).
+[25] I. M. Lifshits and A. M. Kosevich, Zh. Eksp. Teor. Fiz. 29, 730 (1955) [Sov. Phys. JETP 2, 
+636 (1956)].
+[26] A. Isihara and L. Smrcka, J. Phys. C: Solid State Phys. 19, 6777 (1986).
+[27] P. T. Coleridge, R. Stoner, and R. Fletcher, Phys. Rev. B 39, 1120 (1989). 
+[28] P. T. Coleridge, Phys. Rev. B 44, 3793 (1991).
+[29] S. D. Bystrov, A. M. Kreshchuk, S. V. Novikov, T. A. Polyanskaya, I. G. Savel'ev, Fiz. 
+Tekh. Poluprov. 27, 645 (1993) [Semiconductors 27, 358 (1993)].
+[30] S. D. Bystrov, A. M. Kreshchuk, L. Taun, S. V. Novikov, T. A. Polyanskaya, I. G. Savel’ev, 
+and A. Ya. Shik, Fiz. Tekh. Poluprov. 28, 91 (1994) [Semiconductors 28, 55 (1994)].
+[31] D. V. Nomokonov, A. K. Bakarov, A. A. Bykov, in the press.
+[32] A. Gold, Phys. Rev. B 38, 10798 (1988).
+[33] J. H. Davies, The Physics of Low Dimensional Semiconductors (Cambridge Univ. Press, 
+New York, 1998).
+[34] I. A. Dmitriev, A. D. Mirlin, D. G. Polyakov, and M. A. Zudov, Rev. Mod. Phys. 84, 1709 
+(2012).
+[35] A. A. Bykov, I. S. Strygin, A. V. Goran, D. V. Nomokonov, and A. K. Bakarov, JETP Lett. 
+112, 437 (2020).
+[36] M. G. Vavilov and I. L. Aleiner, Phys. Rev. B 69, 035303 (2004). 
+[37] Scott Dietrich, Sergey Vitkalov, D. V. Dmitriev, and A. A. Bykov, Phys. Rev. B 85, 115312 
+(2012).
+[38] A. A. Bykov, A. K. Bakarov, A. V. Goran, N. D. Aksenova, A. V. Popova, A. I. Toropov, 
+JETP Lett. 78, 134 (2003).
+9
+
+0.6
+口1
+2
+0.4
+(sd)
+0.2
+(a)
+0.0
+(b)
+1.2
+0.8
+d
+口
+1
+0.4
+0
+2
+0.0
+1.0
+1.2
+1.4
+1.6
+ne (1016 m*2)(a)
+AlAs/GaAs
+Si-S-doping
+SPSL
+dsi
+GaAs SQW
+SQW
+AlAs/GaAs
+↓ Si-8-doping
+SPSL
+(b)
+AlAs
+GaAs
+Si-
++
++
++
+AIAs18
+Pyy
+12
+1
+3
+2
+6
+4
+(a)
+0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+B (T)
+6
+(b)
+3
+5
+4
+4
+3
+1
+口
+1
+A
+2
+2
+2
+△
+3
+4
+0.0
+0.4
+0.8
+1.2
+1.6
+2.0
+1/B (1/T)60
+1
+40
+2
+3
+20
+4
+(a)
+0
+0.0
+0.6
+1.2
+1.8
+B (T)
+12
+(b)
+2
+0
+0
+8
+口
+(sd)
+1
+口
+4.
+口
+1
+2
+0
+1.1
+1.2
+1.3
+1.4
+1.5
+ne (1016 m*2)

-tAzT4oBgHgl3EQfhPwa/content/tmp_files/2301.01480v1.pdf.txt

@@ -0,0 +1,1864 @@
+A new over-dispersed count model
+Anupama Nandi, Subrata Chakraborty, Aniket Biswas
+Dibrugarh University
+January 5, 2023
+Abstract
+A new two-parameter discrete distribution, namely the PoiG distribution is derived
+by the convolution of a Poisson variate and an independently distributed geometric
+random variable. This distribution generalizes both the Poisson and geometric distri-
+butions and can be used for modelling over-dispersed as well as equi-dispersed count
+data. A number of important statistical properties of the proposed count model,
+such as the probability generating function, the moment generating function, the
+moments, the survival function and the hazard rate function. Monotonic properties
+are studied such as the log concavity and the stochastic ordering are also investi-
+gated in detail. Method of moment and the maximum likelihood estimators of the
+parameters of the proposed model are presented. It is envisaged that the proposed
+distribution may prove to be useful for the practitioners for modelling over-dispersed
+count data compared to its closest competitors.
+Keywords Geometric distribution, Poisson distribution, Conway-Maxwell Poisson dis-
+tribution; BerG distribution; BerPoi distribution; Incomplete gamma function.
+MSC 2010 60E05, 62E15.
+1
+arXiv:2301.01480v1  [stat.ME]  4 Jan 2023
+
+1
+Introduction
+The phenomenon of the variance of a count data being more than its mean is commonly
+termed as over-dispersion in the literature. Over-dispersion is relevant in many modelling
+applications and it is encountered more often compared to the phenomena of under-
+dispersion and equi-dispersion. A number of count models are available in the literature
+for over-dispersed data. However, addition of a simple yet adequate model is of importance
+given the ongoing research interest in this direction ([37], [25], [32], [35], [30], [29], [9],
+[19], [26], [34], [5], [2] and [36]). The simplest and the most common count data model
+is the Poisson distribution. Its equi-dispersion characteristic is well-known. This is a
+limitation for the Poisson model and to overcome this issue, several alternatives have
+been developed and used for their obvious advantage over the classical Poisson model.
+Notable among these distributions are the hyper-Poisson (HP) of Bardwell and Crow
+[6], generalized Poisson distribution of Jain and Consul [20], double-Poisson of Efron
+[16], weighted Poisson of Castillo and Pérez-Casany [15], weighted generalized Poisson
+distribution of Chakraborty [10], Mittag-Leffler function distribution of Chakraborty and
+Ong [13] and the popular COM-Poisson distribution Shmueli et al. [31]. COM-Poisson
+generalizes the binomial and the negative binomial distribution. The classical geometric
+and negative binomial models are also used for over-dispersed count datasets. The gamma
+mixture of the Poisson distribution generates the negative binomial distribution [17].
+Thus unlike the Poisson distribution, these two count models posses the over-dispersion
+characteristic. Consequently, several extensions of the geometric distribution have been
+introduced in the literature for over-dispersed count data modelling ([11], [12], [18], [20],
+[22], [27], [28], and [33] among others). Two most widely used distributions for over-
+dispersed data are of course the negative binomial and COM-Poisson. As pointed out
+earlier, there is still plenty of opportunity for developing new discrete distributions with
+simple structure and explicit interpretation, appropriate for over-dispersed data.
+Recently, Bourguignon et al. have introduced the BerG distribution [8] by using the
+convolution of a Bernoulli random variable and a geometric random variable. In a very
+recent publication, Bourguignon et al. have introduced the BerPoi distribution from a
+similar motivation [7]. This is a convolution of a Bernoulli random variable and a Poisson
+random variable. The first one is capable of modelling over-dispersed, under-dispersed
+and equi-dispersed data whereas the second one is efficient for modelling under-dispersed
+data. This approach is simple and has enormous potential. Here we use this idea to
+develop a novel over-dispersed count model.
+In this article, we propose a new discrete distribution derived from the convolution of
+two independent count random variables. The random variables are Poisson and geomet-
+ric. Hence we identify the proposed model as PoiG. This two-parameter distribution
+has many advantages. Structural simplicity is one of them. It is easy to comprehend
+unlike the COM-Poisson distribution, which involves a difficult normalising constant in
+its probability mass function. A model with closed-form expressions of the mean and the
+variance is well-suited for regression modelling. Unlike the COM-Poisson distribution,
+mean and variance of the proposed distribution can be written in closed form expressions.
+The proposed distribution extends both the Poisson and geometric distributions.
+Rest of the article is organized as follows. In section 2, we present the PoiG distribution.
+In Section 3, we describe its important statistical properties such as recurrence relation,
+generating functions, moments, dispersion index, mode, reliability properties, monotonic
+2
+
+properties and stochastic ordering. In Section 4, we present the moment and the max-
+imum likelihood methods of parameter estimation. We conclude the article with a few
+limitations and future scopes of the current study.
+2
+The PoiG distribution
+In this section, we introduce a novel discrete distribution by considering two independent
+discrete random variables Y1 and Y2.
+Let us denote the set of non-negative integers,
+{0, 1, 2, ...} by N0. Also let, Y1 and Y2 follow the Poisson distribution with mean λ > 0
+and the geometric distribution with mean 0 < 1/θ < 1, respectively. Both Y1 and Y2 have
+the same support N0. For convenience, we write Y1 ∼ P(λ) and Y2 ∼ G(θ). Consider,
+Y = Y1 + Y2. Then,
+Pr(Y = y) =
+y
+�
+i=0
+Pr(Y1 = i) Pr(Y2 = y − i)
+=
+y
+�
+i=0
+e−λλi
+i!
+θ(1 − θ)y−i
+= θ(1 − θ)ye−λ
+y
+�
+i=0
+1
+i!
+�
+λ
+1 − θ
+�i
+,
+y = 0, 1, 2, ... .
+(1)
+The distribution in (1) being the convolution Poisson and geometric, is named the PoiG
+distribution and we write Y ∼ PoiG(λ, θ). Thus, the probability mass function (pmf) of
+PoiG(λ, θ) can be written as
+pY (y) = θ(1 − θ)y
+Γ(y + 1) exp
+� λθ
+1 − θ
+�
+Γ
+�
+y + 1,
+λ
+1 − θ
+�
+,
+y = 0, 1, 2, ... .
+(2)
+Figure 1 exhibits nature of the pmf for different choices of (λ, θ). The cumulative distri-
+bution function (cdf) of PoiG distribution is
+FY (y) = Pr(Y1 + Y2 ≤ y)
+=
+y
+�
+y1=0
+y−y1
+�
+y2=0
+pY (y1)pY (y2)
+=
+y
+�
+y1=0
+FG(y − y1)pY (y1)
+=
+y
+�
+y1=0
+(1 − (1 − θ)y−y1+1)pY (y1)
+=
+y
+�
+y1=0
+e−λλy1
+y1!
+− (1 − θ)y+1e−λ
+y
+�
+y1=0
+1
+y1!
+�
+λ
+1 − θ
+�y1
+.
+(3)
+An explicit expression of (3) is given by
+FY (y) = Γ(y + 1, λ)
+Γ(y + 1)
+− (1 − θ)y+1
+Γ(y + 1) exp
+� λθ
+1 − θ
+�
+Γ
+�
+y + 1,
+λ
+1 − θ
+�
+,
+y = 0, 1, 2, ... .
+(4)
+3
+
+Figure 2 exhibits nature of the cdf for different choices of (λ, θ). The mean and variance
+of the PoiG(λ, θ) distribution are given as follows.
+E(Y ) = µ = λ + 1 − θ
+θ
+and
+V (Y ) = σ2 = λ + 1 − θ
+θ2
+(5)
+Special cases
+• For λ −→ 0, PoiG(λ, θ) behaves like G(θ).
+• For θ −→ 1, PoiG(λ, θ) behaves like P(λ).
+Remark 1
+• The incomplete gamma function [1] is defined as Γ(n, x) =
+� ∞
+x t(n−1)e−tdt and it
+can also be rewrite as Γ(n, x) = (n − 1)! �n−1
+k=0
+e−xxk
+k!
+, which is valid for positive
+values of n and any value of x. Thus the incomplete gamma function in (2) can be
+rewritten as
+Γ
+�
+y + 1,
+λ
+1 − θ
+�
+= Γ(y + 1)
+y
+�
+i=0
+1
+Γ(i + 1) exp
+�
+−
+λ
+1 − θ
+��
+λ
+1 − θ
+�i
+,
+where Γ(y + 1) = y! and Γ(i + 1) = i!.
+• FY (0) = pY (0) = θe−λ. Thus, the proportion of zeros in case of the PoiG distribu-
+tion tends to θ as λ → 0 and to zero as λ → ∞.
+3
+Properties of the PoiG distribution
+In this section, we explore several important statistical properties of the proposed PoiG(λ, θ)
+distribution. Some of the distributional properties studied here are the recurrence relation,
+probability generating function (pgf), moment generating function (mgf), characteristic
+function (cf), cumulant generating function (cgf), moments, coefficient of skewness and
+kurtosis. We also study the reliability properties such as the survival function and the
+hazard rate function. Log-concavity and stochastic ordering of the proposed model are
+also investigated.
+3.1
+Recurrence relation
+Probability recurrence relation helps in finding the subsequent term using the preceding
+term. It usually proves to be advantageous in computing the masses at different values.
+Note that,
+pY (y) = θ(1 − θ)y
+Γ(y + 1) exp
+� λθ
+1 − θ
+�
+Γ
+�
+y + 1,
+λ
+1 − θ
+�
+= θ(1 − θ)ye−λ
+y
+�
+i=0
+1
+Γ(i + 1)
+�
+λ
+1 − θ
+�i
+= θ(1 − θ)ye−λsy.
+4
+
+Figure 1:
+Probability mass function of PoiG(λ, θ) for λ ∈ {0, 0.5, 5, 10} and θ ∈
+{0.2, 0.4, 0.6, 0.8}.
+The (i, j)th plot corresponds to the ith value of λ and jth value of
+θ for i, j = 1, 2, 3, 4.
+5
+
+0.20 
+0.4 f
+0.6 t
+0.8+
+0.5
+0.15
+0.3
+0.4
+0.6
+0.10
+0.2
+0.4
+0.05
+0.1
+0.2
+0.1
+0.2
+0
+10
+15
+20
+0
+2
+4
+to
+10
+0
+2
+0
+2
+3
+4
+5
+0.15 F °
+0.25 
+0.5 §
+0.35
+0.20
+0.30
+0.4
+0.10
+0.15
+0.25
+0.20
+0.3 E
+0.05
+0.10
+0.15
+0.2
+0.05
+0.10
+0.05
+0.1
+0
+5
+10
+15
+20
+2
+4
+6
+8
+10
+12
+0
+2
+4
+6
+8
+0
+2
+3
+d
+5
+6
+0.10 E
+0.14 E
+0.12
+0.15
+0.08
+0.10
+0.06
+0.08
+0.10
+0.10
+0.04
+0.06
+0.04
+0.05
+0.05
+0.02
+0.02
+:
+0
+5
+10
+15
+20
+25
+30
+0
+5
+10
+15
+0
+5
+10
+5
+0
+2
+4
+6
+8
+10 
+0.08
+0.12 
+0.12 E
+0.12 E
+0.10
+0.10
+0.10
+0.06
+0.08
+0.08
+0.08
+0.04
+0.06
+0.06
+0.06
+0.04
+0.02日
+0.04 
+0.04
+0.02
+0.02 
+0.02
+5
+0
+5
+10
+15
+20
+25
+0
+10
+15
+20 
+0
+5
+10
+15
+20Figure 2: Cumulative distribution function of PoiG(λ, ��) for λ ∈ {0, 0.5, 5, 10} and θ ∈
+{0.2, 0.4, 0.6, 0.8} .The (i, j)th plot corresponds to the ith value of λ and jth value of θ for
+i, j = 1, 2, 3, 4.
+6
+
+1.0 E
+1.0 
+1.0 
+.0
+0.8 E
+0.8
+0.8
+0.8.
+0.6
+0.6
+0.6.
+0.6
+0.4
+0.4 
+0.4
+0.4
+0.2.
+0.2 
+0.2 
+0.2
+0
+5
+10
+15
+20
+25
+30
+0
+5
+10
+15
+20 
+25
+30
+0
+5
+10
+15
+20
+25
+30
+0
+5
+10
+15
+20
+25
+30
+1.0 E
+1.0 F
+1.0 E
+1.0 E
+0.8 E
+0.8
+0.8
+0.8 E:
+0.6 E
+0.6
+0.6
+0.6 E
+0.4
+0.4
+0.4 
+0.2
+0.2
+0.2
+0.2
+0
+5
+10
+15
+20
+25
+30
+0
+5
+10
+15
+20 
+25
+30
+0
+5
+10
+15
+20
+25
+30
+0
+5
+10
+15
+20
+25
+30
+1.0 E
+1.0 F
+1.0 E
+1.0 E
+0.8 E
+0.8 E
+0.8 E
+0.8 E
+0.6 E
+0.6
+0.6
+0.6 E
+0.4 E
+0.4
+0.4
+0.4 
+0.2
+0.2
+0.2
+0.2
+0
+5
+10
+15
+20
+25
+30
+5
+10
+15
+20
+25
+30
+10 
+15
+20
+25
+30
+0
+5
+10
+15
+20
+25
+1.0 F
+1.0 F
+1.0 
+1.0 
+0.8 E
+0.8 E
+0.8 E
+180
+0.6 E
+0.6
+0.6
+0.6 F
+0.4 E
+0.4 E
+0.4 
+0.4 E
+0.2
+0.2
+0.2
+0.2
+0
+5
+10
+15
+20 
+25
+30
+5
+10
+15
+20 
+25
+30
+0
+5
+10 
+15
+20 
+25
+30
+0
+5
+10
+15
+20
+25
+30Where,
+sy =
+y
+�
+i=0
+1
+Γ(i + 1)
+�
+λ
+1 − θ
+�i
+and
+sy+1 = sy +
+1
+Γ(y + 2)
+�
+λ
+1 − θ
+�y+1
+.
+Now,
+pY (y + 1) = θ(1 − θ)y+1e−λsy+1
+= θ(1 − θ)y+1e−λ
+�
+sy +
+1
+Γ(y + 2)
+�
+λ
+1 − θ
+�y+1�
+= (1 − θ)pY (y) + θe−λ
+λy+1
+Γ(y + 2).
+(6)
+This is the recurrence formula of the PoiG distribution. It is easy to check that
+sy+1
+sy
+= 1 +
+1
+syΓ(y + 2)
+�
+λ
+1 − θ
+�y+1
+= 1
+as y −→ ∞,
+and
+pY (y + 1)
+pY (y)
+= (1 − θ) + θe−λ
+pY (y)
+λy+1
+Γ(y + 2) = 1 − θ
+as y −→ ∞.
+(7)
+From (7), it is clear that the behaviour of the tail of the distribution depends on θ. When
+θ −→ 0, the tail of the distribution decays relatively slowly, which implies long tail. when
+θ −→ 1, the tail of the distribution decays fast, which implies short tail. This can easily
+be verified from Figure 1.
+3.2
+Generating functions
+We use the notation H to denote a pgf and use the notation of the corresponding random
+variable in the subscript. For Y1 ∼ P(λ) and Y2 ∼ G(θ),
+HY1(s) = eλ(s−1)
+and
+HY2(s) =
+θ
+1 − (1 − θ)s.
+Now by using the convolution property of probability generating function we obtain the
+pgf of PoiG(λ, θ) as
+HY (s) =
+θeλ(s−1)
+1 − s + θs.
+(8)
+Similar methods are used to obtain the other generating functions, including the mgf
+MY (t), cf φY (t) and cgf KY (t). These are given below.
+MY (t) =
+θeλ(t−1)
+1 − (1 − θ)t
+(9)
+7
+
+φY (t) =
+θeλ(eit−1)
+1 − (1 − θ)eit
+(10)
+KY (t) = λ(et − 1) + log
+�
+θ
+1 − (1 − θ)et
+�
+(11)
+Let us discuss some useful definitions and notations for Result 1 given below. The no-
+tation G(θ) has already been introduced in Section 2. Let R be the number of failures
+preceding the first success in a sequence of independent Bernoulli trials. If the probability
+of success is θ ∈ (0, 1), then R is said to follow G(θ). Suppose, we wait for the rth success.
+Then the number of failures is a negative binomial random variable with index r and the
+parameter θ. Let NB(r, θ) denote this distribution. Suppose Ri ∼ G(θ), for i = 1, 2, ..., r
+independently and S ∼ NB(r, θ). Then S = R1 + R2 + ... + Rr. Thus, it is clear that
+the G(θ) is a particular case of NB(r, θ) with r = 1. Similar to the genesis of PoiG
+model, if we add one Poisson random variable and an independently distributed negative
+binomial random variable, it is possible to obtain a generalization of the PoiG model.
+An appropriate notation for this distribution would have been PoiNB. The objective of
+the current work is not to study this three-parameter distribution in detail. However, the
+following result establishes that the generalization from the geometric distribution to the
+negative binomial distribution translates similarly to the PoiG − PoiNB case. This may
+prove to be a motivation for generalizing the proposed model to PoiNB in future.
+Result 1 The distribution of the sum of n independent PoiG random variables is a
+PoiNB random variable for fixed θ. Mathematically, if Yi ∼ PoiG(λi, θ) for each i =
+1, 2, ..., n then,
+n
+�
+i=1
+Yi ∼ PoiNB(
+n
+�
+i=1
+λi, n, θ).
+Proof of Result 1 From (8), the pgf of Yi ∼ PoiG(λi, θ) is
+HYi(s) =
+θeλi(s−1)
+1 − s + θs
+for i = 1, 2, ..., n. We can derive the pgf of sum of n independent PoiG(λi, θ) variates
+based on the convolution property of the pgf. Let, Z = Y1 + Y2 + .... + Yn. Then,
+HZ(s) =
+n
+�
+i=1
+HYi(s)
+=
+θn
+(1 − s + θs)ne
+�n
+i=1 λi(s−1).
+(12)
+The term θn/(1−s+θs)n in (12) is the pgf of NB(n, θ) which is a generalisation of geomet-
+ric distribution and e
+�n
+i=1 λi(s−1) is pgf of P (�n
+i=1 λi). Thus �n
+i=1 Yi ∼ PoiNB (�n
+i=1 λi, n, θ).
+8
+
+3.3
+Moments and related concepts
+The rth order raw moment of Y ∼ PoiG(λ, θ) can be obtained using the general expres-
+sions of the raw moments of Y1 ∼ P(λ) and Y2 ∼ G(θ) as follows.
+E(Y r) = E
+�
+r
+�
+j=0
+�Y
+j
+�
+Y1
+jY2
+y−j
+�
+=
+r
+�
+j=0
+�Y
+j
+�
+E(Y1
+j)E(Y2
+y−j)
+Note that,
+E(Y1
+j) =
+∞
+�
+Y1=0
+Y1
+j e−λλY1
+Y1!
+=
+∞
+�
+Y1=0
+λY1S(j, Y1)
+= φj(λ).
+Here, S(j, Y1) is the Stirling number of the second kind [1] and φj(λ) is the Bell polynomial
+[24]. Again,
+E(Y2
+y−j) =
+∞
+�
+Y2=0
+Y2
+y−jθ(1 − θ)Y2
+= θ Li−(y−j)(1 − θ),
+where Li−(y−j)(1 − θ) is the polylogarithm of negative integers [14]. Hence
+E(Y r) =
+r
+�
+j=0
+�Y
+j
+�
+φj(λ)θ Li−(y−j)(1 − θ).
+(13)
+The rth order raw moment can also be calculated by differentiating the mgf in (9) r times
+with respect to t and putting t = 0. That is,
+E(Y r) = M (r)
+Y (0) = dr
+dtr [MY (t)]t=0.
+Explicit expressions of the first four moments are listed below.
+E(Y ) = λ + 1 − θ
+θ
+(14)
+E(Y 2) = 1
+θ2[θ2(λ2 − λ + 1) + θ(2λ − 3) + 2]
+(15)
+E(Y 3) = 1
+θ3[θ3(λ3 + λ − 1) + θ2(3λ2 − 6λ + 7) + θ(6λ − 12) + 6]
+(16)
+E(Y 4) = 1
+θ4[θ4(λ4 + 2λ3 + λ2 − λ + 1) + θ3(4λ3 − 6λ2 + 14λ − 15)
++ 2θ2(6λ2 − 18λ + 25) + 12θ(2λ − 5) + 24]
+(17)
+9
+
+Using the above, explicit expressions of the first four central moments are given as follows.
+µ1 = 0
+(18)
+µ2 = λ + 1 − θ
+θ2
+(19)
+µ3 = θ3λ + θ2 − 3θ + 2
+θ3
+(20)
+µ4 = θ4λ(3λ + 1) − θ3(6λ + 1) + 2θ2(3λ + 5) − 18θ + 9
+θ4
+(21)
+The first raw and second central moments are mean and variance of the PoiG(λ, θ) dis-
+tribution, respectively. Let γ1 and γ2 denote the coefficients of skewness and kurtosis,
+respectively. Using the central moments, these coefficients can be derived in closed forms
+as follows.
+β1 = µ32
+µ23 = (θ3λ + θ2 − 3θ + 2)2
+(θ2λ − θ + 1)3
+γ1 =
+�
+β1 =
+�
+(θ3λ + θ2 − 3θ + 2)2
+(θ2λ − θ + 1)3
+β2 = µ4
+µ22 = θ4λ(3λ + 1) − θ3(6λ + 1) + 2θ2(3λ + 5) − 18θ + 9
+(θ2λ − θ + 1)2
+γ2 = β2 − 3 = θ4λ(3λ + 1) − θ3(6λ + 1) + 2θ2(3λ + 5) − 18θ + 9
+(θ2λ − θ + 1)2
+− 3
+Remark 3
+• As θ → 1, β1 → 1
+λ and as θ → 0, β1 → 4.
+• As θ → 1, β2 → 3 + 1
+λ and as θ → 0, β2 → 9.
+The statements made in Remark 3 can easily be realized visually from Figure 3 and Figure
+4, respectively. Clearly, as λ → ∞, the distribution tends to attain normal shape with
+β1 → 0 and β2 → 3.
+3.4
+Dispersion index and coefficient of variation
+The
+dispersion index determines whether a distribution is suitable for modelling an
+over, under and equi-dispersed dataset or not. Let IY denote the dispersion index of the
+distribution of the random variable Y . When IY is more or less than one, the distribution
+of Y can accommodate over-dispersion or under-dispersion, respectively. The notion of
+equi-dispersion is indicated when IY = 1. The dispersion index is given by
+IY = σ2
+µ = 1 +
+(1 − θ)2
+θ(1 + λθ − θ).
+10
+
+Figure 3: Skewness of PoiG(λ, θ) for θ ∈ {0.2, 0.4, 0.6, 0.8}. The ith plot corresponds to
+the ith value of θ for different values of λ in the x-axis.
+Figure 4: Kurtosis of PoiG(λ, θ) for θ ∈ {0.2, 0.4, 0.6, 0.8}. The ith plot corresponds to
+the ith value of θ for different values of λ in the x-axis.
+From the expression of IY above, it follows that the PoiG distribution is equi-dispersed
+when θ = 1 and over-dispersed for all 0 < θ < 1. From Figure 5, it can be observed that
+IY increases with decreasing λ and θ.
+The coefficient of variation (CV) is an indicator for data variability. Higher value of the
+CV indicates the capability of a distribution to model data with higher variability. Note
+that,
+CV (Y ) =
+√
+λθ2 − θ + 1
+λθ − θ + 1
+× 100%.
+3.5
+Mode
+In Section 3.7, we show that PoiG(λ, θ) is unimodal. Note that,
+pY (1) ≤ pY (0)
+=⇒
+(1 + λ − θ)θe−λ ≤ θe−λ
+=⇒
+λθe−λ − θ2e−λ ≤ 0
+=⇒
+λ − θ ≤ 0
+=⇒
+λ ≤ θ.
+The converse is trivially true. Thus, the distribution has mode at zero for λ ≤ θ. Figure
+1 clearly shows that the mode is zero for λ = 0, 0.5 and θ > 0, 0.5. For the equality case,
+11
+
+71
+6
+5
+4
+2
+3
+0
+10
+20
+30
+40
+50
+0
+5
+10
+15
+20
+25
+0
+5
+10
+15
+0
+2
+4
+6
+8
+1010.
+12 t
+8
+8
+10 
+6
+8
+6
+2
+0
+10
+20
+30
+40
+50 
+0
+10
+20
+30
+40
+50
+0
+10
+20
+30
+40
+50
+0
+10
+20
+30
+40
+50Figure 5: Dispersion index of PoiG(λ, θ).
+Figure 6: Probability mass function of PoiG(λ, θ) for λ = θ ∈ {0.2, 0.4, 0.6, 0.8}.
+that is λ = θ, the masses at zero and at unity are the same. Figure 6 clearly exhibits this
+fact. However, for the λ > θ case, the distribution has non-zero mode. Unfortunately, an
+explicit expression for this non-zero mode is difficult to find, if not impossible.
+3.6
+Reliability properties
+Reliability function of a discrete random variable Y at y is defined as the probability of
+Y assuming values greater than or equal to y. The reliability function is also termed as
+the survival function. The survival function of Y ∼ PoiG(λ, θ) is
+SY (y) = P(Y ≥ y) = 1 − Γ(y, λ)
+Γy
++ (1 − θ)y
+Γy
+exp
+� λθ
+1 − θ
+�
+Γ
+�
+y,
+λ
+1 − θ
+�
+.
+(22)
+The hazard rate or failure rate of a discrete random variable T at time point t is defined
+as the conditional probability of failure at t, given that the survival time is at least t.
+The hazard rate function (hrf) of Y ∼ PoiG(λ, θ) can be obtained by using (1) and (4)
+12
+
+0=0.75
+入=0 
+入=1 
+入=5
+入=50
+0=0.15
+0=0.30
+0=0.45
+0=0.60
+ly
+ly
+7
+20
+15
+5 
+4
+10
+3
+10
+20 
+30
+40
+50
+0.0
+0.2
+0.4
+0.6
+0.8
+1.00.25
+0.35
+0.35
+0.15
+0.30
+0.20
+0.30
+0.25
+0.25
+0.10
+0.15
+0.20
+0.20
+0.10
+0.15
+0.15
+0.05
+0.05
+0.10
+0.10
+0.05
+0.05
+1
+2
+4
+6
+224
+0
+2
+6
+8
+10
+0
+2
+4
+8as follows.
+hY (y) = P(Y = y)
+P(Y ≥ y) =
+θ(1 − θ)y
+Γ(y + 1) exp
+� λθ
+1 − θ
+�
+Γ
+�
+y + 1,
+λ
+1 − θ
+�
+1 − Γ(y, λ)
+Γy
++ (1 − θ)y
+Γy
+exp
+� λθ
+1 − θ
+�
+Γ
+�
+y,
+λ
+1 − θ
+�
+=
+θ(1 − θ)y exp
+� λθ
+1 − θ
+�
+Γ
+�
+y + 1,
+λ
+1 − θ
+�
+Γ(y + 1) − yΓ(y, λ) + y(1 − θ)y exp
+� λθ
+1 − θ
+�
+Γ
+�
+y,
+λ
+1 − θ
+�.
+(23)
+The hrf for different choices of the parameters are exhibited in Figure 7.
+The PoiG
+distribution exhibits constant failure rate when λ is very small and it exhibits an increasing
+failure rate, up to a specific time period, when λ increases.
+In reliability studies, the mean residual life is the expected additional lifetime given that
+a component has survived until a fixed time. If the random variable Y ∼ PoiG(λ, θ)
+represents the life of a component, then the mean residual life is
+µY (y) = E(Y − y|Y ≥ y)
+=
+�∞
+y=k(y − k)P(Y = y)
+P(Y ≥ y)
+=
+�∞
+y=k ¯F(y)
+¯F(k − 1)
+=
+�∞
+y=k
+�
+1 − Γ(y, λ)
+Γy
++ (1 − θ)y
+Γy
+exp
+� λθ
+1 − θ
+�
+Γ
+�
+y,
+λ
+1 − θ
+��
+1 − Γ(k − 1, λ)
+Γ(k − 1)
++ (1 − θ)k−1
+Γ(k − 1) exp
+� λθ
+1 − θ
+�
+Γ
+�
+k − 1,
+λ
+1 − θ
+�.
+(24)
+3.7
+Monotonic Properties
+Y ∼ PoiG(λ, θ) is log-concave if the following holds for all y ≥ 1.
+p2
+Y (y) ≥ pY (y − 1)pY (y + 1)
+A log-concave distribution possesses several desirable properties. Some of the notable
+examples of log-concave distributions are the Bernoulli, binomial, Poisson, geometric, and
+negative binomial. Convolution of two independent log-concave distributions is also a log-
+concave distribution [21]. Being the convolution of Poisson and Geometric distributions,
+the proposed PoiG distribution is log-concave. Consequently, the following statements
+hold good for the PoiG distribution ([23] and [3]).
+• Strongly unimodal.
+• At most one exponential tail.
+• All the moments exist.
+• Log-concave survival function.
+13
+
+Figure 7: Hazard rate function of PoiG(λ, θ) for λ ∈ {0, 0.5, 5, 10} row-wise and θ ∈
+{0.2, 0.4, 0.6, 0.8} column-wise. The (i, j)th plot corresponds to the ith value of λ and jth
+value of θ for i, j = 1, 2, 3, 4.
+• Monotonically increasing hazard rate function (see Figure 7).
+• Monotonically decreasing mean residual life function.
+14
+
+0.20
+0.4
+0.6
+0.8
+0.5
+0.15
+0.3
+0.4 
+0.6
+0.10
+0.2 
+0.3
+0.4
+0.05
+0.2 
+0.1
+0.1
+0.2
+F.
+10
+15
+20 
+25
+30
+0
+5
+10
+25
+30
+0
+5
+30
+15
+20
+10 
+15
+20
+25
+0
+5
+10
+15
+20
+25
+30
+0.20 E
+0.4 
+0.6 F
+0.8 F
+0.5 
+0.15
+0
+0.4.
+0.6
+0.10
+0.2
+0.3
+0.4
+0.2 
+0.05
+0.1
+0.1
+0.2
+10
+15
+20 
+25
+30
+E
+0
+5
+10
+15
+20 
+25
+30
+0
+5
+10
+15
+20 
+25
+30
+0
+5
+10
+15
+20 
+0.20 E
+0.4 E
+0.6 F
+0.8 t
+0.5 
+0.15
+0.3 
+0.4 
+0.6 
+0.10
+0.2
+0
+0.4
+0.1 
+0.2
+0.05
+0.1
+0.2
+.
+.i
+F.i
+0
+5
+10
+15
+20
+30
+0
+5
+10
+15
+20
+25
+30
+0
+5
+10 
+15
+20
+25
+30
+0
+5
+10
+15
+25
+30
+0.20 E
+0.4 t
+0.6 t
+0.5
+0.6
+0.15 E
+0.3 
+0.5
+0.4 
+0.4 
+0.10
+0.2 
+0.3
+0
+0.05
+0.1 [
+0.2 
+0.2 
+0.1
+0.1
+0
+5
+10
+15
+30
+0
+5
+10
+15
+20
+25
+30
+0
+5
+10 
+15
+20
+25
+30
+0
+5
+10
+15
+20 
+25
+303.8
+Stochastic ordering
+Stochastic order is an important statistical property used to compare the behaviour of
+different random variables [4]. We have considered here the likelihood ratio order ≥lr. Let
+X ∼ PoiG(λ1, θ) and Y ∼ PoiG(λ2, θ). Then Y is said to be smaller than X in the usual
+likelihood ratio order, that is Y ≤lr X) if L(x) = pX(x)/pY (x) is an increasing function
+in x, that is L(x) ≤ L(x + 1) for all 0 < θ < 1 and λ2 < λ1. Note that,
+pX(x) = θ(1 − θ)xe−λ1
+x
+�
+i=0
+1
+Γ(i + 1)
+� λ1
+1 − θ
+�i
+,
+x = 0, 1, 2, ...
+pY (x) = θ(1 − θ)xe−λ2
+x
+�
+i=0
+1
+Γ(i + 1)
+� λ2
+1 − θ
+�i
+,
+x = 0, 1, 2, ... .
+L(x) = exp [−(λ1 − λ2)]
+�x
+i=0
+1
+Γ(i + 1)
+� λ1
+1 − θ
+�i
+�x
+i=0
+1
+Γ(i + 1)
+� λ2
+1 − θ
+�i,
+x = 0, 1, 2, ...
+It is easy to see that, L(x) ≤ L(x + 1) for all 0 < θ < 1 and λ2 < λ1.
+Let Y ≤st X denote P(Y ≥ x) ≤ P(X ≥ x) for all x. This is the notion of stochastic
+ordering. Similarly, the hazard rate order Y ≤hr X implies
+pX(x)
+P(X ≥ x) ≤
+pY (x)
+P(Y ≥ x)
+for all x. The reversed hazard rate order Y ≤rh X implies
+pY (x)
+P(Y ≤ x) ≤
+pX(x)
+P(X ≤ x)
+for all x.
+From the likelihood ratio order of X and Y , the following statements are
+immediate [4].
+• Stochastic order: Y ≤st X.
+• Hazard rate order: Y ≤hr X.
+• Reverse hazard rate order: Y ≤rh X.
+4
+Estimation
+Let Y = (Y1, Y2, ..., Yn) be a random sample of size n from the PoiG(λ, θ) distribution
+and y = (y1, y2, ..., yn) be a realization on Y. The objective of this section is estimate the
+parameters λ and θ based on the available data y. We present two different methods of
+estimation. We also find asymptotic confidence intervals for both the parameters based
+on the maximum likelihood estimates.
+4.1
+Method of moments
+Using the expressions in (14) and (19), the mean and the variance of Y ∼ PoiG(λ, θ) are
+as follows.
+µ
+′
+1 = λ + 1 − θ
+θ
+and µ2 = λ + 1 − θ
+θ2
+15
+
+Now by subtracting µ2 from µ
+′
+1,
+µ
+′
+1 − µ2 = 1 − θ
+θ
+− 1 − θ
+θ2
+=⇒ µ
+′
+1 − µ2 = 1 − θ
+θ
+�
+1 − 1
+θ
+�
+=⇒ µ2 − µ
+′
+1 =
+�1 − θ
+θ
+�2
+=⇒ 1 − θ
+θ
+=
+�
+µ2 − µ
+′
+1
+=⇒ θ =
+1
+1 +
+�
+µ2 − µ
+′
+1
+(25)
+By putting θ from (25) in µ
+′
+1, we obtain
+λ = µ
+′
+1 −
+�
+µ2 − µ
+′
+1
+(26)
+This method involves equating sample moments with theoretical moments.
+Thus, by
+equating the first sample moment about the origin m
+′
+1 = �n
+i=1 yi/n to µ
+′
+1 and the second
+sample moment about the mean m2 = �n
+i=1(yi − ¯y)2/n to µ2 in equation (25) and (26),
+we obtain the following estimators for λ and θ.
+ˆλMM = m
+′
+1 −
+�
+m2 − m
+′
+1
+(27)
+ˆθMM =
+1
+1 +
+�
+m2 − m
+′
+1
+(28)
+4.2
+Maximum likelihood method
+Using the pmf of Y ∼ PoiG(λ, θ) in (1), the log-likelihood function of the parameters λ
+and θ can easily be found as
+l(λ, θ; y) = n log θ + ny log(1 − θ) + nλθ
+1 − θ +
+n
+�
+i=0
+log
+�
+�
+�
+�
+Γ
+�
+yi + 1,
+λ
+1 − θ
+�
+Γ(yi + 1)
+�
+�
+�
+� .
+(29)
+Let us define,
+β =
+λ
+1 − θ
+and for j = 1, 2, 3, ...
+αj(yi) =
+e−β
+Γ (yi + 1, β)
+1
+(1 − θ)j .
+Differentiating (29), with respect to parameters λ and θ, we get the score functions as
+∂
+∂λl(λ, θ; y) =
+nθ
+1 − θ −
+n
+�
+i=1
+α1(yi)βyi
+(30)
+∂
+∂θl(λ, θ; y) = n
+θ + n(λ − ¯y)
+1 − θ
++
+nλθ
+(1 − θ)2 −
+n
+�
+i=1
+λα2(yi)βyi.
+(31)
+16
+
+Ideally, the explicit maximum likelihood estimators are obtained by simultaneously solving
+the two equations obtained by setting right hand sides of (30) and (31) equal to zero.
+Unfortunately, the explicit expressions of the maximum likelihood estimators could not
+be obtained in this case due to the structural complexity. Thus, we directly optimize
+the log-likelihood function with respect to the parameters using appropriate numerical
+technique. Let ˆλML and ˆθML denote the maximum likelihood estimates (MLE) of λ and
+θ respectively.
+Now, our objective is to obtain asymptotic confidence intervals for both the parameters.
+For this purpose, we require the information matrix. The second-order partial derivative
+of the log-likelihood are given below.
+∂2l(λ, θ; y)
+∂λ2
+=
+n
+�
+i=1
+�
+(βyi − yiβyi−1)α2(yi) − β2yiα1(yi)2�
+∂2l(λ, θ; y)
+∂λ∂θ
+=
+n
+(1 − θ)2 +
+n
+�
+i=1
+�
+λ(βyi − yiβyi−1)α3(yi) − βyiα2(yi) − λ(1 − θ)β2yiα1(yi)2�
+∂2l(λ, θ; y)
+∂θ2
+= 2nλ − n¯y(1 − θ)
+(1 − θ)3
+− n
+θ2+
+n
+�
+i=1
+�
+((λ2 − 2λ(1 − θ))βyi − λ2yiβyi−1)α4(yi) − λ2β2yiα2(yi)2�
+The Fisher’s information matrix for (λ, θ) is
+I =
+�
+�
+�
+�
+�
+�
+−E
+�∂2l(λ, θ; y)
+∂λ2
+�
+−E
+�∂2l(λ, θ; y)
+∂λ∂θ
+�
+−E
+�∂2l(λ, θ; y)
+∂λ∂θ
+�
+−E
+�∂2l(λ, θ; y)
+∂θ2
+�
+.
+�
+�
+�
+�
+�
+�
+This can be approximated by
+�I =
+�
+�
+�
+�
+�
+−∂2l(λ, θ; y)
+∂λ2
+−∂2l(λ, θ; y)
+∂λ∂θ
+−∂2l(λ, θ; y)
+∂λ∂θ
+−∂2l(λ, θ; y)
+∂θ2
+.
+�
+�
+�
+�
+�
+(λ,θ)=(ˆλML,ˆθML)
+Under some general regularity conditions, for large n, √n(ˆλML − λ, ˆθML − θ) is bivariate
+normal with the mean vector (0, 0) and the dispersion matrix
+ˆI−1 =
+1
+I11I22 − I12I21
+�
+�
+I22
+−I12
+−I21
+I11
+�
+� =
+�
+�
+J11
+−J12
+−J21
+J22.
+�
+�
+Thus, the asymptotic (1−α)×100% confidence interval for λ and θ are given respectively
+by
+�
+�ˆλML − Zα
+2
+�
+J11 , ˆλML + Zα
+2
+�
+J11
+�
+� and
+�
+�ˆθML − Zα
+2
+�
+J22 , ˆθML + Zα
+2
+�
+J22
+�
+� .
+17
+
+5
+Discussion
+In this article, a new two-parameter distribution is proposed, extensively studied. Core
+of this work is theoretical development, its applied aspect is also important. From the
+application point of view, the proposed model is easy to use for modeling over-dispersed
+data. Despite the availability of several other over-dispersed count models, the proposed
+model may find wide applications due to the interpretability of its parameters.
+The
+parameter λ controls the tail of the distribution while the parameter θ adjusts for the over-
+dispersion present in a given dataset. Their combined effect gives flexibility to the shape
+of the distribution. When θ dominates λ, it keeps the J-shaped mass distribution and for
+large λ, the bell-shaped mass distribution. Consequently, the hump or the concentration of
+the observations is well accommodated. Simulation experiment to investigate performance
+of the point and asymptotic interval estimator and comparative real life data analysis will
+be reported in the complete version of the article.
+18
+
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+

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@@ -0,0 +1,553 @@
+Underwater Robotics Semantic Parser Assistant
+Jake Imyak
+[email protected]
+Parth Parekh
+[email protected]
+Cedric McGuire
+[email protected]
+Abstract
+Semantic parsing is a means of taking natu-
+ral language and putting it in a form that a
+computer can understand. There has been a
+multitude of approaches that take natural lan-
+guage utterances and form them into lambda
+calculus expressions - mathematical functions
+to describe logic. Here, we experiment with
+a sequence to sequence model to take natural
+language utterances, convert those to lambda
+calculus expressions, when can then be parsed,
+and place them in an XML format that can be
+used by a finite state machine. Experimental
+results show that we can have a high accuracy
+model such that we can bridge the gap between
+technical and nontechnical individuals in the
+robotics field.
+1
+Credits
+Jake Imyak was responsible for the creation of
+the 1250 dataset terms and finding the RNN en-
+coder/decoder model. This took 48 Hours. Cedric
+McGuire was responsible for the handling of the
+output logical form via the implementation of the
+Tokenizer and Parser. This took 44 Hours. Parth
+Parekh assembled the Python structure for behavior
+tree as well as created the actions on the robot. This
+took 40 Hours. All group members were responsi-
+ble for the research, weekly meetings, presentation
+preparation, and the paper. In the paper, each group
+member was responsible for explaining their re-
+spective responsibilities with a collaborative effort
+on the abstract, credits, introduction, discussion,
+and references. A huge thanks to our Professor Dr.
+Huan Sun for being such a great guide through the
+world of Natural Language Processing.
+2
+Introduction
+Robotics is a hard field to master. Its one of the few
+fields which is truly interdisciplinary. This leads to
+engineers with many different backgrounds work-
+ing on one product. There are domains within this
+product that engineers within one subfield may not
+be able to work with. This leads to some engineers
+not being able to interact with the product properly
+without supervision.
+As already mentioned, we aim to create an
+interface for those engineers on the Underwa-
+ter Robotics Team (UWRT). Some members on
+UWRT specialize in other fields that are not soft-
+ware engineering. They are not able to create logic
+for the robot on their own. This leads to members
+of the team that are required to be around when
+pool testing the robot. This project wants to reduce
+or remove that component of creating logic for the
+robot. This project can also be applied to other
+robots very easily as all of the main concepts are
+generalized and only require the robots to imple-
+ment the actions that are used to train the project.
+3
+Robotics Background
+3.1
+Usage of Natural Language in Robotics
+Robots are difficult to produce logic for. One big
+problem that most robotics teams have is having
+non-technical members produce logical forms for
+the robot to understand. Those who do not code
+are not able to manually create logic quickly.
+3.2
+Finite State Machines
+One logical form that is common in the robotics
+space is a Finite State Machine (FSM). FSMs are
+popular because they allow a representation to be
+completely general while encoding the logic di-
+rectly into the logical form. This means things
+such as control flow, fallback states, and sequences
+to be directly encoded into the logical form itself.
+As illustrated in Figure 1, we can easily encode
+logic into this representation. Since it easily generi-
+fied, FSM’s can be used across any robot which im-
+arXiv:2301.12134v1  [cs.CL]  28 Jan 2023
+
+Figure 1:
+A FSM represented in Behaviortree.CPP
+(Fanconti, 2020) (Fanconti, 2020)
+plements the commands that are contained within
+it.
+3.3
+Underwater Robotics Team Robot
+Since 2016, The Underwater Robotics Team
+(UWRT) at The Ohio State University has iterated
+on the foundations of a single Autonomous Under-
+water Vehicle (AUV) each year to compete at the
+RoboSub competition. Breaking from tradition, the
+team decided to take the 2019-2021 school years
+to design and build a new vehicle to compete in
+the 2021 competition. Featuring an entirely new
+hull design, refactored software, and an improved
+electrical system, UWRT has created its brand-new
+vehicle, Tempest. (Parekh, 2021)
+3.3.1
+Vehicle
+Tempest is a 6 Degree of Freedom (DOF) AUV
+with vectored thrusters for linear axis motion and
+direct drive heave thrusters. This allows the robot to
+achieve any orientation in all 6 Degrees of freedom
+[X, Y , Z, Roll, Pitch, Yaw].
+Figure 2: A render of Tempest
+3.3.2
+Vehicle Experience
+With this vehicle, the team has focused on creat-
+ing a fully fleshed out experience. This includes
+commanding and controlling the vehicle. One big
+focus of the team was to make sure that any mem-
+ber, technical or non-technical was able to manage
+and operate the robot successfully.
+3.3.3
+Task Code System
+A step to fulfill this focus was to change the
+vehicle’s task code system to use the FSM rep-
+resentation.
+This is done through the library
+BehaviorTree.CPP (Fanconti, 2020). This generic
+FSM representation allows for Tempest to use
+generified logical forms that can be applied to ANY
+robotic plant as long as that plant implements those
+commands. This library also creates and maintains
+a Graphical User Interface (GUI) which allows for
+visual tracking and creation of FSM trees. Any tree
+created by the GUI is stored within an XML file
+to preserve the tree structure. The structure of the
+output of the XML syntax is explained within the
+parser section.
+4
+Data
+A dataset was to be created in order to use natu-
+ral language utterances to lambda calculus expres-
+sions that a parser would be able to recognize to
+convert to a finite state machine. For reference,
+the following datasets were considered: the Geo-
+query set(Zettlemoyer, 2012) and General Purpose
+Service Robotics commands set (Walker, 2019).
+The Geoquery dataset provided a foundation for
+a grammar to follow for the lambda calculus ex-
+pression such that consistency would hold for our
+parser. Moreover, the gpsr dataset provided an
+ample amount of examples and different general
+purpose robotics commands that could be extended
+within the dataset we curated.
+The dataset followed the following form: nat-
+ural language utterance followed by a tab then a
+lambda calculus expression. The lambda calcu-
+lus expression is of the form ( seq ( action0
+( $0 ( parameter ) ) ) ... ( actionN ( $N (
+parameter ) ) ). The power of the following ex-
+pression is that it can be extended to N number of
+actions in a given sequence, meaning that a user
+can hypothetically type in a very complex string
+of action and an expression will be constructed for
+said sequence. Moreover, the format of our dataset
+allows for it to be extended for any type of robotics
+
+Root
+root Fallback
+Sequence
+SubTreeExpanded
+A:PassThroughwindow
+door open sequence
+Collapse
+C: IsDooropen
+A:PassThroughDoor
+Sequence
+door closed sequence
+Inverter
+C RetryUntilSuccesful
+A:PassThroughDoor
+A:CloseDoor
+num_attempts
+4
+C:IsDooropen
+A:OpenDoorcommand that a user may have. They just need to
+include examples in the train set with said action
+and the model will consider it.
+The formal grammar is:
+< seq > : ( seq ( action ) [ (action) ] )
+< action > : actionName [ (parameter ] )
+< parameter > : paramName λ ( $n ( n ) )
+The dataset we created had 1000 entries in the
+training dataset and 250 entries in the test dataset.
+The size of the vocabulary |V | = 171 for the input
+text and |V | = 46 for the output text, which is
+similar in vocabulary size to the GeoQuery dataset.
+The expressions currently increase in complexity
+in terms of the number of actions within the se-
+quence. A way to extend the complexity of the ex-
+pressions would make the < seq > tag a nontermi-
+nal to chain together nested sequences. The actions
+within our dataset currently are as follows: move
+(params: x, y, z, roll, pitch, raw), flatten (params:
+num), say (params: words), clean (params: obj),
+bring (params: val), find (params: val), goal,
+and gate. The most complex sequence is a string
+of seven subsequent actions.
+5
+Model
+5.1
+Seq2Seq Model
+We decided to use the model presented in ”Lan-
+guage to Logical Form with Neural Attention”
+(Dong, 2016). There was an implementation on
+GitHub (AvikDelta, 2018) utilizing Google’s Ten-
+sorflow library to handle all implementation details
+of the following model. The part of the paper that
+was presented was the Sequence to Sequence model
+with an attention mechanism.
+Figure 3: Process of how input natural language are en-
+coded and decoded via recurrent neural networks and
+an attention mechanism to find the utterance’s respec-
+tive natural language form. (Dong and Lapata, 2016)
+The model interprets both the input and output
+from the network as sequences of information. This
+process is represented in Figure 3: input is passed
+to the encoder, then passed through the decoder,
+and through using the attention mechanism, we can
+get an output that is a lambda calculus expression.
+Both of these sequences can be represented as L-
+layer recurrent neural networks with long short-
+term memory (LSTM) that are used to take the
+tokens from the sentences and the expressions we
+have. The model creates 200 (can be changed to
+increase and decrease the size of the network) units
+of both LSTM cells and GRU cells. The GRU
+cells are used to help compensate for the vanishing
+gradient problem. These LSTM and GRU cells
+are used in the input sequence to encode x1, ..., xq
+into vectors. Then these vectors are what form
+the hidden state of the beginning of the sequence
+in the decoder. Then in the decoder, the topmost
+LSTM cell predicts the t-th output token by taking
+the softmax of the parameter matrix and the vector
+from the LSTM cell multiplied by a one-hot vector
+used to compute the probability of the output from
+the probability distribution. The softmax used here
+is sampled softmax, which only takes into account
+a subset of our vocabulary V rather than everything
+to help alleviate the difficulty of finding the softmax
+of a large vocabulary.
+5.2
+Attention Mechanism
+The model also implemented an attention mecha-
+nism to help with the predicted values. The mo-
+tivation behind the attention mechanism is to use
+the input sequence in the decoding process since
+it is relevant information for the prediction of the
+output token. To achieve this, a context vector is
+created which is the weighted sums of the hidden
+vectors in the encoder. Then this context vector is
+used as context to find the probability of generating
+a given output.
+5.3
+Training
+To train the model, the objective is the maximize
+the likelihood of predicting the correct logical form
+given some natural language expression. Hence,
+the goal is to minimize the sum of the log prob-
+ability of predicting logical form a given natural
+language utterance q summed over all training pairs.
+The model used the RMSProp algorithm which
+is an extension of the Adagrad optimizer but uti-
+lizes learning rate adaptation. Dropout is also used
+for regularization which helps out with a smaller
+datasets to prevent overfitting. We performed 90
+epochs.
+5.4
+Inference
+To perform inference, the argmax is found of the
+probability of candidate output given the natural
+
+AttentionLayer
+whatmicrosoftjobs
+answer(J,(compa
+ny(J,'microsoft).j
+do not require a
+ob,not(reqde
+bscs?
+g(J,bscs)))
+Input
+Sequence Sequence/Tree
+Logical
+Utterance
+Encoder
+Decoder
+Formlanguage utterance. Since it is not possible to find
+the probability of all possible outputs, the proba-
+bility is put in a form such that a beam search can
+be employed to generate each individual token of
+lambda calculus expression to get the appropriate
+output.
+6
+Results
+With the default parameters set, the Sequence to Se-
+quence model achieved 86.7% accuracy for exact
+matches on the test dataset. This is consistent with
+the model’s performance on the Geoquery dataset,
+achieving 83.9% accuracy. The test dataset pro-
+vided contained a 250 entries of similar utterances
+to the train dataset of various complexities ranging
+anywhere from one to six actions being performed.
+There are other methods of evaluating we would
+like to look into in the future such as computing
+something such as an F1 score rather than solely
+relying on exact logical form matching.
+This accuracy for exact logical forms is really
+important when using the parser. It allows for FSM
+representation to be easily and quickly built. We
+were able to build the XML representation and
+run basic commands on the robot with the model
+maintaining the order we said them in.
+7
+Logical Form Parser
+The logical form output of our model is sent to a
+custom parser. The goal of this parser is to translate
+the output form into BehaviorTree XML files, in
+which the robot is able to read in as a finite state
+machine.
+7.1
+Tokenizer
+The Tokenizer comprises the initial framework of
+the parser. It accepts the raw logical form as a
+String object and outputs a set of tokens in a Python
+List. These tokens are obtained by looking for sepa-
+rator characters (in our case, a space) present in the
+logical form and splitting them into an array-like
+structure. The Tokenizer method permits custom
+action, parameter, and variable names from the log-
+ical form input, thus allowing ease of scalability
+in implementing new robot actions. Our model’s
+output nature is not able to generate syntactically
+incorrect logical forms, thus our implementation
+does not check for invalid tokens and will assume
+all input is correct. The Tokenizer is stored in a
+static Singleton class such that it can be accessed
+anywhere in the program once initialized. It keeps
+track of the current token (using getToken()) and
+has an implementation to move forward to the next
+token skipToken(). This functionality is impor-
+tant for the object-oriented approach of the parser,
+discussed in the next section.
+7.2
+Parsing Lambda Calculus Expressions
+The output tokens from the Tokenizer must be in-
+terpreted into a proper Python from before they
+are staged to be turned into XML-formatted robot-
+ready trees. This is the function of the middle step
+of the parser, in which a tree of Python objects
+are built. The parser utilizes an object-oriented
+approach.
+As such, we include three objects:
+Sequence, Action, and Parameter, with each
+corresponding to an individual member of our cus-
+tom grammar. The objects orient themselves into
+a short 3-deep tree, consisting of a Sequence root,
+Action children, and Parameter grand-children.
+Each object has its own parse() method that will
+advance the tokenizer, validate the input structure,
+and assemble themselves into a Python structure to
+be staged into an XML file. The validations are en-
+forced through our grammar definitions in Section
+4.
+7.2.1
+Sequence Object
+The Sequence object is the first object initialized
+by the parser, along with the root of our action
+tree. Each Sequence is composed of a list of 0 or
+more child actions to be executed in the order they
+appear. The parseSequence() method will parse
+each individual action using parseSAction(), all
+the while assembling a list of child actions for this
+Sequence object. As of now, Sequence objects
+are unable to be their own children (i.e. nesting
+Sequences is not permitted). However, if required,
+the Sequence object’s parseSequence() method
+can be modified to recognize a nested action se-
+quence and recursively parse it.
+7.2.2
+Action Object
+Action objects define the title of the action be-
+ing performed. Similar to Sequence, Action ob-
+jects have an internally stored list, however with
+Parameter objects as children. There may be
+any number of parameters, including none. When
+parseAction() method is called, the program val-
+idates the tokens and will call parseParameter()
+on each Parameter child identified by the action.
+
+7.2.3
+Parameter Object
+The Parameter object is a simple object that
+stores a parameter’s name and value. The parser
+does not have a check for what the name of the pa-
+rameter is, nor does it have any restrictions to what
+the value can be.
+parseParameter() searches
+through the tokens for these two items and stores
+them as attributes to the Parameter object. This
+implementation of parameter is scalable with robot
+parameters and allows any new configuration of
+parameter to pass by without any changes in the
+parser as a whole. If a new parameter is needed for
+the robot, it only has to be trained into the Seq2Seq
+model on the frontend and into the robot itself on
+the backend; the Parameter object should take care
+of it all the same.
+7.3
+BehaviorTree Output
+In the end, the parser outputs an XML file which
+can be read in to BehaviorTree.CPP (Fanconti,
+2020). An example of this file structure is shown
+in Figure 4.
+Figure 4:
+A FSM that was generated from test input
+through our RNN
+This file structure is useful because it encodes
+sequence of actions within it. The leaves of the
+sequence are always in order. The tree can also
+encode subtrees into the sequence which we have
+not implemented yet.
+8
+Discussion
+8.1
+Summary
+We learned that semantic parsing is excellent tool
+at bridging the gap between both technical and non-
+technical individuals. The power within semantic
+parsing with robotics is that any human can auto-
+mate any task just through using their words. Our
+dataset is written in a way that just extending the
+entries with another robot’s tasks that use a behav-
+ior tree to perform action, that robot’s actions can
+be automated as well.
+8.2
+Future Plans
+Future plans with this project would be to ex-
+pand the logical flow that can be implemented
+with BehaviorTree.CPP. As an FSM library, Behav-
+iorTree.CPP implements many more helper func-
+tions to create more complicated FSMs. These
+include things like if statements fallback nodes,
+and subtrees. This would be a valid expansion
+of our RNN’s logical output and with more time,
+we could support the full range of features from
+BehaviorTree.CPP
+We would also like to implement a front end
+user interface to make this service more accessible
+to anyone who was not technical. Right now, the
+only means of running our program is through the
+command line which is not suitable for individuals
+who are nontechnical. Moreover, including a speak-
+to-text component to this project would elevate it
+since an individual would be able to directly tell a
+robot what commands to do, similar to a human.
+8.3
+Source Code
+You can view the source code here:
+https://
+github.com/jrimyak/parse_seq2seq
+References
+Vinyals, O., Kaiser, L., Koo, T., Petrov, S., Sutskever,
+I. & Hinton, G. Grammar as a Foreign Language.
+(2015),
+Dong, L. & Lapata, M. Language to Logical Form with
+Neural Attention. (2016),
+Yao, Z., Tang, Y., Yih, W., Sun, H. & Su, Y. An Im-
+itation Game for Learning Semantic Parsers from
+User Interaction. Proceedings Of The 2020 Confer-
+ence On Empirical Methods In Natural Language
+Processing (EMNLP). (2020),
+Yao, Z., Su, Y., Sun, H. & Yih, W. Model-based In-
+teractive Semantic Parsing: A Unified Framework
+and A Text-to-SQL Case Study. Proceedings Of The
+2019 Conference On Empirical Methods In Natu-
+ral Language Processing And The 9th International
+Joint Conference On Natural Language Processing
+(EMNLP-IJCNLP). pp. 5450-5461 (2019),
+Walker, N., Peng, Y. & Cakmak, M. Neural Se-
+mantic Parsing with Anonymization for Command
+Understanding in General-Purpose Service Robots.
+Lecture Notes In Computer Science. pp. 337-350
+(2019),
+Dukes, K. Supervised Semantic Parsing of Robotic
+Spatial Commands .SemEval-2014 Task 6. (2014),
+Walker, N. GPSR Commands Dataset. (Zenodo,2019),
+https://zenodo.org/record/3244800,
+
+test.xm
+1
+<root main_tree_to_execute ="test">
+2
+<BehaviorTreeID="test">
+3
+<Seguencename="root_seg">
+4
+<Action
+ID="say"words="so"/
+5
+<Action
+ID="move"X="s1"/>
+6
+</Seguence>
+7
+</BehaviorTree>
+8
+</root>
+6Avikdelta parse seq2seq. GitHub Repository. (2018),
+https://github.com/avikdelta/parse_
+seq2seq,
+Faconti, D. BehaviorTree - Groot. GitHub Repository.
+(2020),
+https://github.com/BehaviorTree/
+Groot,
+Faconti,
+D. BehaviorTree.CPP. Github Repository.
+(2020),
+https://github.com/BehaviorTree/
+BehaviorTree.CPP,
+Hwang, W., Yim, J., Park, S. & Seo, M. A Compre-
+hensive Exploration on WikiSQL with Table-Aware
+Word Contextualization. (2019),
+OSU-UWRT.
+Riptide
+Autonomy.
+GitHub
+Reposi-
+tory. (2021), https://github.com/osu-uwrt/
+riptide_autonomy,
+Parekh, P., et al. The Ohio State University Underwater
+Robotics Tempest AUV Design and Implementa-
+tion
+(2021)
+https://robonation.org/app/
+uploads/sites/4/2021/07/RoboSub_2021_
+The-Ohio-State-U_TDR-compressed.pdf,
+Zettlemoyer, L. & Collins, M. Learning to Map Sen-
+tences to Logical Form: Structured Classification
+with Probabilistic Categorial Grammars. (2012),
+

0tFLT4oBgHgl3EQfpC-v/content/tmp_files/load_file.txt

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+page_content='Underwater Robotics Semantic Parser Assistant  Jake Imyak  imyak.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='1@osu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='edu  Parth Parekh  parekh.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='86@osu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='edu  Cedric McGuire  mcguire.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='389@osu.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='edu  Abstract  Semantic parsing is a means of taking natu-  ral language and putting it in a form that a  computer can understand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' There has been a  multitude of approaches that take natural lan-  guage utterances and form them into lambda  calculus expressions - mathematical functions  to describe logic.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Here, we experiment with  a sequence to sequence model to take natural  language utterances, convert those to lambda  calculus expressions, when can then be parsed,  and place them in an XML format that can be  used by a finite state machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Experimental  results show that we can have a high accuracy  model such that we can bridge the gap between  technical and nontechnical individuals in the  robotics field.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  1  Credits  Jake Imyak was responsible for the creation of  the 1250 dataset terms and finding the RNN en-  coder/decoder model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This took 48 Hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Cedric  McGuire was responsible for the handling of the  output logical form via the implementation of the  Tokenizer and Parser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This took 44 Hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Parth  Parekh assembled the Python structure for behavior  tree as well as created the actions on the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This  took 40 Hours.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' All group members were responsi-  ble for the research, weekly meetings, presentation  preparation, and the paper.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' In the paper, each group  member was responsible for explaining their re-  spective responsibilities with a collaborative effort  on the abstract, credits, introduction, discussion,  and references.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' A huge thanks to our Professor Dr.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  Huan Sun for being such a great guide through the  world of Natural Language Processing.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  2  Introduction  Robotics is a hard field to master.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Its one of the few  fields which is truly interdisciplinary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This leads to  engineers with many different backgrounds work-  ing on one product.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' There are domains within this  product that engineers within one subfield may not  be able to work with.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This leads to some engineers  not being able to interact with the product properly  without supervision.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  As already mentioned, we aim to create an  interface for those engineers on the Underwa-  ter Robotics Team (UWRT).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Some members on  UWRT specialize in other fields that are not soft-  ware engineering.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' They are not able to create logic  for the robot on their own.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This leads to members  of the team that are required to be around when  pool testing the robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This project wants to reduce  or remove that component of creating logic for the  robot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This project can also be applied to other  robots very easily as all of the main concepts are  generalized and only require the robots to imple-  ment the actions that are used to train the project.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  3  Robotics Background  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='1  Usage of Natural Language in Robotics  Robots are difficult to produce logic for.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' One big  problem that most robotics teams have is having  non-technical members produce logical forms for  the robot to understand.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Those who do not code  are not able to manually create logic quickly.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='2  Finite State Machines  One logical form that is common in the robotics  space is a Finite State Machine (FSM).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' FSMs are  popular because they allow a representation to be  completely general while encoding the logic di-  rectly into the logical form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This means things  such as control flow, fallback states, and sequences  to be directly encoded into the logical form itself.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  As illustrated in Figure 1, we can easily encode  logic into this representation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Since it easily generi-  fied, FSM’s can be used across any robot which im-  arXiv:2301.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='12134v1  [cs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='CL]  28 Jan 2023  Figure 1:  A FSM represented in Behaviortree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='CPP  (Fanconti, 2020) (Fanconti, 2020)  plements the commands that are contained within  it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='3  Underwater Robotics Team Robot  Since 2016, The Underwater Robotics Team  (UWRT) at The Ohio State University has iterated  on the foundations of a single Autonomous Under-  water Vehicle (AUV) each year to compete at the  RoboSub competition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Breaking from tradition, the  team decided to take the 2019-2021 school years  to design and build a new vehicle to compete in  the 2021 competition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Featuring an entirely new  hull design, refactored software, and an improved  electrical system, UWRT has created its brand-new  vehicle, Tempest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' (Parekh, 2021)  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='1  Vehicle  Tempest is a 6 Degree of Freedom (DOF) AUV  with vectored thrusters for linear axis motion and  direct drive heave thrusters.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This allows the robot to  achieve any orientation in all 6 Degrees of freedom  [X, Y , Z, Roll, Pitch, Yaw].' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  Figure 2: A render of Tempest  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='2  Vehicle Experience  With this vehicle, the team has focused on creat-  ing a fully fleshed out experience.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This includes  commanding and controlling the vehicle.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' One big  focus of the team was to make sure that any mem-  ber, technical or non-technical was able to manage  and operate the robot successfully.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='3  Task Code System  A step to fulfill this focus was to change the  vehicle’s task code system to use the FSM rep-  resentation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  This is done through the library  BehaviorTree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='CPP (Fanconti, 2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This generic  FSM representation allows for Tempest to use  generified logical forms that can be applied to ANY  robotic plant as long as that plant implements those  commands.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This library also creates and maintains  a Graphical User Interface (GUI) which allows for  visual tracking and creation of FSM trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Any tree  created by the GUI is stored within an XML file  to preserve the tree structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The structure of the  output of the XML syntax is explained within the  parser section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  4  Data  A dataset was to be created in order to use natu-  ral language utterances to lambda calculus expres-  sions that a parser would be able to recognize to  convert to a finite state machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' For reference,  the following datasets were considered: the Geo-  query set(Zettlemoyer, 2012) and General Purpose  Service Robotics commands set (Walker, 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  The Geoquery dataset provided a foundation for  a grammar to follow for the lambda calculus ex-  pression such that consistency would hold for our  parser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Moreover, the gpsr dataset provided an  ample amount of examples and different general  purpose robotics commands that could be extended  within the dataset we curated.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  The dataset followed the following form: nat-  ural language utterance followed by a tab then a  lambda calculus expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The lambda calcu-  lus expression is of the form ( seq ( action0  ( $0 ( parameter ) ) ) .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' ( actionN ( $N (  parameter ) ) ).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The power of the following ex-  pression is that it can be extended to N number of  actions in a given sequence, meaning that a user  can hypothetically type in a very complex string  of action and an expression will be constructed for  said sequence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Moreover, the format of our dataset  allows for it to be extended for any type of robotics  Root  root Fallback  Sequence  SubTreeExpanded  A:PassThroughwindow  door open sequence  Collapse  C: IsDooropen  A:PassThroughDoor  Sequence  door closed sequence  Inverter  C RetryUntilSuccesful  A:PassThroughDoor  A:CloseDoor  num_attempts  4  C:IsDooropen  A:OpenDoorcommand that a user may have.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' They just need to  include examples in the train set with said action  and the model will consider it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  The formal grammar is:  < seq > : ( seq ( action ) [ (action) ] )  < action > : actionName [ (parameter ] )  < parameter > : paramName λ ( $n ( n ) )  The dataset we created had 1000 entries in the  training dataset and 250 entries in the test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  The size of the vocabulary |V | = 171 for the input  text and |V | = 46 for the output text, which is  similar in vocabulary size to the GeoQuery dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  The expressions currently increase in complexity  in terms of the number of actions within the se-  quence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' A way to extend the complexity of the ex-  pressions would make the < seq > tag a nontermi-  nal to chain together nested sequences.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The actions  within our dataset currently are as follows: move  (params: x, y, z, roll, pitch, raw), flatten (params:  num), say (params: words), clean (params: obj),  bring (params: val), find (params: val), goal,  and gate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The most complex sequence is a string  of seven subsequent actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  5  Model  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='1  Seq2Seq Model  We decided to use the model presented in ”Lan-  guage to Logical Form with Neural Attention”  (Dong, 2016).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' There was an implementation on  GitHub (AvikDelta, 2018) utilizing Google’s Ten-  sorflow library to handle all implementation details  of the following model.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The part of the paper that  was presented was the Sequence to Sequence model  with an attention mechanism.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  Figure 3: Process of how input natural language are en-  coded and decoded via recurrent neural networks and  an attention mechanism to find the utterance’s respec-  tive natural language form.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' (Dong and Lapata, 2016)  The model interprets both the input and output  from the network as sequences of information.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This  process is represented in Figure 3: input is passed  to the encoder, then passed through the decoder,  and through using the attention mechanism, we can  get an output that is a lambda calculus expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  Both of these sequences can be represented as L-  layer recurrent neural networks with long short-  term memory (LSTM) that are used to take the  tokens from the sentences and the expressions we  have.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The model creates 200 (can be changed to  increase and decrease the size of the network) units  of both LSTM cells and GRU cells.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The GRU  cells are used to help compensate for the vanishing  gradient problem.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' These LSTM and GRU cells  are used in the input sequence to encode x1, .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='..' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=', xq  into vectors.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Then these vectors are what form  the hidden state of the beginning of the sequence  in the decoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Then in the decoder, the topmost  LSTM cell predicts the t-th output token by taking  the softmax of the parameter matrix and the vector  from the LSTM cell multiplied by a one-hot vector  used to compute the probability of the output from  the probability distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The softmax used here  is sampled softmax, which only takes into account  a subset of our vocabulary V rather than everything  to help alleviate the difficulty of finding the softmax  of a large vocabulary.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='2  Attention Mechanism  The model also implemented an attention mecha-  nism to help with the predicted values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The mo-  tivation behind the attention mechanism is to use  the input sequence in the decoding process since  it is relevant information for the prediction of the  output token.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' To achieve this, a context vector is  created which is the weighted sums of the hidden  vectors in the encoder.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Then this context vector is  used as context to find the probability of generating  a given output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='3  Training  To train the model, the objective is the maximize  the likelihood of predicting the correct logical form  given some natural language expression.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Hence,  the goal is to minimize the sum of the log prob-  ability of predicting logical form a given natural  language utterance q summed over all training pairs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  The model used the RMSProp algorithm which  is an extension of the Adagrad optimizer but uti-  lizes learning rate adaptation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Dropout is also used  for regularization which helps out with a smaller  datasets to prevent overfitting.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' We performed 90  epochs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content="4  Inference  To perform inference, the argmax is found of the  probability of candidate output given the natural  AttentionLayer  whatmicrosoftjobs  answer(J,(compa  ny(J,'microsoft)." metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='j  do not require a  ob,not(reqde  bscs?' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  g(J,bscs)))  Input  Sequence Sequence/Tree  Logical  Utterance  Encoder  Decoder  Formlanguage utterance.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Since it is not possible to find  the probability of all possible outputs, the proba-  bility is put in a form such that a beam search can  be employed to generate each individual token of  lambda calculus expression to get the appropriate  output.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  6  Results  With the default parameters set, the Sequence to Se-  quence model achieved 86.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='7% accuracy for exact  matches on the test dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This is consistent with  the model’s performance on the Geoquery dataset,  achieving 83.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='9% accuracy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The test dataset pro-  vided contained a 250 entries of similar utterances  to the train dataset of various complexities ranging  anywhere from one to six actions being performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  There are other methods of evaluating we would  like to look into in the future such as computing  something such as an F1 score rather than solely  relying on exact logical form matching.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  This accuracy for exact logical forms is really  important when using the parser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' It allows for FSM  representation to be easily and quickly built.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' We  were able to build the XML representation and  run basic commands on the robot with the model  maintaining the order we said them in.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  7  Logical Form Parser  The logical form output of our model is sent to a  custom parser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The goal of this parser is to translate  the output form into BehaviorTree XML files, in  which the robot is able to read in as a finite state  machine.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='1  Tokenizer  The Tokenizer comprises the initial framework of  the parser.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' It accepts the raw logical form as a  String object and outputs a set of tokens in a Python  List.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' These tokens are obtained by looking for sepa-  rator characters (in our case, a space) present in the  logical form and splitting them into an array-like  structure.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The Tokenizer method permits custom  action, parameter, and variable names from the log-  ical form input, thus allowing ease of scalability  in implementing new robot actions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Our model’s  output nature is not able to generate syntactically  incorrect logical forms, thus our implementation  does not check for invalid tokens and will assume  all input is correct.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The Tokenizer is stored in a  static Singleton class such that it can be accessed  anywhere in the program once initialized.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' It keeps  track of the current token (using getToken()) and  has an implementation to move forward to the next  token skipToken().' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This functionality is impor-  tant for the object-oriented approach of the parser,  discussed in the next section.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='2  Parsing Lambda Calculus Expressions  The output tokens from the Tokenizer must be in-  terpreted into a proper Python from before they  are staged to be turned into XML-formatted robot-  ready trees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This is the function of the middle step  of the parser, in which a tree of Python objects  are built.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The parser utilizes an object-oriented  approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  As such, we include three objects:  Sequence, Action, and Parameter, with each  corresponding to an individual member of our cus-  tom grammar.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The objects orient themselves into  a short 3-deep tree, consisting of a Sequence root,  Action children, and Parameter grand-children.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  Each object has its own parse() method that will  advance the tokenizer, validate the input structure,  and assemble themselves into a Python structure to  be staged into an XML file.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The validations are en-  forced through our grammar definitions in Section  4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='1  Sequence Object  The Sequence object is the first object initialized  by the parser, along with the root of our action  tree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Each Sequence is composed of a list of 0 or  more child actions to be executed in the order they  appear.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The parseSequence() method will parse  each individual action using parseSAction(), all  the while assembling a list of child actions for this  Sequence object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' As of now, Sequence objects  are unable to be their own children (i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='e.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' nesting  Sequences is not permitted).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' However, if required,  the Sequence object’s parseSequence() method  can be modified to recognize a nested action se-  quence and recursively parse it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='2  Action Object  Action objects define the title of the action be-  ing performed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Similar to Sequence, Action ob-  jects have an internally stored list, however with  Parameter objects as children.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' There may be  any number of parameters, including none.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' When  parseAction() method is called, the program val-  idates the tokens and will call parseParameter()  on each Parameter child identified by the action.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='3  Parameter Object  The Parameter object is a simple object that  stores a parameter’s name and value.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The parser  does not have a check for what the name of the pa-  rameter is, nor does it have any restrictions to what  the value can be.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  parseParameter() searches  through the tokens for these two items and stores  them as attributes to the Parameter object.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This  implementation of parameter is scalable with robot  parameters and allows any new configuration of  parameter to pass by without any changes in the  parser as a whole.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' If a new parameter is needed for  the robot, it only has to be trained into the Seq2Seq  model on the frontend and into the robot itself on  the backend;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' the Parameter object should take care  of it all the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='3  BehaviorTree Output  In the end, the parser outputs an XML file which  can be read in to BehaviorTree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='CPP (Fanconti,  2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' An example of this file structure is shown  in Figure 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  Figure 4:  A FSM that was generated from test input  through our RNN  This file structure is useful because it encodes  sequence of actions within it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The leaves of the  sequence are always in order.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The tree can also  encode subtrees into the sequence which we have  not implemented yet.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  8  Discussion  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='1  Summary  We learned that semantic parsing is excellent tool  at bridging the gap between both technical and non-  technical individuals.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The power within semantic  parsing with robotics is that any human can auto-  mate any task just through using their words.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Our  dataset is written in a way that just extending the  entries with another robot’s tasks that use a behav-  ior tree to perform action, that robot’s actions can  be automated as well.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='2  Future Plans  Future plans with this project would be to ex-  pand the logical flow that can be implemented  with BehaviorTree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='CPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' As an FSM library, Behav-  iorTree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='CPP implements many more helper func-  tions to create more complicated FSMs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' These  include things like if statements fallback nodes,  and subtrees.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' This would be a valid expansion  of our RNN’s logical output and with more time,  we could support the full range of features from  BehaviorTree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='CPP  We would also like to implement a front end  user interface to make this service more accessible  to anyone who was not technical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Right now, the  only means of running our program is through the  command line which is not suitable for individuals  who are nontechnical.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Moreover, including a speak-  to-text component to this project would elevate it  since an individual would be able to directly tell a  robot what commands to do, similar to a human.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  8.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='3  Source Code  You can view the source code here:  https://  github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='com/jrimyak/parse_seq2seq  References  Vinyals, O.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
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+page_content=' Grammar as a Foreign Language.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
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+page_content=' Language to Logical Form with  Neural Attention.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
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+page_content=' Proceedings Of The 2020 Confer-  ence On Empirical Methods In Natural Language  Processing (EMNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
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+page_content=' Model-based In-  teractive Semantic Parsing: A Unified Framework  and A Text-to-SQL Case Study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Proceedings Of The  2019 Conference On Empirical Methods In Natu-  ral Language Processing And The 9th International  Joint Conference On Natural Language Processing  (EMNLP-IJCNLP).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' 5450-5461 (2019),  Walker, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=', Peng, Y.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' & Cakmak, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Neural Se-  mantic Parsing with Anonymization for Command  Understanding in General-Purpose Service Robots.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  Lecture Notes In Computer Science.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' pp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' 337-350  (2019),  Dukes, K.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Supervised Semantic Parsing of Robotic  Spatial Commands .' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='SemEval-2014 Task 6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' (2014),  Walker, N.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' GPSR Commands Dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' (Zenodo,2019),  https://zenodo.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='org/record/3244800,  test.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='xm  1  <root main_tree_to_execute ="test">  2  <BehaviorTreeID="test">  3  <Seguencename="root_seg">  4  <Action  ID="say"words="so"/  5  <Action  ID="move"X="s1"/>  6  </Seguence>  7  </BehaviorTree>  8  </root>  6Avikdelta parse seq2seq.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' GitHub Repository.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' (2018),  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='com/avikdelta/parse_  seq2seq,  Faconti, D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' BehaviorTree - Groot.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' GitHub Repository.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  (2020),  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='com/BehaviorTree/  Groot,  Faconti,  D.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' BehaviorTree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='CPP.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Github Repository.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  (2020),  https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='com/BehaviorTree/  BehaviorTree.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='CPP,  Hwang, W.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=', Yim, J.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=', Park, S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' & Seo, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' A Compre-  hensive Exploration on WikiSQL with Table-Aware  Word Contextualization.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' (2019),  OSU-UWRT.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  Riptide  Autonomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='  GitHub  Reposi-  tory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' (2021), https://github.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='com/osu-uwrt/  riptide_autonomy,  Parekh, P.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=', et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' The Ohio State University Underwater  Robotics Tempest AUV Design and Implementa-  tion  (2021)  https://robonation.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='org/app/  uploads/sites/4/2021/07/RoboSub_2021_  The-Ohio-State-U_TDR-compressed.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content='pdf,  Zettlemoyer, L.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' & Collins, M.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' Learning to Map Sen-  tences to Logical Form: Structured Classification  with Probabilistic Categorial Grammars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}
+page_content=' (2012),' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/0tFLT4oBgHgl3EQfpC-v/content/2301.12134v1.pdf'}

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+arXiv:2301.02840v1  [cs.NI]  7 Jan 2023
+Network Slicing: Market Mechanism and
+Competitive Equilibria
+Panagiotis Promponas, and Leandros Tassiulas
+Department of Electrical Engineering and Institute for Network Science, Yale University, USA
+{panagiotis.promponas, leandros.tassiulas}@yale.edu
+Abstract—Towards addressing spectral scarcity and enhancing
+resource utilization in 5G networks, network slicing is a
+promising technology to establish end-to-end virtual networks
+without requiring additional infrastructure investments. By
+leveraging Software Defined Networks (SDN) and Network
+Function Virtualization (NFV), we can realize slices completely
+isolated and dedicated to satisfy the users’ diverse Quality
+of Service (QoS) prerequisites and Service Level Agreements
+(SLAs). This paper focuses on the technical and economic
+challenges that emerge from the application of the network
+slicing architecture to real-world scenarios. We consider a market
+where multiple Network Providers (NPs) own the physical
+infrastructure and offer their resources to multiple Service
+Providers (SPs). Then, the SPs offer those resources as slices
+to their associated users. We propose a holistic iterative model
+for the network slicing market along with a clock auction that
+converges to a robust ǫ-competitive equilibrium. At the end of
+each cycle of the market, the slices are reconfigured and the SPs
+aim to learn the private parameters of their users. Numerical
+results are provided that validate and evaluate the convergence
+of the clock auction and the capability of the proposed market
+architecture to express the incentives of the different entities of
+the system.
+Index Terms—Network Slicing, Mechanism Design, Network
+Economics, Bayesian Inference
+I. INTRODUCTION
+The ascending trend of the volume of the data traffic,
+as well as the vast number of connected devices, puts
+pressure on the industries to enhance resource utilization in
+5G wireless networks. With the advent of 5G networks and
+Internet of Things (IoT), researchers aim at a technological
+transformation to simultaneously improve throughput, extend
+network coverage and augment the users’ quality of service
+without wasting valuable resources. Despite the significant
+advances brought by the enhanced network architectures and
+technologies, spectral scarcity will still impede the realization
+of the full potential of 5G technology.
+In the future 5G networks, verticals need distinct network
+services as they may differ in their Quality of Service (QoS)
+requirements, Service Level Agreements (SLAs), and key
+performance indicators (KPIs). Such a need highlights the
+inefficiency of the previous architecture technologies which
+were based on a ”one network fits all” nature. In this
+This paper appeared in INFOCOM 2023.
+The research work was supported by the Office of Naval Research under
+project numbers N00014-19-1-2566, N00173-21-1-G006 and by the National
+Science Foundation under the project number CNS-2128530.
+direction, network slicing is a promising technology that
+enables the transition from one-size-fits-all to one-size-per-
+service abstraction [1], which is customized for the distinct
+use cases in a contemporary 5G network model.
+Using Software Defined Networks (SDN) and Network
+Function Virtualization (NFV), those slices are associated with
+completely isolated resources that can be tailored on-demand
+to satisfy the diverse QoS prerequisites and SLAs. Resource
+allocation in network slicing plays a pivotal role in load
+balancing, resource utilization and networking performance
+[2]. Nevertheless, such a resource allocation model faces
+various challenges in terms of isolation, customization, and
+end-to-end coordination which involves both the core but also
+the Radio Access Network (RAN) [3].
+In a typical network slicing scenario, multiple Network
+Providers (NPs), own the physical infrastructure and offer
+their resources to multiple Service Providers (SPs). Possible
+services of the SPs include e-commerce, video, gaming, virtual
+reality, wearable smart devices, and other IoT devices. The
+SPs offer their resources as completely isolated slices to their
+associated users. Thereby, such a system contains three types
+of actors that interact with each other and compete for the same
+resources, either monetary or networking. This paper focuses
+on the technical and economic challenges that emerge from
+the application of this architecture to real-world scenarios.
+A. Related Work
+User
+Satisfaction
+&
+Sigmoid
+Functions:
+Network
+applications can be separated into elastic (e.g. email, text
+file transfer) and inelastic (e.g. audio/video phone, video
+conference, tele-medicine) [4]. Utilities for elastic applications
+are modeled as concave functions that increase with the
+resources with diminishing returns [4]. On the other hand,
+the utility function for an inelastic traffic is modeled as
+a non-concave and usually as a sigmoid function. Such
+non-concavities impose challenges for the optimization of
+a network, but are suitable with the 5G era where the
+services may differ in their QoS requirements [5]. In that
+direction, multiple works in the literature employ sigmoid
+utility functions for the network users [5]–[13]. Nevertheless,
+all of these works consider either one SP and model the
+interaction between the users, or multiple SPs that compete
+for a fixed amount of resources (e.g. bandwidth).
+Network
+Slicing
+in
+5G
+Networks: Network slicing
+introduces various challenges to the resource allocation in 5G
+
+networks in terms of isolation, customization, elasticity, and
+end-to-end coordination [2]. Most surveys on network slicing
+investigate its multiple business models motivated by 5G, the
+fundamental architecture of a slice and the state-of-the-art
+algorithms of network slicing [2], [14], [15]. Microeconomic
+theories such as non-cooperative games and/or mechanism
+design arise as perfect tools to model the trading of network
+infrastructure and radio resources that takes place in network
+slicing [9], [16]–[18].
+Mechanism Design in Network Slicing: Multiple auction
+mechanisms have been used to identify the business model
+of a network slicing market (see a survey in [16]). Contrary
+to our work, the majority of the literature considers a single-
+sided auction, a model that assumes that a single NP owns the
+whole infrastructure of the market [9], [18]–[22]. For example,
+[9] considers a Vickrey–Clarke–Groves (VCG) auction-based
+model where the NP plays the role of an auctioneer and
+distributes discrete physical resource blocks. We find [3] and
+[17] to be closer to our work, since the authors employ
+the double-sided auction introduced by [23] to maximize the
+social welfare of a system with multiple NPs. Contrary to our
+work, the auction proposed in [23] assumes concave utility
+functions for the different actors and requires the computation
+of their gradients for its convergence. The aforementioned
+assumptions might lead to an over-simplification of a more
+complex networking architecture (e.g. that of the network
+slicing model) where the utility function for a user with
+inelastic traffic is expressed as a sigmoid function [9] and that
+of an SP as an optimization problem [3].
+B. Contributions
+Our work develops an iterative market model for the
+network
+slicing
+architecture,
+where
+multiple
+NPs
+with
+heterogeneous Radio Access Technologies (RATs), own the
+physical infrastructure and offer their resources to multiple
+SPs. The latter offer the resources as slices to their associated
+users. Specifically, we propose a five-step iterative model
+for the network slicing market that converges to a robust ǫ-
+competitive equilibrium even when the utility functions of
+the different actors are non-concave. In every cycle of the
+proposed model, the slices are reconfigured and the SPs learn
+the private parameters of their associated end-users to make the
+equilibrium of the next cycle more efficient. The introduced
+market model, can be seen as a framework that suits well
+to various networking problems where three types of actors
+are involved: those who own the physical infrastructure, those
+who lease part of it to sell services and those who enjoy the
+services (e.g. data-offloading [23]).
+For the interaction between the SPs and the NPs and for
+the convergence of the market to an equilibrium, we propose
+an iterative clock auction. Such dynamic auctions are used
+in the literature to auction divisible goods [24], [25]. The
+key differentiating aspects of the proposed auction, are (i) the
+relaxation of the common assumptions that the utility functions
+are concave and their gradients can be analytically computed,
+(ii) it provides highly usable price discovery, and (iii) it is a
+double-sided auction, and thus appropriate for a market with
+multiple NPs. Numerical results are provided that validate
+and evaluate the convergence of the clock auction and the
+capability of the proposed market architecture to express the
+incentives of the different entities of the system.
+II. MARKET MODEL & INCENTIVES
+In this section we describe the different entities of the
+network slicing market and their conflicting incentives.
+A. Market Model
+A typical slicing system model [2], [3], [14], [15] consists of
+multiple SPs represented by M = {1, 2, . . ., M} and multiple
+NPs that own RANs of possibly different RATs, represented
+by a set K = {1, 2, . . ., K}. Each SP owns a slice with a
+predetermined amount of isolated resources (e. g., bandwidth)
+and is associated with a set of users, Um, that serves through its
+slices. For the rest of the paper and without loss of generality
+we assume that each NP owns exactly one RAN, so we use
+the terms RAN and NP interchangeably.
+1) Network Providers: The multiple NPs of the system
+can quantify their radio resources as the performance level of
+the same network metric (e.g., downlink throughput) [3]. Let
+x(m,k) denote the amount of resources NP k allocates to SP
+m, and the vector xm := (x(m,k))k∈K to denote the amount of
+resources m gets from every NP. Without loss of generality [3],
+capacity Ck limits the amount of resources that can be offered
+from NP k, i.e., �M
+m=1 x(m,k) ≤ Ck. Let C = (Ck)k∈K. For
+the rest of the paper, we assume that there is a constant cost
+related to operation and management overheads induced to the
+NP. The main goal of every NP k is to maximize its profits
+by adjusting the price per unit of resources, denoted by ck.
+2) Service Providers & Associated Users: The main goal of
+an SP is to purchase resources from a single or multiple NPs in
+order to maximize its profit, which depends on its associated
+users’ satisfaction. The connectivity of a user i ∈ Um is
+denoted by a vector βi = (β(k,i))k∈K, where β(k,i) is a non-
+negative number representing factors such as the link quality
+i.e., numbers in (0, 1] that depend on the path loss. Moreover,
+each user i of the SP m, is associated with a service class,
+c(i), depending on their preferences. We denote the set of the
+possible service classes of SP m as Cm = {Cm
+1 , . . . , Cm
+cm}
+and thus c(i) ∈ Cm,
+∀i ∈ Um. Each SP m, is trying to
+distribute the resources purchased from the NPs, i.e., xm,
+to maximize its profit. This process, referred to as intra-slice
+resource allocation, is described in detail in Section II-B.
+Throughout the paper, we assume that the number of users
+of every SP m, i.e., |Um|, is much greater than the number
+of SPs, which is much greater than the number of NPs in
+the market. This assumption is made often in the mechanism
+design literature and is sufficient to ensure that the end-users
+and the SPs have limited information of the market [23], [26].
+The latter let us consider them as price-takers. In the following
+section, we describe in detail the intra-slice resource allocation
+problem from the perspective of an SP who tries to maximize
+the satisfaction of its associated users.
+
+B. Intra-Slice Resource Allocation
+The problem of the intra-slice resource allocation concerns
+the distribution of the resources, xm, from the SP m to
+its associated users. Specifically, every SP m allocates a
+portion of x(m,k) to its associated user i, denoted as r(k,i).
+Let ri := (r(k,i))k∈K and rm := (ri)i∈Um. For ease of
+notation, the resources, ri, of a user i ∈ Um, as well as the
+connectivities, βi, are not indexed by m because i is assumed
+to be a unique identifier for the user. Although every user i
+is assigned with r(k,i) resources from RAN k, because of its
+connectivity βi, the aggregated amount of resources it gets
+is zi := βT
+i ri. Moreover, let zm := (zi)i∈Um. In a feasible
+intra-slice allocation it should hold that xm ⪰ �
+i∈Um ri for
+each SP m.
+Every SP should distribute the obtained resources among
+its users to maximize their satisfaction. Towards providing
+intuition behind the employment of sigmoidal functions in the
+literature to model user satisfaction (e.g. see [5]–[12]), note
+that by making the same assumption as logistic regression,
+we model the logit1 of the probability that a user is satisfied,
+as a linear function of the resources. Hence, the probability
+that user i is satisfied with the amount of resources zi, say
+P[QoS sati], satisfies log(
+P [QoS sati]
+1−P [QoS sati]) = tz
+c(i)(zi − kc(i))
+and thus:
+P[QoS sati] =
+etz
+c(i)(zi−kc(i))
+1 + etz
+c(i)(zi−kc(i)) ,
+(1)
+where kc(i) ≥ 0 denotes the prerequisite amount of resources
+of the user i and tz
+c(i)
+≥ 0 expresses how ”tight” this
+prerequisite is. Note that the probability of a user being
+satisfied with respect to the value of zi, is a sigmoid function
+with inflection point kc(i). We assume that the user’s service
+class fully determines its private parameters, hence every user
+i ∈ c(i) has QoS prerequisite kc(i) and sensitivity parameter
+tz
+c(i). These parameters are unknown to the users, so the SP’s
+goal to eventually learn them is challenging (Section III-C).
+Given the previous analysis, the aggregated satisfaction of
+the users of the SP m is um(rm) := �
+i∈Um ui(ri) ( [10],
+[7]), where
+ui(ri) :=
+etz
+c(i)(βT
+i ri−kc(i))
+1 + etz
+c(i)(βT
+i ri−kc(i)) .
+(2)
+Note that the function ui(·) can be expressed as a function of
+zi as well. With a slight abuse of notation, we switch between
+the two by changing the input variable. We can write the final
+optimization problem for the intra-slice allocation of SP m as:
+(IN-SL):
+max
+rm
+um(rm)
+s.t.
+ri ⪰ 0,
+∀i ∈ Um
+xm ⪰
+�
+i∈Um
+ri
+In case the amount of resources obtained from every NP, xm,
+is not given, SP m can optimize it together with the intra-
+1The logit function is defined as logit(p) = log(
+p
+1−p ).
+slice resource allocation. Hence, SP m can solve the following
+problem
+(P):
+max
+rm,xm
+Ψm(rm, xm) := um(rm) − cT xm
+s.t.
+ri ⪰ 0,
+∀i ∈ Um
+xm ⪰
+�
+i∈Um
+ri
+Recall that ck denotes the price per unit of resources
+announced from every NP k. In Problem P , the objective
+function Ψm can be thought of as the profit of SP m. Let the
+solution of the above problem be ψ∗
+m.
+Problems IN-SL and P are maximization problems of
+a summation of sigmoid functions over a linear set of
+constraints. In [27] the problem of maximizing a sum of
+sigmoid functions over a convex constraint set is addressed.
+This work shows that this problem is generally NP-hard and
+it proposes an approximation algorithm, using a branch-and-
+bound method, to find an approximate solution to the sigmoid
+programming problem.
+In the rest of the section, we study three variations of
+problem P. Specifically, in Section II-B1, we study the case
+where the end-users are charged to get the resources from
+the SPs and in Sections II-B2 and II-B3 we regularize and
+concavify P respectively, something that will facilitate the
+analysis of the rest of the paper.
+1) Price Mechanism in P: In this subsection we argue that
+Problem P is expressive enough to capture the case where
+every user i is charged for its assigned resources. Let pi be
+the amount of money that user i should pay to receive the zi
+resources. In that case, the SPs should modify Problems IN-
+SL and P accordingly. First, note that user i’s satisfaction may
+depend also on pi. Similarly with the previous section, we can
+express the satisfaction of user i with respect to the price pi
+using a sigmoid function as P[price sati] =
+1
+1+e
+tp
+c(i)(pi−bc(i)) ,
+where bc(i) ≥ 0 is the budget of the user i for the prerequisite
+resources kc(i), and tp
+c(i) ≥ 0 expresses how ”tight” is this
+budget. We can now model the acceptance probability function
+[7] as P[sati] = P[price sati]P[QoS sati], and hence the
+expected total revenue, or the new utility of SP m, u
+′
+m, is
+modeled as
+u
+′
+m(rm, pm) :=
+�
+i∈Um
+P[sati]pi.
+(3)
+From Eq. (3), it is possible for SP m to immediately determine
+the optimal price ˆpi to ask from any user i ∈ Um. This follows
+from the fact that for positive pi the function admits a unique
+critical point, ˆp. Therefore, by just adding proper coefficients
+to the terms of Problem IN-SL and P, we can embed a pricing
+mechanism for the end-users in the model. For the rest of the
+paper, without loss of generality in our model, we assume that
+the end-users are not charged for the obtained resources.
+2) Regularization of P : We can regularize Problem P ,
+with a small positive λm. In that manner, we encourage dense
+
+solutions and hence we avoid situations where a problem in
+one RAN completely disrupts the operation of the SP.
+( ¯
+P ):
+max
+rm,xm
+Ψm(rm, xm) − λm∥xm∥2
+2
+s.t.
+ri ⪰ 0,
+∀i ∈ Um
+xm ⪰
+�
+i∈Um
+ri
+In the regularized problem
+¯
+P , note that larger values of
+λm penalize the vectors xm with greater L2 norms. Let the
+solution of Problem ¯
+P be ¯ψ∗
+m. The Lemma below, shows that
+for small λm, the optimal values ¯ψ∗
+m and ψ∗
+m are close. Its
+proof is simple and thus ommited for brevity.
+Lemma 1. Let (r∗
+m, x∗
+m) and (¯r∗
+m, ¯x∗
+m) be solutions of
+Problems P and ¯
+P respectively. Then,
+ψ∗
+m − λm∥x∗
+m∥2
+2 ≤ ¯ψ∗
+m ≤ ψ∗
+m − λm∥¯x∗
+m∥2
+2
+Lemma 1, proves that the regularization of P was (almost)
+without loss of optimality. In the next section, we proceed by
+concavifying Problem ¯
+P . The new concavified problem will
+be a fundamental building block of the auction analysis in
+Section III-A.
+3) Concavification of
+¯P : To concavify
+¯P , we replace
+every summand of um with its tightest concave envelope,
+i.e., the pointwise infimum over all concave functions that are
+greater or equal. For the sigmoid function ui(zi) the concave
+envelope, ˆui(zi), has a closed form given by
+ˆui(zi) =
+�
+ui(0) + ui(w)−ui(0)
+w
+zi
+0≤zi≤w
+ui(zi)
+w≤zi
+,
+for some w > ki which can be found easily by bisection
+[27]. Fig. 1 depicts the concavification of the aforementioned
+sigmoid functions for kc(·) = 100 and three different values
+for tz
+c(·). Note that for the lowest tz
+c(·) (elastic traffic) we get the
+best approximation whilst for the largest (inelastic traffic/tight
+QoS prerequisites) we get the worst.
+To exploit the closed form of the envelope ˆui(zi), instead
+of problem ¯P , we will concavify the equivalent problem:
+( ˜
+P ):
+max
+rm,xm,zm,
+�
+i∈Um
+fi(ri, zi) − cT xm − λm∥xm∥2
+2,
+s.t.
+(ri, zi) ∈ Si,
+∀i ∈ Um
+xm ⪰
+�
+i∈Um
+ri
+where Si
+:=
+{(ri, zi)
+:
+ri
+⪰
+0, zi
+=
+βT
+i ri } and
+fi(ri, zi) := ui(zi) with domain Si. The following lemma
+uses the concave envelope of the sigmoid function ui(zi),
+to compute the concave envelope of fi(ri, zi) and hence the
+concavification of the problem ˜
+P . Its proof is based on the
+definition of the concave envelope and is omitted for brevity.
+Lemma 2. The concave envelope of the function fi(ri, zi) :=
+e
+tz
+c(i)(zi−kc(i))
+1+e
+tz
+c(i)(zi−kc(i)) with domain Si, ˆfi(ri, zi), has the following
+closed form (with domain Si):
+ˆfi(ri, zi) = ˆui(zi),
+∀(ri, zi) ∈ Si.
+Therefore, SP m can concavify ˜P as follows:
+( ˆ
+P ):
+max
+rm,xm,zm
+�
+i∈Um
+ˆfi(ri, zi) − cT xm − λm∥xm∥2
+2
+s.t.
+(ri, zi) ∈ Si,
+∀i ∈ Um
+xm ⪰
+�
+i∈Um
+ri
+Note that ˆ
+P is strongly concave and thus admits a unique
+maximizer. Let the solution and the optimal point of problem
+ˆ
+P be ˆψ∗
+m and (ˆx∗
+m, ˆr∗
+m) respectively. Ultimately, we would
+like to compare the solution of the concavified ˆ
+P with the
+one of the original problem P . Towards that direction, we
+first define the nonconcavity of a function as follows [28]:
+Definition 1 (Nonconcavity of a function). We define the
+nonconcavity ρ(f) of a function f : S → R with domain
+S, to be
+ρ(f) = sup
+x ( ˆf(x) − f(x)).
+Let F denote a set of possibly non-concave functions. Then
+define ρ[j](F) to be the jth largest of the nonconcavities of
+the functions in F. The theorem below, summarizes the main
+result of this section, which is that every SP can solve the
+concavified ˆ
+P instead of the original P , since the former
+provides a constant bound approximation of the latter. Recall
+that Ψm(ˆr∗
+m, ˆx∗
+m) is the profit of SP m, evaluated at the
+solution of ˆ
+P and that K is the number of the NPs.
+Theorem 1. Let (r∗
+m, x∗
+m) and (¯r∗
+m, ¯x∗
+m) be solutions of
+Problems P
+and
+¯
+P
+respectively. Moreover, let
+ˆF
+:=
+{ui}i∈Um. Then,
+ψ∗
+m − ǫ − δ1(λm) ≤ Ψm(ˆr∗
+m, ˆx∗
+m) ≤ ψ∗
+m + δ2(λm),
+where δ1(λm)
+:=
+λm(∥x∗
+m∥2
+2 − ∥ˆx∗
+m∥2
+2), δ2(λm)
+:=
+λm(∥ˆx∗
+m∥2
+2 − ∥¯x∗
+m∥2
+2) and ǫ = �K
+j=1 ρ[j]( ˆF).
+Proof:
+Note that ¯ψ∗
+m is also given by solving ˜
+P and that (ˆr∗
+m, ˆx∗
+m)
+with the corresponding optimal value ˆψ∗
+m, are given by solving
+ˆ
+P . Therefore, from [28, Th. 1], we have that
+¯ψ∗
+m −
+K
+�
+j=1
+ρ[j]( ˆF) ≤ um(ˆr∗
+m) − cT ˆx∗
+m − λm∥ˆx∗
+m∥2
+2 ≤ ¯ψ∗
+m
+The result follows from Lemma 1.
+Remark 1. The values of δ1 and δ2 decrease as λm decreases
+and hence for small regularization penalties they can get
+arbitrarily close to zero.
+Remark 2. The approximation error, ǫ, depends on the K
+greatest nonconcavities of the set {ui}i∈Um. There are two
+conditions that ensure negligible approximation error, i.e.,
+ǫ << ψ∗
+m: i) the end-users have concave utility functions
+(in that case ǫ → 0) or, ii) the market is profitable enough
+for every SP m and hence ψ∗
+m >> K. Condition ii) makes
+the error negligible since ǫ ≤ K, and it can be satisfied for
+example when the supply of the market, C, is sufficiently large.
+
+0
+50
+100
+150
+200
+250
+300
+z
+i
+0.2
+0.4
+0.6
+0.8
+1.0
+utility
+Sigmoid Utility
+Concave Envelope
+(a)
+0
+50
+100
+150
+200
+250
+300
+z
+i
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+utility
+Sigmoid Utility
+Concave Envelope
+(b)
+0
+50
+100
+150
+200
+250
+300
+z
+i
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+utility
+Sigmoid Utility
+Concave Envelope
+(c)
+Fig. 1: Concave Envelopes of sigmoid utility functions with kc(·) =
+100 and (a) tz
+c(·) = 0.02, (b) tz
+c(·) = 0.2 and (c) tz
+c(·) = 2.
+Theorem 1, implies that every SP can solve Problem ˆ
+P ,
+which is a concave program with a unique solution, to find
+an approximate solution to P . This observation fosters the
+convergence analysis of the proposed auction in Section III-A.
+III. NETWORK SLICING MARKET CYCLE
+In this section, we study the evolution of the network slicing
+market using an iterative model that consists of 5-step cycles.
+We refer to the following sequence of steps as a market cycle:
+S1. |Um| prospective users appear to every SP m.
+S2. The vector xm, i.e., the distribution of the resources from
+the NPs to SP m is determined for every m. To achieve
+that in a distributed fashion, an auction between the SPs
+and the NPs should be realized.
+S3. Given xm, each SP m determines the vectors ri and
+hence the amount of resources zi for every user i ∈ Um
+(intra-slice resource allocation).
+S4. After receiving the resources, each user i determines and
+reports to the SP whether the QoS received was enough
+or not to complete its application.
+S5. The SPs exploit the responses of their users, to estimate
+their private parameters and hence to distribute the
+resources more efficiently in the next cycle.
+It is important for the vector xm to be determined before
+the intra-slice resource allocation, since the first serves as the
+capacity in the resources available to SP m. In the following,
+we expand upon each (non-trivial) step of the market cycle.
+A. Step S2 - Clock Auction for the Network Slicing Market
+In this section, we develop and analyze a clock auction
+between the SPs and the NPs, that converges to a market’s
+equilibrium. Specifically, we describe the goal (Section
+III-A1), the steps (Section III-A2), and the convergence
+(Section III-A3) of the auction.
+1) Auction Goal: Note that the solutions of the problems
+P and ˆ
+P appear to be a function of the prices c1, . . . , cK. Let
+the demand of SP m, given the price vector c, be denoted as
+x∗
+m(c) or ˆx∗
+m(c) depending on whether SP m uses Problem
+P or ˆ
+P to ask for resources. Let also r∗
+m(c) and ˆr∗
+m(c)
+be optimal intra-slice resource allocation vectors respectively.
+Hence, (r∗
+m(c), x∗
+m(c)) and (ˆr∗
+m(c), ˆx∗
+m(c)) are maximizers
+of P and ˆ
+P respectively (given c). Since Problem P may
+admit multiple solutions, let the set Dm(c) be defined as
+Dm(c) :=
+�
+x∗
+m : {∃r∗
+m : {Ψm(r∗
+m, x∗
+m) = ψ∗
+m given c}
+�
+.
+We define a Competitive equilibrium as follows:
+Definition
+2
+(Competitive
+equilibrium).
+Competitive
+equilibrium of the Network Slicing Market is defined to be
+any price vector c† and allocation of the resources of the
+NPs x†, such that:
+i. x†
+m ∈ Dm(c†) for every SP m, and
+ii. C = �
+m∈M x†
+m (the demand equals the supply).
+Note that in a competitive equilibrium, every SP m gets
+resources that could maximize its profit given the price vector.
+Because a competitive equilibrium sets a balance between the
+interests of all participants, it appears to be the settling point
+of the markets in economic analysis [26], [29]. Nevertheless,
+since the SPs’ demands are expressed by solving a non-
+concave program, we define an ǫ-competitive equilibrium
+which will be the ultimate goal of the proposed clock auction.
+Definition
+3
+(ǫ-Competitive
+equilibrium).
+ǫ-Competitive
+equilibrium of the Network Slicing Market is defined to be
+any price vector ˆc† and allocation of the resources of the NPs
+ˆx†, such that:
+i. For every SP m, there exists an ǫ ≥ 0 and a feasible intra-
+slice resource allocation vector ˆr†
+m (given ˆx†
+m), such that:
+ψ∗
+m − ǫ ≤ Ψm(ˆr†
+m, ˆx†
+m) ≤ ψ∗
+m + ǫ, and
+ii. C = �
+m∈M ˆx†
+m (the demand equals the supply).
+Observe that the first condition of the above definition
+ensures that every SP is satisfied (up to a constant) with
+the obtained resources in a sense that it operates close to its
+maximum possible profit. From Theorem 1, note that if there
+exists a price vector ˆc† such that C = �
+m∈M ˆx∗
+m(ˆc†), then
+the prices in ˆc† with the allocation ˆx† := ˆx∗(ˆc†) form an
+ǫ-competitive equilibrium. Finding such a price vector, is the
+motivation of the proposed clock auction. For the rest of the
+paper we make the following assumption:
+Assumption 1. The SPs calculate their demand and intra-
+resource allocation by solving Problem ˆ
+P .
+This is a reasonable assumption since in Theorem 1 and the
+corresponding Remarks 1 and 2, we proved that by solving
+a (strictly) concave problem, every SP can operate near its
+optimal profit. Therefore, for the rest of the paper, we call
+ˆx∗
+m(c), the demand of SP m given the prices c.
+2) Auction Description: We propose the following clock
+auction that converges to an ǫ-competitive equilibrium of the
+Network Slicing market (Theorem 2). As we will prove in
+Theorem 3, this equilibrium is robust since the convergent
+price vector is the unique one that clears the market, i.e., makes
+the demand to equal the supply.
+
+i. An
+auctioneer
+announces
+a
+price
+vector
+c,
+each
+component of which corresponds to the price that an NP
+sells a unit of its resources.
+ii. The bidders (SPs) report their demands.
+iii. If the aggregated demand received by an NP is greater
+than its available supply, the price of that NP is increased
+and vice versa. In other words, the auctioneer adjusts the
+price vector according to Walrasian tatonnement.
+iv. The process repeats until the price vector converges.
+Note that the components of the price vector change
+simultaneously and independently. Hence different brokers
+can cooperate to jointly clear the market efficiently in a
+decentralized fashion [23]. Let the excess demand, Z(c), be
+the difference between the aggregate demand and supply:
+Z(c) = −C + �
+m∈M ˆx∗
+m(c). In Walrasian tatonnement, the
+price vector adjusts in continuous time according to excess
+demand as ˙c = f(Z(c(t))), where f is a continuous, sign-
+preserving transformation [24]. For the rest of the paper, we
+set f to be the identity function and thus ˙c = Z(c(t)). In
+auctions based on Walrasian tatonnement, the payments are
+only valid after the convergence of the mechanism [30].
+3) Auction Convergence: Towards proving the convergence
+of the auction, we provide the lemma below which proves that
+the concavified version of the intra-slice resource allocation
+problem IN − SL, can be thought of as a concave function.
+The proof is ommitted as a direct extension of [3] and [31].
+Lemma 3. The function Um(xm) shown below is concave.
+Um(xm) := max
+rm,zm
+�
+i∈Um
+ˆfi(ri, zi)
+s.t.
+(ri, zi) ∈ Si,
+∀i ∈ Um
+xm ⪰
+�
+i∈Um
+ri
+(4)
+Using the function Um, we can rewrite Problem ˆ
+P as
+max
+xm⪰0
+Um(xm) − λm − cT xm∥xm∥2
+2.
+The following theorem studies the convergence of the auction.
+Theorem 2. Starting from any price vector cinit, the proposed
+clock auction converges to an ǫ-competitive equilibrium.
+Proof: The proof relies on a global stability argument
+similarly to [24], [29]. Let Vm(·) denote m’s net indirect
+utility function:
+Vm(c) = max
+xm⪰0
+{Um(xm) − λm∥xm∥2
+2 − cT xm}.
+Let a candidate Lyapunov function be V(c) := cT C +
+�
+m∈M Vm(c). To study the convergence of the auction we
+should find the time derivative of the above Lyapunov function:
+˙V(c)= ˙c·
+�
+CT +�
+m∈M
+d
+dc
+�
+maxxm⪰0{Um(xm)−λm∥xm∥2
+2−cT xm}
+��
+.
+Hence, we deduce that:
+˙V(c) =
+�
+CT +
+�
+m∈M
+{−ˆx∗T
+m (c)}
+�
+· ˙c = −ZT(c(t)) · Z(c(t)).
+The above holds true since the function h(xm) := Um(xm)−
+λm∥xm∥2
+2, has as concave conjugate the function (see [31])
+h∗(s) = max
+xm⪰0{h(xm) − cT xm},
+and hence ∇h∗(s) = arg maxxm⪰0{Um(xm)− λm∥xm∥2
+2 −
+cT xm}. Therefore, V(·) is a decreasing function of time and
+converges to its minimum. Note that in the convergent point
+the supply equals the demand for every NP.
+The market might admit multiple ǫ-competitive equilibria.
+Nevertheless, the equilibrium point that the clock auction
+converges is robust in the following sense: given Assumption
+1, the price vector that clears the market is unique. Therefore,
+essentially, in Theorem 2 we proved that the proposed clock
+auction converges to that unique price vector. This is formally
+proposed by the following theorem.
+Theorem 3. There exists a unique price vector c† such that
+�
+m∈M ˆx∗
+m(c†) = C.
+Towards proving Theorem 3 we provide Lemmata 4 and 5.
+First, we show that if a component in the price vector changes,
+the demand of an SP who used to obtain resources from the
+corresponding NP, should change as well.
+Lemma 4. For two distinct price vectors c, ¯c with ∃k : ck ̸=
+¯ck, it holds true that
+ˆx∗
+m(c) = ˆx∗
+m(¯c) ⇒ ˆx∗
+(m,k)(c) = ˆx∗
+(m,k)(¯c) = 0.
+Proof: Let such price vectors, ¯c and c, with ck ̸= ¯ck.
+Since ˆx∗
+m(c) is the optimal point of problem ˆ
+P given c,
+applying KKT will give:
+ˆx∗
+(m,k)(c) = 0
+or
+∂{Um(xm) − λm∥xm∥2
+2}
+∂x(m,k)
+����
+ˆx∗m(c)
+= ck. (5)
+However, ˆx∗
+m(¯c) is optimal for ˆ
+P given ¯c. Employing a similar
+equation as (5) proves that if ˆx∗
+m(c) = ˆx∗
+m(¯c) then it can only
+hold that ˆx∗
+(m,k)(c) = ˆx∗
+(m,k)(¯c) = 0.
+Definition
+4
+(WARP property). The aggregate demand
+function satisfies the Weak Axiom of Revealed Preferences
+(WARP), if for different price vectors c and ¯c, it holds that:
+cT ·
+�
+m∈M
+ˆx∗
+m(¯c) ≤ cT ·
+�
+m∈M
+ˆx∗
+m(c) ⇒
+¯cT ·
+�
+m∈M
+ˆx∗
+m(¯c) < ¯cT ·
+�
+m∈M
+ˆx∗
+m(c)
+Lemma 5. The aggregate demand function satisfies the WARP
+for distinct price vectors c, ¯c such that �
+m∈M ˆx∗
+m(c) ≻ 0
+and �
+m∈M ˆx∗
+m(¯c) ≻ 0.
+Proof: Since c ̸= ¯c then ∃k ∈ K : ck ̸= ¯ck. Furthermore,
+we have that �
+m∈M ˆx∗
+m(c) ≻ 0 and hence ∃m1 ∈ M
+such that ˆx∗
+m1,k(c) > 0. Using Lemma 4 we conclude that
+ˆx∗
+m1(c) ̸= ˆx∗
+m1(¯c). Hence, since Problem ˆ
+P admits a unique
+global maximum we have that:
+�
+m∈M
+�
+Um(ˆx∗
+m(c)) − λm∥ˆx∗
+m(c)∥2
+2 − cT · ˆx∗
+m(c)
+�
+>
+
+�
+m∈M
+�
+Um(ˆx∗
+m(¯c)) − λm∥ˆx∗
+m(¯c)∥2
+2 − cT · ˆx∗
+m(¯c)
+�
+Now, the above combined with the WARP hypothesis,
+�
+m∈M
+cT · ˆx∗
+m(¯c) ≤
+�
+m∈M
+cT · ˆx∗
+m(c),
+gives:
+�
+m∈M
+�
+Um(ˆx∗
+m(c)) − λm∥ˆx∗
+m(c)∥2
+2
+�
+>
+�
+m∈M
+�
+Um(ˆx∗
+m(¯c)) − λm∥ˆx∗
+m(¯c)∥2
+2
+�
+.
+(6)
+The result follows by switching the roles of c and ¯c and
+combine the inequalities.
+We can now prove Theorem 3 as follows.
+proof of Theorem 3:
+Towards a contradiction, assume
+that there exist two distinct (non-zero) price vectors c and ¯c
+that satisfy �
+m∈M ˆx∗
+m(¯c) = �
+m∈M ˆx∗
+m(c) = C and thus
+cT ·
+� �
+m∈M
+ˆx∗
+m(¯c) −
+�
+m∈M
+ˆx∗
+m(c)
+�
+= 0.
+(7)
+Therefore, from Lemma 5 we know that:
+¯cT ·
+�
+m∈M
+ˆx∗
+m(¯c) < ¯cT ·
+�
+m∈M
+ˆx∗
+m(c),
+(8)
+which is a contradiction because of the hypothesis.
+Remark 3. Theorems 2 and 3 together with Remarks 1 and 2
+imply that if the users’ traffic is elastic, or the total capacity
+C of the NPs is sufficiently large, the clock auction converges
+monotonically to the unique competitive equilibrium of the
+market.
+At the end of step S2, the final price vector ˆc† and the final
+demands of each SP m, ˆx∗
+m, have been determined.
+B. Intra-Slice Resource Allocation & Feedback (Steps S3, S4)
+At the beginning of step S3, every SP m is aware of the
+convergent point ˆx∗
+m and hence it can allocate the resources
+either by solving the sigmoid program IN − SL, or by
+using the convergent approximate solution, ˆr∗
+m. At that step,
+an SP can also determine whether it will overbook network
+resources. Overbooking, is a common practice in airlines and
+hotel industries and is now being used in the network slicing
+problem [32], [33]. This management model allocates the
+same resources to users of the network expecting that not
+everyone uses their booked capacity. In that case, SP m solves
+Problem IN−SL whilst setting increased obtained resources,
+xov
+m = ˆx∗
+m +α%◦ ˆx∗
+m, for a relatively small positive α. Here,
+◦ denotes the component-wise multiplication operator.
+During the step S4 of the cycle, each user i, receives their
+resources ri, and provide feedback on whether it was satisfied
+or not. In the next step, the SPs can use the these responses
+to learn the private parameters of the different service classes.
+C. Learning the Parameters (Step S5)
+At the final step of the cycle, the SPs exploit the data they
+obtained to learn the private parameters of their users. In that
+fashion, the market ”learns” its equilibrium. For the rest of
+the paper, for generality, we assume the pricing mechanism
+introduced in Section II-B1. Therefore, for every user i, the
+SPs get to know whether it is satisfied by the pair of resources-
+price (zi, pi). A Bayesian inference model needs the data, a
+model for the private parameters and a prior distribution.
+Model: The observed data is the outcome of the Bernoulli
+variables sati|θc(i)
+∼ Bernoulli(P[sati]) for every user
+i, where θc(i)
+=
+(tp
+c(i), bc(i), tz
+c(i), kc(i)) is the tuple of
+the private parameters that we want to infer. Prior: Let
+the prior distribution for every parameter of θc(i) have
+probability density functions πtp
+c(i)(·), πbc(i)(·), πtz
+c(i)(·) and
+πkc(i)(·) respectively. The SPs infer the private parameters
+θc(i) for each service class using the Bayes rule separately:
+p(θc(i)|data) ∝ Ln(data|θc(i))π(θc(i)), where p(θc(i)|data)
+is the posterior distribution of θc(i), Ln(data|θc(i)) is the
+likelihood of the data given our model and π(θc(i)) is the
+prior distribution. Assuming independent private parameters,
+π(θc(i)) is the product of the distinct prior distributions, and
+for each class c we have that:
+Ln(data|θc(i)) =
+�
+i∈Cm
+c
+P[sati]fi(1 − P[sati])1−fi,
+where fi is 1 when user i is satisfied and 0 when not.
+The SPs can use Marcov Chain Monte Carlo (MCMC) with
+Metropolis Sampling, to find the posterior distribution after
+each market cycle. As the market evolves, the SPs exploit the
+previous posterior distributions to find better priors for the next
+cycle.
+IV. CENTRALIZED SOLUTION
+In case there exists a centralized entity that knows the utility
+function of every SP, it can optimize the social welfare, i.e.,
+the summation of the utility functions of the service and the
+network providers. This centralized problem can be formulated
+as follows:
+(SWM):
+max
+rm
+�
+m∈M
+um(rm)
+s.t.
+ri ⪰ 0,
+∀i ∈ Um
+�
+m∈M
+�
+i∈Um
+ri ⪯ C
+The SW M problem, can be solved with any chosen positive
+approximation error, using the framework of sigmoidal
+programming [27].
+V. NUMERICAL RESULTS
+A. Auction Convergence & Parameter Tuning
+In this section we study the convergence of the clock
+auction, as well as the impact that the various parameters have
+on its behavior. For this simulation, we assume a small market
+with 3 NPs with capacities C1 = 850, C2 = 750, C3 = 755
+
+0
+2
+4
+6
+8
+10
+12
+14
+Iterations
+0
+1
+2
+3
+4
+5
+6
+7
+L2 Norm of the Excess Demand
+1e6
+cinit = [0.62, 0.64, 0.58]
+cinit = [1.2, 1.4, 1.1]
+cinit = [0.2, 0.4, 0.1]
+cinit = [0.4, 0.4, 1.1]
+(a)
+0
+10
+20
+30
+40
+50
+Iterations
+0
+2500
+5000
+7500
+10000
+12500
+15000
+17500
+L2 Norm of the Excess Demand
+κ = 10^{-4}
+κ = 10^{-5}
+κ = 10^{-6}
+(b)
+Fig. 2: L2 norm of the excess demand vector throughout the clock
+auction (a) for κ = 10−4 and various initialization price vectors
+cinit, and (b) for cT
+init = [0.62, 0.64, 0.58] and different values of
+κ.
+Cost of NP1
+0.30.40.50.60.7 0.8 0.9 1.0 1.1
+Cost of NP2
+0.4
+0.6
+0.8
+1.0
+1.2
+Cost of NP3
+0.4
+0.5
+0.6
+0.7
+0.8
+0.9
+1.0
+cinit = [0.62, 0.64, 0.58]
+cinit = [1.2, 1.4, 1.1]
+cinit = [0.2, 0.4, 0.1]
+cinit = [0.4, 0.4, 1.1]
+Fig. 3: Illustrating Theorem 2. Starting from any price vector cinit,
+the clock auction converges to the market clearing prices c†.
+and 5 SPs with 6 users and 3 distinct service classes each.
+The users’ private parameters are set as follows: for an i in
+the first class tz
+c(i) = tp
+c(i) = 0.2, kc(i) = bc(i) = 100, for the
+second class tz
+c(i) = tp
+c(i) = 2, kc(i) = bc(i) = 120, and for the
+third class tz
+c(i) = tp
+c(i) = 20, kc(i) = bc(i) = 150. Such values
+indicate that the users wish to pay a unit of monetary value
+for a unit of offered resources.
+To discretize the auction, we change the cost vector
+according to a step value, κ, as ct+1 = ct + κZ(ct). Fig. 2
+depicts the L2 norm of the excess demand vector throughout
+the clock auction for different cost vector initializations cinit
+(Fig 2a), and for different step values κ (Fig. 2b). By
+simulating the clock auction, we deduce that the clearing price
+vector is c†T = [0.6116, 0.6273, 0.5811]. In Fig. 2a note that
+the closer the initialization cost vector is to c†T , the faster
+the convergence becomes. Fig. 2b, connotes the need for a
+proper choice of the step value κ. Clearly, κ = 10−4 gives
+the fastest convergence and as we decrease the step values
+it becomes slower. Nevertheless, since Theorem 2 is proved
+for the continuous case, large values of κ cannot guarantee
+the convergence of the auction to an equilibrium. In Fig. 3
+observe that the convergence of the auction does not depend
+on the initialization of the cost vector (Theorem 2).
+SP1/NP1
+SP1/NP2
+SP2/NP1
+SP2/NP2
+Service Provider/Network Provider
+0
+200
+400
+600
+800
+1000
+1200
+1400
+x
+m,
+k
+Auction
+SPP
+oSPP(5%)
+SWM
+Fig. 4: Total amount of resources obtained by every SP m from
+every NP k in the market, x(m,k).
+B. Visualization of the Resource Allocation
+In this section, we get insights on the allocation of
+the resources in the market. We assume 2 NPs with
+C1 = C2 = 1400 and 2 SPs with 10 users each and one shared
+service class with tz
+c(i) = tp
+c(i) = 0.2 and kc(i) = bc(i) = 100
+for all i. The first SP (SP1) is near the first NP (NP1)
+and far from NP2 and hence, we set [β(1,1), . . . , β(1,10)] =
+[0.99, 0.96, 0.87, 0.85, 0.82, 0.81, 0.80, 0.80, 0.70, 0.70]
+and
+β(2,i) = 0.2, ∀i ∈ U1. Moreover, for the users of SP2 we set
+β1,i = β2,i = 0.8, ∀i ∈ U2.
+We compare the resource allocation of four different
+methods. First, ’Auction’ refers to the resource allocation that
+results immediately after the auction. ’SPP’ takes ˆx∗
+m from the
+equilibrium but performs the intra-slice of every SP by solving
+IN − SL. We also study the method ’oSPP(5%)’, which
+mimics the SPP method but with 5% overbooked resources.
+Finally, ’SWM’ refers to the solution of the Problem SW M.
+Fig. 4 shows the amount of resources obtained from the
+two SPs. All methods allocate the majority of the resources
+of NP1 to SP1 since its users have greater connectivity with
+it. Although the users of SP2 have equally high connectivity
+with both NPs, all of the four methods were flexible enough
+to allocate the resources of NP2 to SP2. Note that none of the
+methods gives resources from NP2 to SP1.
+Fig. 5 depicts the intra-slice resource allocations. In Fig.
+5a observe that the greater the connectivity of a user is,
+the less resources it gets. That is because users with good
+connectivity factors meet their prerequisite QoS using less
+resources and hence SP1 could maximize its expected profit
+by giving them less. Note that ’SPP’ gives no resources to the
+user with the worst connectivity whereas with the overbooking,
+SP1 gets enough resources to make attractive offers to every
+user. Therefore, ’SPP’ might make an unfair allocation, since
+when the resources are not enough, it neglects the users with
+bad connectivity. In Fig. 5c, note that the homogeneity in the
+connectivities of the users of SP2 forces every method to fairly
+divide the resources among them.
+Fig. 6a shows the expected value of the total revenue, or the
+social welfare. ’SWM’ gives the greatest revenue among the
+methods that do not overbook. Nevertheless, although ’SPP’
+is a completely distributed solution and was not designed to
+maximize the total revenue, it performs very close to ’SWM’.
+Moreover, a 5% overbooking leads to greater revenues.
+
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+User ID of SP1
+0
+25
+50
+75
+100
+125
+150
+175
+r
+1,
+i
+Auction
+SPP
+oSPP(5%)
+SWM
+(a)
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+User ID of SP2
+0
+10
+20
+30
+40
+50
+r
+1,
+i
+Auction
+SPP
+oSPP(5%)
+SWM
+(b)
+1
+2
+3
+4
+5
+6
+7
+8
+9
+10
+User ID of SP2
+0
+20
+40
+60
+80
+100
+120
+140
+160
+r
+2,
+i
+Auction
+SPP
+oSPP(5%)
+SWM
+(c)
+Fig. 5: The solution of the intra-slice resource allocation problem from the perspective of the two different SPs of the market. Specifically,
+how (a) SP1 distributed the resources of NP1, i.e., r1,i for every i in U1, (b) SP2 distributed the resources of NP1, i.e., r1,i for every i in
+U2, and (c) SP2 distributed the resources of NP2, i.e., r2,i for every i in U2.
+Auction
+SPP
+oSPP(5%)
+SWM
+Resource Allocation Method
+0
+200
+400
+600
+800
+1000
+1200
+1400
+1600
+Expected T
+otal Revenue
+1575.31
+1598.16
+1677.81
+1611.54
+(a)
+Auction
+SPP
+oSPP(5%)
+SWM
+Resource Allocation Method
+0
+100
+200
+300
+400
+500
+600
+700
+800
+Expected Revenue of SP1
+746.85
+769.65
+827.42
+806.49
+(b)
+Auction
+SPP
+οSPP(5%)
+SWM
+Resource Allocation Method
+0
+100
+200
+300
+400
+500
+600
+700
+800
+Expected Revenue of SP2
+828.46
+828.51
+850.39
+805.06
+(c)
+Fig. 6: Illustrating the expected revenue (given by Eq. (3)) for the four different resource allocation methods. Fig. (a) shows the aggregated
+expected revenue, Fig. (b) shows the expected revenue of SP1, and Fig. (c) shows the expected revenue of SP2.
+C. Impact of Bayesian Inference
+The previous results are extracted after a sufficient number
+of cycles, when the SPs have learned the parameters of the
+end-users. In this section, we consider an SP with 10 users
+and one service class that employs Bayesian inference to learn
+the private parameter tz
+c(i) for every i. We set the true value
+of the parameter to be tz
+c(i) = 2. The other parameters are
+set tp
+c(i) = 2, kc(i) = bc(i) = 120 and β1,i = 0.9, ∀i ∈ U1.
+We assume one more SP with a unique service class with
+tp
+c(i) = tz
+c(i) = 0.2, kc(i) = bc(i) = 100 and β2,i = 0.9∀i ∈ U2.
+Finally, there are 2 NPs with C1 = C2 = 1200.
+In this example, SP1 sets as prior distribution the normal
+N(0.02, 2) and hence assumes elastic traffic. At the end
+of each market cycle, the SP makes an estimation, ˆtz
+c(i),
+by calculating the mean of the posterior distribution. Fig. 7
+depicts the histogram of the posterior distribution for the first
+two market cycles. Observe that even in the third market cycle,
+SP1 can estimate with high accuracy the actual value of the
+parameter. In Table I, note that the perceived revenue, i.e., the
+expected revenue calculated using the estimation, is different
+between the cycles that ˆtz
+c(i) differs from tz
+c(i). Hence, it is
+impossible for the SPs to maximize their expected profits
+when they don’t know the actual values of the parameters.
+Indeed, observe that the bad estimate of ˆtz
+c(i) = 0.02 gives
+poor expected revenue compared to the last two cycles.
+VI. CONCLUDING REMARKS
+In this paper we focus on the technical and economic
+challenges that emerge from the application of the network
+slicing architecture to real world scenarios. Taking into
+0
+2
+4
+6
+8
+0.0
+0.1
+0.2
+0.3
+0.4
+tc(i)
+z
+(a)
+0
+1
+2
+3
+4
+5
+6
+0.0
+0.1
+0.2
+0.3
+0.4
+0.5
+tc(i)
+z
+(b)
+Fig. 7: Posterior distribution of the unknown private parameter tz
+c(i)
+in (a) the first Market Cycle, and (b) in the second Market Cycle.
+Cycle
+ˆtz
+c(i)
+Acquired
+Resources
+Perceived
+Revenue
+Actual
+Revenue
+1
+0.02
+1087
+530.26
+699
+2
+1.68
+1370
+1160.77
+1163.48
+3
+2.01
+1365
+1161.42
+1161.42
+TABLE I: Bayesian inference in different market cycles.
+consideration the heterogenity of the users’ service classes
+we introduce an iterative market model along with a clock
+auction that converges to a robust ǫ-competitive equilibrium.
+Finally, we propose a Bayesian inference model, for the SPs
+to learn the private parameters of their users and make the
+next equilibria more efficient. Numerical results validate the
+convergence of the clock auction and the capability of the
+proposed framework to capture the different incentives.
+
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+This figure "fig1.png" is available in "png"� format from:
+http://arxiv.org/ps/2301.02840v1
+

4NAzT4oBgHgl3EQf9f64/content/tmp_files/2301.01921v1.pdf.txt

@@ -0,0 +1,2025 @@
+Control over Berry Curvature Dipole with Electric Field in WTe2
+Xing-Guo Ye,1,* Huiying Liu,2,* Peng-Fei Zhu,1,* Wen-Zheng Xu,1,* Shengyuan A. Yang,2
+Nianze Shang,1 Kaihui Liu,1 and Zhi-Min Liao
+1,†
+1State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for Nano-optoelectronics, School of Physics,
+Peking University, Beijing 100871, China
+2Research Laboratory for Quantum Materials, Singapore University of Technology and Design, Singapore, 487372, Singapore
+Berry curvature dipole plays an important role in various nonlinear quantum phenomena. However, 
+the maximum symmetry allowed for nonzero Berry curvature dipole in the transport plane is a single 
+mirror line, which strongly limits its effects in materials. Here, via probing the nonlinear Hall effect, we 
+demonstrate the generation of Berry curvature dipole by applied dc electric field in WTe2, which is used to 
+break the symmetry constraint. A linear dependence between the dipole moment of Berry curvature and the 
+dc electric field is observed. The polarization direction of the Berry curvature is controlled by the relative 
+orientation of the electric field and crystal axis, which can be further reversed by changing the polarity of 
+the dc field. Our Letter provides a route to generate and control Berry curvature dipole in broad material 
+systems and to facilitate the development of nonlinear quantum devices.
+Berry curvature is an important geometrical property
+of Bloch bands, which can lead to a transverse velocity of
+Bloch electrons moving under an external electric field
+[1–6]. Hence, it is often regarded as a kind of magnetic field
+in momentum space, leading to various exotic transport
+phenomena, such as anomalous Hall effect (AHE) [1],
+anomalous Nernst effect [7], and extra phase shift in
+quantum oscillations [8]. The integral of Berry curvature
+over the Brillouin zone for fully occupied bands gives rise
+to the Chern number [5], which is one of the central
+concepts of topological physics.
+Recently, Sodemann and Fu [9] proposed that the dipole
+moment of Berry curvature over the occupied states, known
+as Berry curvature dipole (BCD), plays an important role in
+the second-order nonlinear AHE in time-reversal-invariant
+materials. For transport in the x-y plane which is typical in
+experiments, the relevant BCD components form an in-
+plane pseudovector with Dα ¼
+R
+k f0ð∂αΩzÞ [9], where Dα
+is the BCD component along direction α, k is the wave
+vector, the integral is over the Brillouin zone and with
+summation over the band index, f0 is the Fermi distribution
+(in the absence of external field), Ωz is out-of-plane Berry
+curvature, and ∂α ¼ ∂=∂kα. It results in a second-harmonic
+Hall voltage in response to a longitudinal ac probe current,
+which could find useful applications in high-frequency
+rectifiers, wireless charging, energy harvesting, and infra-
+red detection, etc. BCD and its associated nonlinear AHE
+have been predicted in several material systems [9–11]
+and experimentally detected in systems such as two-
+dimensional (2D) monolayer or few-layer WTe2 [12–15],
+Weyl semimetal TaIrTe4 [16], 2D MoS2, and WSe2
+[17–20], corrugated bilayer graphene [21], and a few
+topological materials [22–25]. However, a severe limitation
+is that BCD obeys a rather stringent symmetry constraint.
+In the transport plane, the maximum symmetry allowed
+for Dα is a single mirror line [9]. In several previous
+Letters [17–21], one needs to perform additional material
+engineering such as lattice strain or interlayer twisting to
+generate a sizable BCD. This constraint limits the available
+material platforms with nonzero BCD, unfavorable for the
+in-depth exploration of BCD-related physics and practical
+applications.
+Recent works suggested an alternative route to obtain
+nonzero BCD, that is, utilizing the Berry connection
+polarizability to achieve a field-induced BCD, where the
+additional lattice engineering is unnecessary [26,27]. The
+Berry connection polarizability is also a band geometric
+quantity, related to the field-induced positional shift of
+Bloch electrons [28]. It is a second-rank tensor, defined as
+GabðkÞ ¼ ½∂Að1Þ
+a ðkÞ=∂Eb�, where Að1Þ is the field-induced
+Berry connection, E is the applied electric field [28], and
+the superscript “(1)” represents that the physical quantity is
+the first order term of electric field. Then, the E field
+induced Berry curvature is given by Ωð1Þ ¼ ∇k × ðG
+↔
+EÞ
+[27], where the double arrow indicates a second-rank
+tensor. This field-induced Berry curvature will lead to a
+field-induced BCD Dð1Þ
+α . Considering transport in the x-y
+plane and applied dc E field also in the plane, we
+have Dð1Þ
+α ¼
+R
+kf0ð∂αΩð1Þ
+z Þ¼εzγμ
+R
+kf0½∂αð∂γGμνÞ�Eν, where
+α; γ; μ; ν ¼ x, y, and εzγμ is the Levi-Civita symbol. In
+systems where the original BCD is forbidden by the crystal
+symmetry, the field-induced BCD by an external E field
+1
+
+could generally be nonzero and become the dominant
+contribution. In such a case, the symmetry is lowered by
+the applied E field, and the induced BCD should be linear
+with E and its direction also controllable by the E field. So
+far, this BCD caused by Berry connection polarizability
+and its field control have not been experimentally demon-
+strated yet, and the nonlinear Hall effect derived from this
+mechanism has not been observed.
+In this Letter, we report the manipulation of electric field
+induced BCD due to the Berry connection polarizability.
+Utilizing a dc electric field Edc to produce BCD in bulk
+WTe2 (for which the inherent BCD is symmetry forbid-
+den), the second-harmonic Hall voltage V2ω
+H is measured as
+a response to an applied ac current Iω. Both orientation and
+magnitude of the induced BCD are highly tunable by the
+applied Edc. Our Letter provides a general route to extend
+BCD to abundant material platforms with high tunability,
+promising for practical applications.
+The WTe2 devices were fabricated with circular disc
+electrodes (device S1) or Hall-bar shaped electrodes
+(device S2). The WTe2 flakes were exfoliated from
+bulk crystal and then transferred onto the prefabricated
+electrodes (Supplemental Material, Note 1 [29]). The WTe2
+thickness of device S1 is 8.4 nm (Supplemental Material,
+Fig. S1 [29]), corresponding to a 12-layer WTe2, and we
+present the results from device S1 in the main text. The
+crystal orientations of WTe2 devices were identified
+by their long, straight edges [12] and further confirmed
+by both polarized Raman spectroscopy (Supplemental
+Material, Note 2 [29]) and angle-dependent transport
+measurements (Supplemental Material, Note 3 [29]). The
+electron mobility of device S1 is ∼ 4974 cm2=V s at 5 K
+(Supplemental Material, Note 4 [29]).
+In our experiments, we use thick Td-WTe2 samples
+(thickness ∼8.4 nm), which have an effective inversion
+symmetry in the x-y plane (which is the transport plane).
+This is formed by the combination of the mirror symmetry
+Ma and the glide mirror symmetry ˜Mb, as indicated in
+Fig. 1(c). The in-plane inversion leads to the absence
+of inherent in-plane BCD and hence the nonlinear Hall
+effect in bulk (see Supplemental Material, Note 5 [29] for
+detailed symmetry analysis). Because ˜Mb involves a half-
+cell translation along the c axis and hence is broken on the
+sample surface, a small but nonzero intrinsic BCD may
+exist on the surface. In fact, such BCD due to surface
+symmetry breaking has already been reported [13], and is
+also observed in our samples, although the signal is much
+weaker in thicker samples (see Supplemental Material,
+Fig. S9 [29]).
+To induce BCD in bulk WTe2 through Berry connection
+polarizability, a dc electric field Edc is applied in the x-y
+plane. As shown in Figs. 1(a) and 1(b), the field-induced
+Berry curvature shows a dipolelike distribution with non-
+zero BCD (theoretical calculations; see Supplemental
+Material, Note 6 [29]). The induced BCD can be controlled
+by the dc E field and should satisfy the following symmetry
+requirements. Because the presence of a mirror symmetry
+would force the BCD to be perpendicular to the mirror
+plane [9], the induced BCD Dð1Þ must be perpendicular to
+Edc when Edc is along the a or b axis. Control experiments
+were carried out in device S1 to confirm the above
+expectations. The measurement configuration is shown
+in Fig. 1(d) (see Supplemental Material, Fig. S2 [29],
+for circuit schematic). The probe ac current with ac field Eω
+and frequency ω was applied approximately along the −a
+axis, satisfying Eω ≪ Edc, and the second-harmonic Hall
+(c)
+(d)
+(e)
+(f)
+(a)
+(b)
+FIG. 1.
+(a) and (b) The field-induced Berry curvature Ωð1Þ
+c ðkÞ in the kz ¼ 0 plane by a dc electric field Edc ¼ 3 kV=m applied along
+(a) a or (b) b axis, respectively. The unit of Ωð1Þ
+c ðkÞ is Å2. The green arrows indicate the direction of Edc. The gray lines depict the Fermi
+surface. (c) The a-b plane of monolayer Td-WTe2. (d) The optical image of device S1, where an angle θ is defined. (e) and (f) The
+second-harmonic Hall voltage V2ω
+H as Edc (e) along b axis (θ ¼ 0°), and (f) along −a axis (θ ¼ 90°) at 5 K. The Eω is applied along −a
+axis, as schematized in (d).
+2
+
+voltage V2ω
+H was measured to reveal the nonlinear Hall
+effect. The Edc that is used to produce BCD was applied
+along the direction characterized by the angle θ, which is
+the angle between the direction of Edc and the baseline of a
+pair of electrodes [white line in Fig. 1(d)] that is approx-
+imately along the b axis. Then Edc along θ ¼ 0° (b axis)
+and θ ¼ 90° (−a axis) correspond to the induced Dð1Þ along
+the a axis and b axis, respectively. Because the nonlinear
+Hall voltage V2ω
+H
+is proportional to Dð1Þ · Eω [9], the
+nonlinear Hall effect should be observed for EωkDð1Þ
+and be vanishing for Eω⊥Dð1Þ.
+As shown in Fig. 1(e), when Edc along θ ¼ 0°, nonlinear
+Hall voltage V2ω
+H is indeed observed as expected. The Edc
+along the b axis induces BCD along the a axis, leading to
+nonzero V2ω
+H since Eω is applied along the −a axis. The
+second-order nature is verified by both the second-
+harmonic signal and parabolic I-V characteristics. It is
+found that the nonlinear Hall voltage is highly tunable by
+the magnitude of Edc. The sign reverses when Edc is
+reversed. Moreover, the nonlinear Hall voltage is linearly
+proportional to Edc (Supplemental Material [29] Fig. S11),
+as we expected. As for Edc along θ ¼ 90°, as shown in
+Fig. 1(f), the V2ω
+H is much suppressed, which is at least one
+order of magnitude smaller than the V2ω
+H
+in Fig. 1(e).
+Because in this case the Edc along the a axis induces BCD
+along the b axis, Eω is almost perpendicular to BCD,
+leading to negligible nonlinear Hall effect. Similar results
+are also reproduced in device S2 (Supplemental Material
+[29], Fig. S12). Such control experiments are well con-
+sistent with our theoretical expectation and confirm the
+validity of field-induced BCD.
+Besides the crystalline axis (θ ¼ 0° and 90°), we also
+study the case when Edc is applied along arbitrary θ
+directions to obtain the complete angle dependence of
+field-induced BCD. Here, Eω is applied along the −a or b
+axis, to detect the BCD component along the a or b axis,
+i.e., Dð1Þ ¼ ½Dð1Þ
+a ðθÞ; Dð1Þ
+b ðθÞ�, where Dð1Þ
+a
+and Dð1Þ
+b
+are the
+BCD components along the a and b axis, respectively. The
+measurement configurations are shown in Figs. 2(a) and
+2(d). Figures 2(b) and 2(e) show the second-order Hall
+voltage as a function of θ, with the magnitude of Edc fixed
+at 3 kV=m. The second-order Hall response ½E2ω
+H =ðEωÞ2� is
+calculated by E2ω
+H ¼ ðV2ω
+H =WÞ and Eω ¼ ðIωRk=LÞ, where
+W is the channel width, Rk is the longitudinal resistance,
+and L is the channel length. As shown in Figs. 2(c) and 2(f),
+½E2ω
+H =ðEωÞ2� demonstrates a strong anisotropy, closely
+related to the inherent symmetry of WTe2. First of all, it
+is worth noting that the second-order Hall signal is
+negligible at Edc ¼ 0. This is consistent with our previous
+analysis that the inherent bulk in-plane BCD is symmetry
+forbidden [26,27]. Second, ½E2ω
+H =ðEωÞ2� almost vanishes
+when EdckEω along a or b axis. This is constrained by the
+mirror symmetries Ma or
+˜Mb, forcing the BCD to be
+perpendicular to the mirror plane in such configurations.
+(a)
+(b)
+(c)
+(d)
+(e)
+(f)
+FIG. 2.
+(a) and (d) Measurement configuration for the second-order AHE with (a) Eωk − a axis and (d) Eωkb axis, respectively. The
+Edc, satisfying Edc ≫ Eω, is rotated to along various directions. (b) and (e) The second-order Hall voltage V2ω
+H as a function of Iω at
+fixed Edc ¼ 3 kV=m but along various directions and at 5 K with (b) Eωk − a axis and (e) Eωkb axis, respectively. (c) and (f) The
+second-order Hall signal ½E2ω
+H =ðEωÞ2� as a function of θ at 5 K with (c) Eωk − a axis and (f) Eωkb axis, respectively.
+3
+
+Thus, when EdckEω along the a or b axis, the induced BCD
+is perpendicular to Edc and Eω, satisfying Dð1Þ · Eω ¼ 0,
+which leads to almost vanished second-order Hall signals.
+Moreover, ½E2ω
+H =ðEωÞ2� exhibits a sensitive dependence on
+the angle θ, indicating the BCD is highly tunable by the
+orientation of Edc. A local minimum of ½E2ω
+H =ðEωÞ2� is
+found at an intermediate angle around θ ¼ 30° when
+Eωk − a axis in Fig. 2(c). This is because ½E2ω
+H =ðEωÞ2�
+depends not only on ðDð1Þ · c
+EωÞ, i.e., the projection of the
+pseudovector Dð1Þ to the direction of Eω, but also on the
+anisotropy of conductivity in WTe2. The two terms show
+different dependence on the angle θ, leading to a local
+minimum around θ ¼ 30°.
+Through control experiments and symmetry analysis, the
+extrinsic effects, such as diode effect, thermal effect, and
+thermoelectric effect, could be safely ruled out as the main
+reason of the observed second-order nonlinear AHE (see
+Supplemental Material, Note 9 [29]). To further investigate
+this effect, the temperature dependence and scaling law of
+the second-order nonlinear Hall signal are studied. By
+changing the temperature, V2ω
+H and longitudinal conduc-
+tivity σxx were collected, where the magnitude of Edc was
+fixed at 3 kV=m. Figures 3(a) and 3(c) show the V2ω
+H at
+different temperatures with Eωk − a axis, θ ¼ 0° and Eωkb
+axis, θ ¼ 90°, respectively. A relatively small but nonzero
+second-order Hall signal is observed at 286 K. The scaling
+law, that is, the second-order Hall signal ½E2ω
+H =ðEωÞ2�
+versus σxx, is presented and analyzed in Figs. 3(b) and
+3(d) for different angles θ. The σxx was calculated by
+σxx ¼ð1=RkÞðL=WdÞ, where d is the thickness of WTe2,
+and was varied by changing temperature. According to
+Ref. [42], the scaling law between ½E2ω
+H =ðEωÞ2� and σxx
+satisfies ½E2ω
+H =ðEωÞ2� ¼ C0 þ C1σxx þ C2σ2xx. The coeffi-
+cients C2 and C1 involve the mixing contributions from
+various skew scattering processes [42–45], such as impu-
+rity scattering, phonon scattering, and mixed scattering
+from both phonons and impurities [42]. C0 is mainly
+contributed by the intrinsic mechanism, i.e., the field-
+induced BCD here. As shown in Figs. 3(b) and 3(d), the
+scaling law is well fitted for all angles θ.
+It
+is
+found
+that
+C0
+shows
+strong
+anisotropy
+(Supplemental Material [29], Fig. S18), indicating the
+field-induced BCD is also strongly dependent on angle
+θ. The value of field-induced BCD can be estimated
+through D ¼ ð2ℏ2n=m�eÞ½E2ω
+H =ðEωÞ2� [12], where ℏ is
+the reduced Planck constant, e is the electron charge, m� ¼
+0.3me is the effective electron mass, n is the carrier density.
+Here, we replace the ½E2ω
+H =ðEωÞ2� by the coefficient C0
+from the scaling law fitting. The two components of BCD
+along the a and b axes, denoted as Dð1Þ
+a
+and Dð1Þ
+b , are
+calculated from the fitting curves with the magnitude of Edc
+fixed at 3 kV=m under the Eωk − a axis and the Eωkb axis,
+respectively. As shown in Figs. 4(a) and 4(b), it is found
+that Dð1Þ
+a
+shows a cos θ dependence on θ, whereas Dð1Þ
+b
+(a)
+(b)
+(c)
+(d)
+FIG. 3.
+(a) and (c) The second-harmonic Hall voltage at various
+temperatures with the magnitude of Edc fixed at 3 kV=m (a) under
+Eωk − a axis, θ ¼ 0° and (c) under Eωkb axis, θ ¼ 90°. (b),(d)
+Second-order Hall signal ½E2ω
+H =ðEωÞ2� as a function of σxx
+(b) under Eωk − a axis and (d) under Eωkb axis at various θ
+with the magnitude of Edc fixed at 3 kV=m. The temperature
+range for the scaling law in (b) and (d) is 50–286 K.
+(a)
+(b)
+(c)
+FIG. 4.
+The induced Berry curvature dipole as a function of θ with the magnitude of Edc fixed at 3 kV=m for (a) the component along
+a axis, Dð1Þ
+a and (b) the component along b axis, Dð1Þ
+b . (c) The relationship between the field-induced Berry curvature dipole Dð1Þ and the
+applied Edc ¼ 3 kV=m along different directions. The scale bar of Dð1Þ is 0.2 nm.
+4
+
+shows a sin θ dependence. Such angle dependence is
+well consistent with the theoretical predications (see
+Supplemental Material [29], Note 6). According to the
+two components Dð1Þ
+a
+and Dð1Þ
+b , the field induced BCD
+vector of Dð1Þ is synthesized for Edc along various
+directions, as presented in Fig. 4(c). It is found that both
+the magnitude and orientation of the field-induced BCD are
+highly tunable by the dc field.
+In summary, we have demonstrated the generation,
+modulation, and detection of the induced BCD due to
+the Berry connection polarizability in WTe2. It is found that
+the direction of the generated BCD is controlled by the
+relative orientation between the applied Edc direction
+and the crystal axis, and its magnitude is proportional to
+the intensity of Edc. Using independent control of the
+two applied fields, our Letter demonstrates an efficient
+approach to probe the nonlinear transport tensor symmetry,
+which is also helpful for full characterization of nonlinear
+transport coefficients. Moreover, the manipulation of BCD
+up to room temperature by electric means without addi-
+tional symmetry breaking will greatly extend the BCD-
+related physics [46,47] to more general materials and
+should be valuable for developing devices utilizing the
+geometric properties of Bloch electrons.
+This work was supported by National Key Research and
+Development Program of China (No. 2018YFA0703703),
+National Natural Science Foundation of China (Grants
+No. 91964201 and No. 61825401), and Singapore MOE
+AcRF Tier 2 (MOE-T2EP50220-0011). We are grateful to
+Dr. Yanfeng Ge at SUTD for inspired discussions.
+*These authors contributed equally to this work.
+†[email protected]
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+6
+
+1 
+ 
+Supplemental Material for 
+Control over Berry curvature dipole with electric field in WTe2 
+Xing-Guo Ye1,+, Huiying Liu2,+, Peng-Fei Zhu1,+, Wen-Zheng Xu1,+, Shengyuan A. 
+Yang2, Nianze Shang1, Kaihui Liu1, and Zhi-Min Liao1,* 
+1 State Key Laboratory for Mesoscopic Physics and Frontiers Science Center for 
+Nano-optoelectronics, School of Physics, Peking University, Beijing 100871, China. 
+2 Research Laboratory for Quantum Materials, Singapore University of Technology 
+and Design, Singapore, 487372, Singapore. 
++ These authors contributed equally. 
+* Email: [email protected] 
+This file contains supplemental Figures S1-S18 and Notes 1-10. 
+Note 1: Device fabrication, experimental and calculation methods. 
+Note 2: Polarized Raman spectroscopy of WTe2. 
+Note 3: Angle-dependent longitudinal resistance and third-order nonlinear Hall effect. 
+Note 4: Magnetotransport properties of WTe2. 
+Note 5: Symmetry analysis of WTe2. 
+Note 6: Theoretical analysis and calculations of field-induced Berry curvature dipole. 
+Note 7: Electric field dependence of second-order Hall signals. 
+Note 8: Control experiments in device S2. 
+Note 9: Discussions of other possible origins of the second order AHE. 
+Note 10: Angle dependence of parameter C0 obtained from the fittings of scaling law. 
+ 
+ 
+
+2 
+ 
+Supplemental Note 1: Device fabrication, experimental and calculation methods. 
+1) Device fabrication 
+The WTe2 flakes were exfoliated from bulk crystal by scotch tape and then 
+transferred onto the polydimethylsiloxane (PDMS). The PDMS was then covered onto 
+a Si substrate with 285 nm-thick SiO2, where the Si substrate was precleaned by air 
+plasma, and further heated for about 1 minute at 90℃ to transfer the WTe2 flakes onto 
+Si substrate. Disk and Hall bar-shaped Ti/Au electrodes (around 10 nm thick) were 
+prefabricated on individual SiO2/Si substrates with e-beam lithography, metal 
+deposition and lift-off. Exfoliated BN (around 20 nm thick) and WTe2 flakes (around 
+5-20 nm thick) were sequentially picked up and then transferred onto the Ti/Au 
+electrodes using a polymer-based dry transfer technique [30]. The atomic force 
+microscope image of device S1 is shown in Fig. S1. The thickness of this sample is 8.4 
+nm, corresponding to a 12-layer WTe2. The whole exfoliation and transfer processes 
+were done in an argon-filled glove box with O2 and H2O content below 0.01 parts per 
+million to avoid sample degeneration. 
+ 
+Figure S1: (a) The atomic force microscope image of device S1. (b) The line profile 
+shows the thickness of the WTe2 sample is 8.4 nm. 
+ 
+0
+1
+2
+3
+4
+5
+0
+3
+6
+9
+Height (nm)
+Line profile (mm)
+8.4 nm
+3
+WTe2
+(a)
+(b)
+
+3 
+ 
+2) Electrical transport measurements and circuit schematic 
+All the transport measurements were carried out in an Oxford cryostat with a 
+variable temperature insert and a superconducting magnet. First-, second- and third-
+harmonic signals were collected by standard lock-in techniques (Stanford Research 
+Systems Model SR830) with frequency ω . Frequency  equals 17.777 Hz unless 
+otherwise stated.  
+The circuit schematic with multiple sources in experiments is depicted in Fig. S2. 
+The a.c. and d.c. sources are both effective current sources. The original SR830 a.c. 
+source is a voltage source. In experiments, we connected the SR830 voltage source and 
+a protective resistor with resistance value 𝑅𝑝 in series (𝑅𝑝 = 100 kΩ for device S1 
+and 𝑅𝑝 = 10 kΩ for device S2), as shown in Fig. S2. The resistance of WTe2 channel 
+is in the order of 10 Ω, much less than 𝑅𝑝, which makes the SR830 source an effective 
+current source with excitation current 𝐼𝜔 ≅ 𝑈𝜔 𝑅𝑝
+⁄
+, where 𝑈𝜔 is the source voltage. 
+The Keithley 2400 current source is used for the d.c source. As shown in Fig. S2, 
+the positive and negative terminals of the Keithley source are connected to a pair of 
+diagonal electrodes to form a loop circuit, i.e., a floating loop. The d.c. electric field is 
+obtained by 𝐸𝑑𝑐 =
+𝐼𝑑𝑐𝑅𝜃
+𝐿 , where 𝐼𝑑𝑐 is the applied d.c. current, 𝑅𝜃 is the resistance 
+of WTe2 along direction 𝜃, and 𝐿 is the channel length of WTe2. The impedance of 
+the floating Keithley source to ground is measured to be ~60 MΩ. While, the negative 
+terminal of SR830 source is directly connected to the ground.  
+
+4 
+ 
+ 
+Figure S2: Schematic structure of the circuit for measurements in device S1. 
+ 
+3) Spectral purity of lock-in measurements 
+For the lock-in measurements, the used integration time is 300 ms and the filter 
+roll-off is 24 dB/octave, that is, the cutoff (-3 dB) frequency for the low-pass filter is 
+0.531 Hz and the filter roll-off is 24 dB per octave. For our lock-in measurements, the 
+narrow detection bandwidth (±0.531 Hz) effectively avoided the spectral leakage.  
+The spectral purity of the lock-in homodyne circuit is verified by the control 
+experiments of the lock-in measurements of a resistor. The first-, second- and third-
+harmonic voltages of a resistor with resistance ~100 Ω are measured using the same 
+frequency (17.777 Hz), integration time (300 ms) and filter roll-off (24 dB/octave) as 
+used in experiments, as shown in Fig. S3. The first-harmonic voltage shows linear 
+dependence on the alternating current, consistent with the resistance value ~100 Ω. The 
+second- and third-harmonic voltages are four orders of magnitude smaller than the first-
+harmonic voltage, which indicates the high purity of spectrum of the lock-in homodyne 
+circuit. 
+Keithley 2400 
+current source
+SR830 voltage 
+source
+SR830 lock-in 
+measurement
+
+5 
+ 
+ 
+Figure S3: Lock-in measurements for a resistor with resistance ~𝟏𝟎𝟎 𝛀. 
+a, The first-harmonic voltage versus the alternating current. 
+b, The second- and third-harmonic voltages versus the alternating current. 
+ 
+4) Validity of electrical measurements with the two sources 
+In our experiments, the Keithley source is used as the d.c. current source, which 
+has an output impedance ~20 MΩ. The a.c. current source is realized by connecting a 
+resistor 𝑅𝑝 in series (𝑅𝑝 = 100 kΩ for device S1 and 𝑅𝑝 = 10 kΩ for device S2) in 
+series with the SR830 voltage source. Both the a.c. and d.c. current sources have 
+effectively large output impedance comparing to the sample resistance ~10 Ω, so that 
+they can be considered as independent current sources. These two current sources can 
+be applied to the device simultaneously, having well-defined potential differences. To 
+further confirm the validity of our electrical measurements with the two current sources, 
+we design a test circuit, as shown in Fig. S4(a). The a.c. current flowing through 𝑅2 
+was calculated by measuring the first-harmonic voltage 𝑉ω of 𝑅2 and 𝐼𝜔 = 𝑉𝜔/𝑅2. 
+The d.c. current is applied by the Keithley current source and is measured by measuring 
+the d.c. voltage 𝑉𝑑𝑐 of 𝑅2 and 𝐼𝑑𝑐 = 𝑉𝑑𝑐/𝑅2. As shown in Fig. S4(b), where the a.c. 
+voltage of SR830 source is fixed at 1 V, it is found that the 𝐼𝜔 is unchanged when 
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0
+10
+20
+30
+40
+50
+V (mV)
+I (mA)
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+-1
+0
+1
+ n = 2
+ n = 3
+Vn (mV)
+I (mA)
+(a)
+(b)
+
+6 
+ 
+varying the d.c. current by Keithley source, while measured 𝐼𝑑𝑐 is almost the same as 
+the output current of the Keithley source. In Fig. S4(c), where the d.c. current of 
+Keithley source is fixed, it is found that 𝐼𝜔  well satisfies 𝐼𝜔 = 𝑈𝜔/(𝑅1 + 𝑅2 +
+𝑅3) ≅ 𝑈𝜔 𝑅𝑝
+⁄
+  with 𝑈𝜔  as the SR830 source voltage and 𝑅𝑝 = 𝑅1 . These results 
+clearly confirm the a.c. and d.c. sources are effectively independent with negligible 
+current shunt between each other. 
+ 
+Figure S4: Validity of the electrical measurements with two sources. 
+a, Schematic of the test circuit. 
+b, The 𝐼𝜔 and 𝐼𝑑𝑐 as a function of the Keithley source current with SR830 source 
+voltage 𝑈𝜔 fixed at 1 V. 
+c, The 𝐼𝜔  and 𝐼𝑑𝑐  as a function of the SR830 source voltage 𝑈𝜔  with Keithley 
+source current fixed at 1 mA. 
+ 
+SR830 voltage source
+Keithley 2400 current source
+SR830 lock-in 
+measurement
+(a)
+(b)
+(c)
+0
+1
+2
+3
+4
+5
+0
+10
+20
+30
+40
+50
+I (mA)
+U (V)
+0.9
+1
+1.1
+Keithley source current=1 mA
+Idc (mA)
+-4
+-2
+0
+2
+4
+8
+10
+12
+I (mA)
+Keithley source current (mA)
+U = 1 V
+-4
+-2
+0
+2
+4
+Idc (mA)
+
+7 
+ 
+5) Calculation methods 
+First-principles calculations were performed to reveal the properties of the Berry 
+connection polarizability tensor and field-induced Berry curvature dipole in WTe2. The 
+electronic structures were carried out in the framework of density functional theory as 
+implemented in the Vienna ab initio simulation package [31,32] with the projector 
+augmented wave method [33] and Perdew, Burke, and Ernzerh of exchange correlation 
+functionals [34]. For the convergence of the results, the spin–orbit coupling was 
+included self-consistently in the calculations of electronic structures with the kinetic 
+energy cutoff of 600 eV and Monkhorst-Pack k mesh of 14 × 8 × 4. We used d orbitals 
+of W atom and p orbitals of Te atoms to construct Wannier functions [35]. While 
+evaluating the band geometric quantities, we consider the finite temperature effect in 
+the distribution function and a lifetime broadening of 𝑘𝐵𝑇 with 𝑇 = 5 K. 
+ 
+ 
+ 
+
+8 
+ 
+Supplemental Note 2: Polarized Raman spectroscopy of WTe2. 
+The crystalline orientation of WTe2 device was determined by the polarized 
+Raman spectroscopy in the parallel polarization configuration [36]. Figure S5 shows 
+the polarized Raman spectrum of device S2 as an example. The optical image of device 
+S2 is displayed in Fig. S5(a). Raman spectroscopy was measured with 514 nm 
+excitation wavelengths through a linearly polarized solid-state laser beam. The 
+polarization of the excitation laser was controlled by a quarter-wave plate and a 
+polarizer. We collected the Raman scattered light with the same polarization as the 
+excitation laser. A typical Raman spectroscopy of device S2 is shown in Fig. S5(b), 
+where five Raman peaks are identified, belonging to the A1 modes of WTe2 [36]. We 
+further measured the polarization dependence of intensities of peaks P2 and P11 
+[denoted in Fig. S5(b)] in Figs. S5(c) and S5(d), respectively. Based on previous 
+reports [36], the polarization direction with maximum intensity was assigned as the b 
+axis. The measured crystalline orientation is further indicated in the optical image [Fig. 
+S5(a)], where the applied a.c. current is approximately parallel to a axis. 
+
+9 
+ 
+ 
+Figure S5: Polarized Raman spectroscopy of WTe2 to determine the crystalline 
+orientation.  
+a, Optical image of device S2. The crystalline axes, i.e., a axis and b axis, determined 
+by the polarized Raman spectroscopy, are denoted by the black arrows. The applied a.c. 
+current is also noted by the red arrow, which is approximately aligned with a axis. 
+b, A typical Raman spectrum measured with 514 nm excitation wavelengths, where the 
+polarization direction is approximately along b axis. Five Raman peaks are observed, 
+which belong to the A1 modes of WTe2 [36].  
+c,d, Polarization dependence of intensities of peaks (c) P2 and (d) P11. Here the 
+polarization angle takes 0° along the b axis, along which maximum intensity is 
+observed [36]. 
+ 
+ 
+60
+120
+180
+240
+300
+0
+100
+200
+300
+Intensity (a.u.)
+Wavenumber (cm-1)
+0
+60
+120
+180
+240
+300
+0
+60
+120
+180
+240
+300
+b
+a
+10 mm
+(a)
+(b)
+(c)
+(d)
+P2
+P10
+P11
+P2
+P11
+b axis
+b axis
+
+10 
+ 
+Supplemental Note 3: Angle-dependent longitudinal resistance and third-order 
+nonlinear Hall effect. 
+The third-order anomalous Hall effect (AHE) is investigated in device S1, as 
+shown in Fig. S6(a). By exploiting the circular disc electrode structure, the angle-
+dependence of the third-order AHE is measured. It shows highly sensitive to the 
+crystalline orientation, as shown in Fig. S6(c), which inherits from the intrinsic 
+anisotropy of WTe2 [26]. Based on the symmetry of WTe2 [26], the third-order AHE 
+shows angle-dependence following the formula 
+E𝐻
+3ω
+(𝐸𝜔)3 ∝
+cos(θ−θ0)sin(θ−θ0)[(χ22r4−3χ12r2)sin2(θ−θ0)+(3χ21r2−χ11)cos2(θ−θ0)]
+(cos2(θ−θ0)+𝑟sin2(θ−θ0))3
+, 
+where 𝐸𝐻
+3𝜔 =
+𝑉𝐻
+3𝜔
+𝑊 , 𝐸𝜔 =
+𝐼𝜔𝑅∥
+𝐿 , 𝑉𝐻
+3𝜔 is the third-harmonic Hall voltage, 𝐼𝜔 is the 
+applied a.c. current, 𝑅∥ is the longitudinal resistance, 𝑊 and 𝐿 are channel width 
+and length, respectively, r is the resistance anisotropy, 𝜒𝑖𝑗 are elements of the third-
+order susceptibility tensor, 𝜃0  is the angle misalignment between 𝜃 = 0°  and 
+crystalline b axis. The fitting curve for this angle dependence is shown by the red line 
+in Fig. S6(c), which yields the misalignment 𝜃0 ~1.5°. In addition to the third-order 
+AHE, the longitudinal (𝑅∥) resistance also shows strong anisotropy [13], as shown in 
+Fig. S6(b), following  
+𝑅∥(𝜃) = 𝑅𝑏𝑐𝑜𝑠2(𝜃 − 𝜃0) + 𝑅𝑎𝑠𝑖𝑛2(𝜃 − 𝜃0), 
+consistent with previous results [13], where 𝑅𝑎  and 𝑅𝑏  are resistance along 
+crystalline a and b axis, respectively. 
+
+11 
+ 
+ 
+Figure S6: Angle-dependence of third-order nonlinear Hall effect in device S1 at 
+5 K. 
+a, The third-harmonic anomalous Hall voltages at various 𝜃. Here 𝜃 is defined as the 
+relative angle between the alternating current and the baseline (approximately along b 
+axis). 
+b,c, (b) Rxx and (c) third-order Hall signal 
+E𝐻
+3ω
+(𝐸𝜔)3 as a function of 𝜃, respectively. 
+ 
+ 
+ 
+0
+0.5
+1
+-15
+-10
+-5
+0
+5
+10
+15
+ 0
+ 30
+ 60
+V3
+H  (mV)
+E (kV/m)
+ 90
+ 120
+ 150
+16
+24
+Rxx (W)
+0
+60
+120
+180
+240
+300
+360
+-50
+0
+50
+V3
+H /(V)3 (V-2)
+q ()
+(a)
+(b)
+(c)
+
+12 
+ 
+Supplemental Note 4: Magnetotransport properties of WTe2. 
+The magneto-transport properties of the device S1 were investigated. Figure S7(a) 
+shows the resistivity as a function of temperature. The resistivity decreases upon 
+decreasing temperature with a residual-resistivity at low temperatures, showing typical 
+metallic behaviors. Figure S7(b) shows the magnetoresistance (MR) and Hall 
+resistance as a function of magnetic field. MR is defined as 
+𝑅𝑥𝑥(𝐵)−𝑅𝑥𝑥(0)
+𝑅𝑥𝑥(0)
+× 100%. The 
+low residual resistance and large, non-saturated MR indicate the high quality of the 
+WTe2 devices [37,38]. The carrier mobility of device S1 is estimated as high as 
+4974.4 cm2/(V ⋅ s). Moreover, resistance oscillations due to the formations of Landau 
+levels are also observed, as shown in Fig. S7(c), indicative of the high crystal quality. 
+The oscillation ∆𝑅𝑥𝑥 is obtained by subtracting a parabolic background. The fast 
+Fourier transform (FFT) is performed, as shown in Fig. S7(d). Three frequencies are 
+observed, indicating the multiple Fermi pockets in WTe2, which is consistent with 
+previous work [37-39]. The dominant peak of FFT 𝑓1 is around 44 T. 
+
+13 
+ 
+ 
+Figure S7: Transport properties of the device S1. 
+a, The resistivity as a function of temperature. 
+b, Magnetoresistance and Hall resistance at 5 K. 
+c, Oscillations of Rxx at 5 K. The ∆𝑅𝑥𝑥  is obtained by subtracting a parabolic 
+background. 
+d, The FFT analysis of ∆𝑅𝑥𝑥 oscillations, where three peaks are obtained. 
+ 
+ 
+0
+50
+100 150 200 250 300
+0
+20
+40
+60
+80
+100
+rxx (cm×mW)
+T (K)
+-15 -10
+-5
+0
+5
+10
+15
+0
+500
+1000
+1500
+2000
+MR (%)
+B (T)
+-60
+-40
+-20
+0
+20
+40
+Rxy (W)
+0.05
+0.1
+0.15
+0.2
+0.25
+-6
+-3
+0
+3
+6
+DRxx (W)
+1/B (T-1)
+100
+200
+300
+0
+200
+400
+600
+800
+FFT amplitude (a.u.)
+Frequency (T)
+f1
+f2
+f3
+(a)
+(b)
+(c)
+(d)
+
+14 
+ 
+Supplemental Note 5: Symmetry analysis of WTe2. 
+Td-WTe2 has a distorted crystal structure with low symmetry. Here we analyze the 
+thickness dependence of the symmetry in WTe2 in details. Figure S8(a) shows the b-c 
+plane of monolayer WTe2. Each monolayer consists of a layer of W atoms sandwiched 
+between two layers of Te atoms, denoted as Te1 (denoted in yellow) and Te2 (denoted 
+in red), respectively. The inversion symmetry of the monolayer is approximately 
+satisfied, and Te1 is equivalent to Te2. The presence of inversion symmetry forces Berry 
+curvature dipole (BCD) to be zero. However, as a perpendicular displacement field is 
+applied to break the inversion symmetry, the Te1 is no longer equivalent to Te2. As 
+shown in the bottom of Fig. S8(a), an in-plane electric polarization along b axis can be 
+induced by the out-of-plane displacement field. The electric polarization along b axis 
+plays a similar role as the d.c. electric field in our work, leading to nonzero BCD along 
+a axis. 
+Nonzero BCD in bilayer WTe2 origins from crystal symmetry breaking. The 
+largest symmetry in bilayer WTe2 is a single mirror symmetry 𝑀𝑎 with bc plane as 
+mirror plane. As shown in Fig. S8(b), the stacking between the two layers makes bilayer 
+WTe2 inversion symmetry breaking. Under inversion operation, the top and bottom 
+layers are swapped, which fails to coincide with each other. As shown in Fig. S8(b), 
+Te1 is not equivalent to Te2 due to the stacking arrangement in bilayer. Therefore, an 
+in-plane electric polarization P along b axis exists, similar to the case in monolayer with 
+an out-of-plane displacement field. The polarization P is able to induce nonzero BCD 
+along the perpendicular crystalline axis, i.e., along a axis. 
+
+15 
+ 
+In fact, such in-plane polarization P along b axis in monolayer and bilayer WTe2 is 
+already evidenced by the circular photogalvanic effect [14]. The symmetry breaking 
+induced polarization is also confirmed in various 2D materials, such as WSe2/black 
+phosphorus heterostructures [40]. 
+In trilayer and thicker WTe2, as shown in Fig. S8(c), the Te1 and Te2 are equivalent 
+in bulk, leading to vanished electric polarization. The in-plane inversion symmetry in 
+bulk forbids the presence of in-plane BCD. However, the inversion is broken on surface. 
+Therefore, for trilayer and thicker WTe2, a small but nonzero BCD may occur on surface. 
+ 
+Figure S8: Crystal structure of Td-WTe2. 
+a, b-c plane of monolayer Td-WTe2. 
+b, b-c plane of bilayer Td-WTe2. The stacking arrangement breaks the inversion 
+symmetry. 
+c, b-c plane of trilayer Td-WTe2. 
+ 
+Importantly, the surface BCD and it induced second-order AHE in few-layer WTe2 
+Inversion operation
+W
+Te2
+c
+b
+Te1
+E
+b
+(a)
+(b)
+(c)
+
+16 
+ 
+is reported in Ref. [13], which is also observed in our device. We measured the second-
+order AHE without the application of Edc in a WTe2 device, as shown in Fig. S9. This 
+second-order AHE is observable when applying 𝐼𝜔  in the order of 1 mA. By 
+comparison, the second-order AHE induced by d.c. field is observable when applying 
+𝐼𝜔 smaller than 0.05 mA (Fig. 1 of main text). The calculated BCD along a axis 𝐷𝑎 
+without the application of Edc is ~0.03 nm, which is one order of magnitude smaller 
+than 𝐷𝑎
+(1) ~0.29 nm measured under Edc = 3kV/m (Fig. 4 of main text). These results 
+confirm the validity of Edc induced BCD in our work. 
+ 
+Figure S9: The second-order AHE without external d.c. electric field in WTe2 at 
+1.8 K. 
+ 
+ 
+ 
+0
+0.5
+1
+1.5
+2
+0
+10
+20
+30
+40
+V2
+H  (mV)
+I (mA)
+
+17 
+ 
+Supplemental Note 6: Theoretical analysis and calculations of field-induced Berry 
+curvature dipole. 
+The electric field-induced Berry curvature depends on the Berry connection 
+polarizability tensor and the applied d.c. field with the relation that 
+𝛀(1) = 𝛁𝐤 × (𝐆⃡𝐄𝑑𝑐), 
+Ωβ
+(1)(𝑛, 𝒌) = εβγμ[∂γ𝐺μν(𝑛, 𝒌)]𝐸ν
+dc, 
+with 𝐺μν(𝑛, 𝒌) = 2𝑒Re ∑
+(𝐴μ)𝑛𝑚(𝐴ν)𝑚𝑛
+ε𝑛−ε𝑚
+𝑚≠𝑛
+ , where 𝐴𝑚𝑛  is the interband Berry 
+connection and 𝑒  is the electron charge. The superscript “(1)” represents that the 
+physical quantity is the first order term of electric field. Here the Greek letters refer to 
+the spatial directions, 𝑚, 𝑛 refer to the energy band indices, εβγμ is the Levi-Civita 
+symbol, and 𝜕𝛾  is short for 𝜕/𝜕𝑘𝛾 . The Berry connection polarizability tensor of 
+WTe2 is calculated and shown in Figs. S10(a)-(c). From the definition, the field-induced 
+BCD is 
+𝐷αβ
+(1) = ∫ [𝑑𝒌]𝑓0 (∂αΩβ
+(1))
+𝑘
+= εβγμ ∫ [𝑑𝒌]𝑓0[∂α(∂γ𝐺μν)]𝐸ν
+dc
+𝑘
+, 
+where ∫ [𝑑𝒌]
+𝑘
+= ∑
+1
+(2π)3 ∭ 𝑑𝒌
+𝑛
+ is taken over the first Brillouin zone of the system and 
+summed over all energy bands. 
+In two-dimensional systems, 𝛀(1) is constrained to the out of plane direction, and 
+BCD behaves as a pseudo vector in the plane. Here we choose our coordinate frame 
+along the crystal principal axes 𝑎, 𝑏, 𝑐 . By applying a d.c. electric field 𝐄dc =
+(Ea
+dc, Eb
+dc) in the 𝑎𝑏 plane, the induced Ω𝑐
+(1) reads 
+Ω𝑐
+(1)(𝑛, 𝒌) = (𝜕𝑎𝐺𝑏𝑎 − 𝜕𝑏𝐺𝑎𝑎)Ea
+dc + (𝜕𝑎𝐺𝑏𝑏 − 𝜕𝑏𝐺𝑎𝑏)Eb
+dc. 
+𝐷α
+(1) defined in a few-layer 2D system can be approximately derived from 𝐷αc(bulk)
+(1)
+ of 
+
+18 
+ 
+the bulk system by 𝐷α
+(1)  = 𝑑𝐷αc(bulk)
+(1)
+ , where 𝑑  is the thickness of the film. The 
+independent components of 𝐷α
+(1)  are related to the Berry connection polarizability 
+tensor, 𝐄dc and 𝑑. The mirror symmetry 𝑀𝑎 and the glide symmetry 𝑀̃𝑏 in WTe2 
+constrain 𝐷α
+(1) to be 
+𝐷𝑎
+(1) = ∫[𝑑𝑘] f0[∂a(∂aGbb) − ∂a(∂bGab)]Eb
+dc𝑑
+k
+, 
+𝐷𝑏
+(1) = ∫[𝑑𝑘] f0[∂b(𝜕𝑎𝐺𝑏𝑎) − ∂b(𝜕𝑏𝐺𝑎𝑎)]Ea
+dc𝑑
+k
+, 
+where the other terms are prohibited by symmetry. In the experiment, the d.c. electric 
+field is applied along a direction with an angle 𝜃  between 𝑏  axis, which can be 
+expressed 
+as 
+𝐄dc = 𝐸dc(− sin 𝜃 , cos 𝜃) . 
+The 
+induced 
+BCD 
+𝐃(1)(𝜃) =
+(𝐷𝑎
+(1)(𝜃), 𝐷𝑏
+(1)(𝜃)) hence reads 
+𝐷𝑎
+(1)(𝜃) = ∫[𝑑𝑘] f0[∂a(∂aGbb) − ∂a(∂bGab)]Edc
+k
+cos 𝜃 𝑑, 
+𝐷𝑏
+(1)(𝜃) = ∫[𝑑𝑘] f0[∂b(∂bGaa) − ∂b(∂aGba)]Edc
+k
+sin 𝜃 𝑑. 
+With the field-induced BCD, the second-order Hall current of an a.c. electric field 
+𝐄ω is [9] 
+𝑗𝛼
+2ω = −εαμγ
+𝑒3𝜏
+2(1 + 𝑖ωτ)ℏ2 𝐷βμ
+(1)𝐸β
+ω𝐸γ
+ω. 
+    In two-dimensional systems, where 𝛀(1)  is along out of plane direction and 
+𝐷αc
+(1) = ∫ [𝑑𝒌]𝑓0(∂αΩc
+(1))
+𝑘
+, it is equivalent to 
+𝒋2ω = −
+𝑒3𝜏
+2(1 + 𝑖ωτ)ℏ2 (𝒛̂ × 𝐄ω)[D(1)(𝜃) ⋅ Eω]. 
+The magnitude of induced second-order Hall conductivity is determined by  
+D(1)(𝜃) ⋅ 𝐄̂ω, which is the projection of the pseudo vector 𝐃(1) to the direction of 𝐄ω, 
+
+19 
+ 
+and the direction of Hall current is perpendicular to 𝐄ω. Consequently, we can measure 
+the 𝐄dc  induced BCD 𝐃(1)  by detecting its projective component 𝐷𝑎
+(1)(𝜃)  or 
+𝐷𝑏
+(1)(𝜃) with an a.c. electric field along the corresponding direction. From the above 
+derivation, when the direction of the d.c electric field varies in the 𝑎𝑏  plane, the 
+independent components of induced BCD 𝐷𝑎
+(1) and 𝐷𝑏
+(1) change as a cosine and a sine 
+function, respectively. This relation is clearly demonstrated by our experimental results 
+in Fig. 4 of main text. 
+With first-principles calculations, we estimate the extreme value of 𝐷𝑎
+(1)(0°) and 
+𝐷𝑏
+(1)(90°), as shown in Fig. S10(d). It is taken that 𝑑 ∼ 8.4 nm and 𝐸dc ∼ 3 kV/m 
+according to the experiment. 𝐷𝑎
+(1)(0°) and 𝐷𝑏
+(1)(90°) refer to 𝐷𝑎
+(1) and 𝐷𝑏
+(1) as the 
+applied 𝐸dc  along the b axis and -a axis, respectively. It is found that 𝐷𝑏
+(1)(90°) 
+varies from ~-0.14 nm to 0 as tuning chemical potential away from 0, and 𝐷𝑎
+(1)(0°) 
+shows a non-monotonic change between 0.18 and -0.13 nm as changing chemical 
+potential. The experimental results of 𝐷𝑏
+(1)(90°) ~-0.05 nm and 𝐷𝑎
+(1)(0°) ~-0.28 nm 
+(Fig. 4 in main text) agree well with the calculations on the order of magnitude.  
+ 
+Figure S10: Calculations of Berry connection polarizability tensor and field-
+(a)
+(b)
+(c)
+(d)
+
+0.2
+-D(0°)
+(nm)
+0.1
+.-.D"(90°)
+0
+D(1)
+-0.1
+=3kV/m
+-0.2
+-20
+-10
+0
+10
+20
+μ(meV)106
+G
+104
+102
+X
+0
+-102
+-104
+-106
+Y
+Gbb
+10°
+104
+102
+X
+0
+-102
+-104
+-106
+Y106
+104
+102
+X
+0
+-102
+-104
+-106
+Y20 
+ 
+induced Berry curvature dipole in WTe2. 
+a-c, The calculated distribution of Berry connection polarizability tensor elements (a) 
+𝐺𝑎𝑎, (b) 𝐺𝑏𝑏, (c) 𝐺𝑎𝑏 in the 𝑘𝑧 = 0 plane of the Brillouin Zone for the occupied 
+bands. The unit of BCP is Å2 ⋅ V−1. The grey lines depict the Fermi surface. 
+d, Calculated field-induced BCD 𝐷𝑎
+(1)(0°)  and 𝐷𝑏
+(1)(90°)  with respect to the 
+chemical potential 𝜇 when 𝐸dc = 3 kV/m. In the calculations, the finite temperature 
+effect is considered with a boarding of 𝑘𝐵𝑇 at 5 K. 
+ 
+ 
+
+21 
+ 
+Supplemental Note 7: Electric field dependence of second-order Hall signals. 
+The second-harmonic I-V characteristics in Fig. 1(e) of main text are converted 
+into the 𝑉𝐻
+2𝜔 versus (𝑉𝜔)2 in Fig. S11(a), where linear relationships are observed. 
+The 
+E𝐻
+2ω
+(𝐸𝜔)2 as a function of the applied 𝐸𝑑𝑐 is further calculated and presented in Fig. 
+S11(b). 
+ 
+Figure S11: Second-order AHE modulated by d.c. electric field at 5 K. 
+a, The second-harmonic Hall voltage 𝑉𝐻
+2𝜔 as a function of (𝑉𝜔)2 as 𝐄𝑑𝑐 along b 
+axis and 𝐄𝜔 along -a axis. 
+b, The second-order Hall signal 
+E𝐻
+2ω
+(𝐸𝜔)2 as a function of 𝐸𝑑𝑐 at 𝜃 = 0° and 𝜃 = 90° 
+with 𝐄𝜔 ∥ −𝑎 axis. 
+ 
+ 
+ 
+0
+5
+10
+15
+20
+25
+30
+-6
+-4
+-2
+0
+2
+4
+6
+Edc (kV/m)
+ 3  
+ 1.5
+ 0
+ -1.5
+ -3
+V2
+H  (mV)
+(V)2 (10-8 V2)
+q = 0
+E  -a axis
+-3
+-2
+-1
+0
+1
+2
+3
+-9
+-6
+-3
+0
+3
+6
+9
+     q
+ 0
+ 90
+E2
+H /(E)2 (10-5 m/V)
+Edc (kV/m)
+E  -a axis
+(a)
+(b)
+
+22 
+ 
+Supplemental Note 8: Control experiments in device S2. 
+To demonstrate the symmetry constraint in WTe2, control experiments were 
+carried out in device S2. As schematically shown in Figs. S12(a), (d), the a.c. and d.c. 
+current sources are applied. The SR830 is an effective a.c. current source as connecting 
+a resistor in series with output impedance 10 kΩ. The d.c. source is the Keithley current 
+source with output impedance ~20 MΩ. For the d.c. field applied along a and b axis, 
+respectively, the first-harmonic Hall voltage shows no obvious dependence on 𝐄𝑑𝑐, as 
+shown in Figs. S12(b) and S12(e), which indicate the independence of the two electric 
+sources. When applying 𝐄𝑑𝑐 ∥  𝐄𝜔 ∥ 𝑎 axis, no second-order nonlinear Hall effect can 
+be observed in Fig. S12(c). Nevertheless, upon applying 𝐄𝑑𝑐 ⊥  𝐄𝜔 and 𝐄𝜔 ∥ 𝑎 axis, 
+as shown in Fig. S12(f), nonzero second-order nonlinear Hall effect emerges due to the 
+𝐄𝑑𝑐 induced Berry curvature dipole along a axis. 
+ 
+Figure S12: The measurements by applying both d.c. electric field 𝐄𝒅𝒄 and a.c. 
+current in devices S2 at 1.8 K. 
+a, Schematic of the measurement configuration for (b) and (c). 
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+-2
+-1
+0
+1
+2
+3
+Edc (104 V/m)
+ -10.7  
+ -5.2
+ -1.5    
+ 0
+ 1.5     
+ 5.2
+ 10.7
+V2
+⊥  (mV)
+I (mA)
+E ⊥ Edc
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+-1
+-0.5
+0
+0.5
+1
+Edc
+  (104 V/m)
+ 2.5
+ -2.5
+V2
+⊥  (mV)
+I (mA)
+E  Edc
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0
+0.5
+1
+1.5
+Edc (104 V/m)
+ -5.2
+ 5.2
+V
+H (mV)
+I (mA)
+E ⊥ Edc
+0
+0.1
+0.2
+0.3
+0.4
+0.5
+0
+0.5
+1
+1.5
+Edc (104 V/m)
+ 2.5
+ -2.5
+V
+H (mV)
+I (mA)
+E  Edc
+SR830
+voltage source
+Keithley 2400 
+current source
+SR830
+voltage source
+Keithley 2400 
+current source
+b
+a
+b
+a
+(a)
+(b)
+(c)
+(d)
+(e)
+(f)
+
+23 
+ 
+b, First-harmonic Hall voltage 𝑉𝐻
+𝜔 under 𝐄𝑑𝑐 ∥  𝐄𝜔 ∥ 𝑎 axis. 
+c, There is no clear second-harmonic Hall voltage 𝑉𝐻
+2𝜔 under 𝐄𝑑𝑐 ∥  𝐄𝜔 ∥ 𝑎 axis. 
+d, Schematic of the measurement configuration for (e) and (f). 
+e, The 𝑉𝐻
+𝜔 under various 𝐄𝑑𝑐 with 𝐄𝑑𝑐 ⊥  𝐄𝜔 and 𝐄𝜔 ∥ 𝑎 axis. 
+f, The 𝑉𝐻
+2𝜔 under various 𝐄𝑑𝑐 with 𝐄𝑑𝑐 ⊥  𝐄𝜔 and 𝐄𝜔 ∥ 𝑎 axis. 
+ 
+ 
+
+24 
+ 
+Supplemental Note 9: Discussions of other possible origins of the second order 
+AHE. 
+1) Diode effect. An accidental diode due to the contact can lead to a rectification, 
+causing high-order transport, which, however, can be safely ruled out in this work due 
+to the following reasons: 
+(a) Extrinsic signals of this origin should be strongly contact dependent. Thus, the 
+angle-dependence should be also coupled to extrinsic contacts. Nevertheless, the angle-
+dependence of second-order AHE in Fig. 2 and Fig. S12 is well consistent with the 
+inherent symmetry of WTe2, which excludes the extrinsic origins. 
+(b) The two-terminal d.c. measurements for all the diagonal electrodes show linear 
+I-V characteristics, as shown in Fig. S13(a), excluding the existence of diode effect. 
+Linear fittings are performed for the two-terminal I-V curves. The R-square of the linear 
+fittings is at least larger than 0.99997, indicating perfect linearity. Further, the deviation 
+from linearity is analyzed by subtracting the linear-dependent part, as shown in Fig. 
+S13(b). It is found ∆Vdc, i.e., the deviation part, is four orders of magnitude smaller 
+than the original Vdc, indicating a negligible nonlinearity. Moreover, the ∆Vdc shows 
+no obvious current or angle dependence (Fig. S13(b)), and its magnitude is also much 
+smaller than that of the higher-harmonic Hall voltages (Fig. S13(c)), further indicating 
+that the observed higher-order transport in this work is failed to be attributed to the 
+diode effect induced by contact. 
+ 
+
+25 
+ 
+ 
+Figure S13: Two-terminal d.c. measurements at 5 K in device S1.  
+a, Current-voltage curves from two-terminal d.c. measurements for all the diagonal 
+electrodes. 
+b, The current dependence of ∆Vdc, that is, the deviations from the linearity of the 
+current-voltage curves in Fig. S13a. 
+c, The comparation of the ∆Vdc, 𝑉𝐻
+2𝜔 and 𝑉𝐻
+3𝜔. For ∆Vdc and 𝑉𝐻
+3𝜔, the excitation 
+current is applied at 𝜃 = 30°, while for 𝑉𝐻
+2𝜔, the excitation current is applied along a 
+axis and a d.c. field 3 kV/m is applied at 𝜃 = 30°. 
+ 
+2) Capacitive effect. Contact resistance is generally inevitable between the metal 
+electrodes and two-dimensional materials, which would induce an accidental capacitive 
+effect, resulting in higher-order transport effect. Here, the second-order AHE shows a 
+negligible dependence on frequency, as shown in Fig. S14(a), excluding the capacitive 
+effect. The phase of the second-harmonic Hall voltage is also investigated, where the Y 
+signal dominates over the X signal (Fig. S14(b)). The phase of the second-harmonic 
+Hall voltage is approximately ±90°, as shown in Fig. S14(c). These features further 
+exclude the capacitive effect. 
+-0.6
+0
+0.6
+-10
+0
+10
+Vdc (mV)
+Idc (mA)
+ 90
+ 120
+ 150
+ 0
+ 30
+ 60
+(a)
+(b)
+(c)
+-0.6
+-0.4
+-0.2
+0
+0.2
+0.4
+0.6
+-0.04
+-0.02
+0
+0.02
+0.04
+ 0
+ 30
+ 60
+DVdc (mV)
+Idc (mA)
+ 90
+ 120
+ 150
+0
+0.2
+0.4
+-5
+0
+5
+10
+V (mV)
+Excitation current (mA)
+ DVdc
+ V2
+H
+ V3
+H
+
+26 
+ 
+ 
+Figure S14: Frequency-dependence and phase of second-order AHE in device S1 
+at 5 K and with 𝐄𝐝𝐜 = 𝟑 𝐤𝐕/𝐦 at 𝜽 = 𝟔𝟎°. 
+a, The second-order Hall signals at different frequencies. 
+b, The X and Y signals of the second-order Hall voltages.  
+c, The absolute value of the phase of the second-order Hall voltages. 
+ 
+3) Thermal effect. The thermal effect can also induce a second-order signal [41]. If the 
+observed nonlinear Hall effect origins from thermal effect, it should response to both 
+longitudinal and transverse d.c. electric field. However, as shown in Fig. S12, when 
+applying 𝐄𝑑𝑐 ∥  𝐄𝜔 ∥ 𝑎  axis, no second-order nonlinear Hall effect is observed. 
+Nevertheless, upon applying 𝐄𝜔 ⊥ 𝐄𝑑𝑐 , nonzero second-order nonlinear Hall effect 
+emerges. This observation is clearly inconsistent with the thermal effect. Moreover, the 
+observed second-order nonlinear Hall effect shows strong anisotropy, as shown in Fig. 
+2 of main text. The angle-dependence of the d.c. field-induced second-order Hall effect 
+is well consistent with the inherent symmetry of WTe2, which is failed to be explained 
+by the thermal effect.  
+4) Thermoelectric effect. Joule heating induced temperature gradient across the 
+sample can drive a thermoelectric voltage, leading to second-order nonlinear Hall effect. 
+This thermoelectric effect can also be excluded due to the following reasons: 
+0.01
+0.02
+0.03
+0.04
+0.05
+0
+20
+40
+60
+80
+100
+abs(phase) ()
+I (mA)
+0
+0.01 0.02 0.03 0.04 0.05
+-2.5
+-2
+-1.5
+-1
+-0.5
+0
+ X signal
+ Y signal
+V2
+H  (mV)
+I (mA)
+(b)
+(c)
+0
+0.01 0.02 0.03 0.04 0.05
+-2.5
+-2
+-1.5
+-1
+-0.5
+0
+ 17.777 Hz  
+ 77.777 Hz
+ 177.77 Hz
+ 777.77 Hz
+ 1777.7 Hz
+V2
+H  (mV)
+I (mA)
+(a)
+
+27 
+ 
+(a) Uniform Joule heating will not induce a temperature gradient and thus no 
+thermoelectric voltage across the sample. 
+(b) To generate thermoelectric voltage, the Joule heating should couple with 
+external asymmetry, such as contact junction or flake shape, which should be unrelated 
+to the inherent symmetry of WTe2. However, the anisotropy of second-order nonlinear 
+Hall effect is well consistent with the inherent symmetry analysis, as shown in Fig. 2 
+of main text. 
+5) A residue of the first-harmonic Hall response 𝑽𝑯
+𝝎. The influence of 𝑉𝐻
+𝜔 on the 
+𝑉𝐻
+2𝜔 can be ruled out because the first- and second-harmonic signals show different 
+dependence on the d.c. electric field. As shown in Fig. S15, the first-harmonic Hall 
+signal (𝑉𝐻
+𝜔) shows that the I-V curves under 𝐸𝑑𝑐 = ±3 kV/m overlap with each other. 
+By comparison, the second-harmonic Hall signal (𝑉𝐻
+2𝜔 ) shows an anti-symmetric 
+dependence on 𝐸𝑑𝑐, where the sign of 𝑉𝐻
+2𝜔 is changed upon changing the sign of 𝐸𝑑𝑐. 
+This indicates that the existence of the first order signal 𝑉𝐻
+𝜔  will not affect the 
+measurements of the second order signal 𝑉𝐻
+2𝜔. 
+ 
+Figure S15: The first- and second-harmonic signals at 5 K as 𝐄𝒅𝒄 along b axis 
+(𝜽 = 𝟎°) and 𝐄𝝎 along -a axis.  
+a, The first-harmonic Hall voltage 𝑉𝐻
+𝜔 as a function of 𝐼𝜔 at 𝐸𝑑𝑐 = ±3 kV/m.  
+0
+0.01 0.02 0.03 0.04 0.05
+-6
+-4
+-2
+0
+2
+4
+6
+Edc (kV/m)
+ 3  
+ -3
+V2
+H  (mV)
+I (mA)
+q = 0
+(a)
+(b)
+0
+0.01 0.02 0.03 0.04 0.05
+0
+0.01
+0.02
+0.03
+0.04
+0.05
+Edc (kV/m)
+ 3 
+ -3 
+V
+H (mV)
+I (mA)
+
+28 
+ 
+b, The second-harmonic Hall voltage 𝑉𝐻
+2𝜔. 
+ 
+6) Trivial effect by d.c. source. We measured the first-harmonic longitudinal voltage 
+upon applying Edc = 3 kV/m , as shown in Fig. S16. It is clearly found that when 
+reversing the sign of d.c. electric field, the I-V curves overlapped with each other. The 
+results show that the d.c. source will not affect the a.c. measurements. 
+ 
+Figure S16: The first-harmonic longitudinal voltage versus current under 
+different d.c. electric fields at 5 K. The 𝐄𝝎 and 𝐄𝒅𝒄 are along a axis. 
+ 
+7) Longitudinal nonlinearity originating from a circuit artifact. We have measured 
+both the second-harmonic Hall and longitudinal voltage at all the angles, as shown in 
+Fig. S17. The measurement configuration is shown in the inset of Fig. S17(d) with d.c. 
+field applied at angle 𝜃. It is clearly found that the Hall nonlinearity is dominated over 
+longitudinal one, which guarantees that the observed second-order Hall effect doesn’t 
+originate from the longitudinal nonlinearity induced by a circuit artifact. 
+0
+0.01 0.02 0.03 0.04 0.05
+0
+0.2
+0.4
+0.6
+0.8
+V
+xx (mV)
+I (mA)
+Edc (kV/m)
+ 3
+ -3
+
+29 
+ 
+ 
+Figure S17: The second-harmonic Hall 𝑽𝑯
+𝟐𝝎 and longitudinal voltage 𝑽𝑳
+𝟐𝝎 with 
+𝐄𝝎 ∥ −𝒂 axis and 𝐄𝒅𝒄 = 𝟏. 𝟓 𝐤𝐕/𝐦 along different angles at 5 K. The angle 𝜽 is 
+defined in Fig. 1(d) of main text. 
+ 
+ 
+ 
+0
+0.01 0.02 0.03 0.04 0.05
+0
+0.2
+0.4
+0.6
+ V2
+H
+ V2
+L
+V2 (mV)
+I (mA)
+0
+0.01 0.02 0.03 0.04 0.05
+-0.5
+0
+0.5
+1
+1.5
+2
+2.5
+ V2
+H
+ V2
+L
+V2 (mV)
+I (mA)
+0
+0.01 0.02 0.03 0.04 0.05
+-0.5
+0
+0.5
+1
+1.5
+2
+ V2
+H
+ V2
+L
+V2 (mV)
+I (mA)
+0
+0.01 0.02 0.03 0.04 0.05
+0
+0.5
+1
+1.5
+2
+2.5
+ V2
+H
+ V2
+L
+V2 (mV)
+I (mA)
+0
+0.01 0.02 0.03 0.04 0.05
+-2.5
+-2
+-1.5
+-1
+-0.5
+0
+ V2
+H
+ V2
+L
+V2 (mV)
+I (mA)
+0
+0.01 0.02 0.03 0.04 0.05
+-1.5
+-1
+-0.5
+0
+ V2
+H
+ V2
+L
+V2 (mV)
+I (mA)
+a
+b
+(a)
+(b)
+(c)
+(d)
+(e)
+(f)
+
+30 
+ 
+Supplemental Note 10: Angle dependence of parameter C0 obtained from the 
+fittings of scaling law. 
+The second-order Hall signal 
+EH
+2ω
+(𝐸𝜔)2 is found to satisfy scaling law 
+EH
+2ω
+(𝐸𝜔)2 = 𝐶0 +
+𝐶1𝜎𝑥𝑥 + 𝐶2𝜎𝑥𝑥
+2 . For 𝐄𝑑𝑐 = 3 kV/m with a fixed direction (angle 𝜃), a set of curves of 
+VH
+2ω vs. Iω is measured at different temperatures as Iω is applied along -a axis and b 
+axis, respectively. Through varying temperature, the 𝜎𝑥𝑥  is changed accordingly. 
+Therefore, for a fixed angle 𝜃, the relationship between 
+EH
+2ω
+(𝐸𝜔)2 and 𝜎𝑥𝑥 is plotted. By 
+fitting the experimental data, the parameter 𝐶0 is then obtained and presented in Fig. 
+S18. 
+ 
+Figure S18: Angle-dependence of the coefficient 𝑪𝟎. 
+a,b, The coefficient 𝐶0 as a function of 𝜃 with the amplitude of 𝐄𝑑𝑐 fixed at 3 kV/m 
+for (a) 𝐄𝜔 ∥ −𝑎 axis and (b) 𝐄𝜔 ∥ 𝑏 axis.   
+     
+0
+60
+120
+180
+240
+300
+360
+-0.6
+-0.4
+-0.2
+0
+0.2
+0.4
+0.6
+C0 (10-7 m/V) 
+q (o)
+0
+60
+120
+180
+240
+300
+360
+-2
+-1
+0
+1
+2
+C0 (10-7 m/V) 
+q (o)
+(a)
+(b)
+axis
+axis
+

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+MNRAS 000, 1–4 (2022)
+Preprint 30 December 2022
+Compiled using MNRAS LATEX style file v3.0
+A Bayesian Neural Network Approach to identify Stars and AGNs
+observed by XMM Newton ★
+Sarvesh Gharat,1† and Bhaskar Bose2
+1 Centre for Machine Intelligence and Data Science, Indian Institute of Technology Bombay, 400076, Mumbai, India
+2 Smart Mobility Group, Tata Consultancy Services, 560067, Bangalore, India
+Accepted XXX. Received YYY; in original form ZZZ
+ABSTRACT
+In today’s era, a tremendous amount of data is generated by different observatories and manual classification of data is something
+which is practically impossible. Hence, to classify and categorize the objects there are multiple machine and deep learning
+techniques used. However, these predictions are overconfident and won’t be able to identify if the data actually belongs to the
+trained class. To solve this major problem of overconfidence, in this study we propose a novel Bayesian Neural Network which
+randomly samples weights from a distribution as opposed to the fixed weight vector considered in the frequentist approach. The
+study involves the classification of Stars and AGNs observed by XMM Newton. However, for testing purposes, we consider CV,
+Pulsars, ULX, and LMX along with Stars and AGNs which the algorithm refuses to predict with higher accuracy as opposed
+to the frequentist approaches wherein these objects are predicted as either Stars or AGNs. The proposed algorithm is one of
+the first instances wherein the use of Bayesian Neural Networks is done in observational astronomy. Additionally, we also make
+our algorithm to identify stars and AGNs in the whole XMM-Newton DR11 catalogue. The algorithm almost identifies 62807
+data points as AGNs and 88107 data points as Stars with enough confidence. In all other cases, the algorithm refuses to make
+predictions due to high uncertainty and hence reduces the error rate.
+Key words: methods: data analysis – methods: observational – methods: miscellaneous
+1 INTRODUCTION
+Since the last few decades, a large amount of data is regularly
+generated by different observatories and surveys. The classification
+of this enormous amount of data by professional astronomers is
+time-consuming as well as practically impossible. To make the
+process simpler, various citizen science projects (Desjardins et al.
+2021) (Cobb 2021) (Allf et al. 2022) (Faherty et al. 2021) are
+introduced which has been reducing the required time by some
+extent. However, there are many instances wherein classifying the
+objects won’t be simple and may require domain expertise.
+In this modern era, wherein Machine Learning and Neural Net-
+works are widely used in multiple fields, there has been significant
+development in the use of these algorithms in Astronomy. Though
+these algorithms are accurate with their predictions there is certainly
+some overconfidence (Kristiadi et al. 2020) (Kristiadi et al. 2021)
+associated with it. Besides that, these algorithms tend to classify
+every input as one of the trained classes (Beaumont & Haziza 2022)
+irrespective of whether it actually belongs to those trained classes
+eg: The algorithm trained to classify stars will also predict AGNs as
+one of the stars. To solve this major issue, in this study we propose a
+Bayesian Neural Network (Jospin et al. 2022) (Charnock et al. 2022)
+★ Based on observations obtained with XMM-Newton, an ESA science mis-
+sion with instruments and contributions directly funded by ESA Member
+States and NASA
+† E-mail: [email protected]
+which refuses to make a prediction whenever it isn’t confident about
+its predictions. The proposed algorithm is implemented on the data
+collected by XMM-Newton (Jansen et al. 2001). We do a binary
+classification to classify Stars and AGNs (Małek et al. 2013) (Golob
+et al. 2021). Additionally to test our algorithm with the inputs which
+don’t belong to the trained class we consider data observed from CV,
+Pulsars, ULX, and LMX. Although, the algorithm doesn’t refuse to
+predict all these objects, but the number of objects it predicts for
+these 4 classes is way smaller than that of trained classes.
+For the trained classes, the algorithm gives its predictions for al-
+most 64% of the data points and avoids predicting the output when-
+ever it is not confident about its predictions. The achieved accuracy
+in this binary classification task whenever the algorithm gives its
+prediction is 98.41%. On the other hand, only 14.6% of the incor-
+rect data points are predicted as one of the classes by the algorithm.
+The percentage decrease from 100% to 14.6% in the case of different
+inputs is what dominates our model over other frequentist algorithms.
+2 METHODOLOGY
+In this section, we discuss the methodology used to perform this
+study. This section is divided into the following subsections.
+• Data Collection and Feature Extraction
+• Model Architecture
+• Training and Testing
+© 2022 The Authors
+
+2
+S. Gharat et al.
+Class
+Catalogue
+AGN
+VERONCAT (Véron-Cetty & Véron 2010)
+LMX
+NGC3115CXO (Lin et al. 2015)
+RITTERLMXB (Ritter & Kolb 2003)
+LMXBCAT (Liu et al. 2007)
+INTREFCAT (Ebisawa et al. 2003)
+M31XMMXRAY (Stiele et al. 2008)
+M31CFCXO (Hofmann et al. 2013)
+RASS2MASS (Haakonsen & Rutledge 2009)
+Pulsars
+ATNF (Manchester et al. 2005)
+FERMIL2PSR (Abdo et al. 2013)
+CV
+CVC (Drake et al. 2014)
+ULX
+XSEG (Drake et al. 2014)
+Stars
+CSSC (Skiff 2014)
+Table 1. Catalogues used to create labeled data
+Class
+Training Data
+Test Data
+AGN
+8295
+2040
+LMX
+0
+49
+Pulsars
+0
+174
+CV
+0
+36
+ULX
+0
+261
+Stars
+6649
+1628
+Total
+14944
+4188
+Table 2. Data distribution after cross-matching all the data points with cata-
+logs mentioned in Table 1
+2.1 Data Collection and Feature Extraction
+In this study, we make use of data provided in "XMM-DR11 SEDs"
+Webb et al. (2020). We further cross-match the collected data with
+different vizier (Ochsenbein et al. 2000) catalogs. Please refer to
+Table 1 to view all the catalogs used in this study. As the proposed
+algorithm is a "supervised Bayesian algorithm", this happens to be
+one of the important steps for our algorithm to work.
+The provided data has 336 different features that can increase
+computational complexity by a larger extent and also has a lot of
+missing data points. Therefore in this study, we consider a set of
+18 features corresponding to the observed source. The considered
+features for all the sources are available on our Github repository,
+more information of which is available on the official webpage 1 of
+the observatory. After cross-matching and reducing the number of
+features, we were left with a total of 19136 data points. The data
+distribution can be seen in Table 2. We further also plot the sources
+(Refer Figure1) based on their "Ra" and "Dec" to confirm if the
+data coverage of the considered sources matches with the actual data
+covered by the telescope.
+1 http://xmmssc.irap.omp.eu/Catalogue/4XMM-DR11/col_unsrc.
+html
+Figure 1. Sky map coverage of considered data points
+The collected data is further classified into train and test according
+to the 80 : 20 splitting condition. The exact number of data points is
+mentioned in Table 2
+2.2 Model Architecture
+The proposed model has 1 input, hidden and output layers (refer
+Figure 2) with 18, 512, and 2 neurons respectively. The reason for
+having 18 neurons in the input layer is the number of input features
+considered in this study. Further, to increase the non-linearity of the
+output, we make use of "Relu" (Fukushima 1975) (Agarap 2018) as
+an activation function for the first 2 layers. On the other hand, the
+output layer makes use of "Softmax" to make the predictions. This
+is done so that the output of the model will be the probability of
+image belonging to a particular class (Nwankpa et al. 2018) (Feng
+& Lu 2019).
+The "optimizer" and "loss" used in this study are "Adam" (Kingma
+et al. 2020) and "Trace Elbo" (Wingate & Weber 2013) (Ranganath
+et al. 2014) respectively. The overall idea of BNN (Izmailov et al.
+2021) (Jospin et al. 2022) (Goan & Fookes 2020) is to have a pos-
+terior distribution corresponding to all weights and biases such that,
+the output distribution produced by these posterior distributions is
+similar to that of the categorical distributions defined in the training
+dataset. Hence, convergence, in this case, can be achieved by min-
+imizing the KL divergence between the output and the categorical
+distribution or just by maximizing the ELBO (Wingate & Weber
+2013) (Ranganath et al. 2014). We make use of normal distributions
+which are initialized with random mean and variance as prior (For-
+tuin et al. 2021), along with the likelihood derived from the data to
+construct the posterior distribution.
+2.3 Training and Testing
+The proposed model is constructed using Pytorch (Paszke et al.
+2019) and Pyro (Bingham et al. 2019). The training of the model
+is conducted on Google Colaboratory, making use of NVIDIA
+K80 GPU (Carneiro et al. 2018). The model is trained over 2500
+epochs with a learning rate of 0.01. Both these parameters i.e
+number of epochs and learning rate has to be tuned and are done by
+iterating the algorithm multiple times with varying parameter values.
+The algorithm is further asked to make 100 predictions corre-
+sponding to every sample in the test set. Every time it makes the
+prediction, the corresponding prediction probability varies. This is
+due to random sampling of weights and biases from the trained dis-
+tributions. Further, the algorithm considers the "mean" and "standard
+deviation" corresponding to those probabilities to make a decision
+as to proceed with classification or not.
+MNRAS 000, 1–4 (2022)
+
+4
+45°
+31
+15*
+15*
+30*
+45*
+60
+-75"BNN Classifier
+3
+Figure 2. Model Architecture
+AGN
+Stars
+AGN
+1312
+6
+Stars
+31
+986
+Table 3. Confusion Matrix for classified data points
+Class
+Precision
+Recall
+F1 Score
+AGN
+0.99
+0.97
+0.98
+Stars
+0.97
+0.99
+0.98
+Average
+0.98
+0.98
+0.98
+Table 4. Classification report for classified data points
+3 RESULTS AND DISCUSSION
+The proposed algorithm is one of the initial attempts to implement
+"Bayesian Neural Networks" in observational astronomy which
+has shown significant results. The algorithm gives the predictions
+with an accuracy of more than 98% whenever it agrees to make
+predictions for trained classes.
+Table 3 represents confusion matrix of classified data. To calculate
+accuracy, we make use of the given formula.
+Accuracy =
+𝑎11 + 𝑎22
+𝑎11 + 𝑎12 + 𝑎21 + 𝑎22
+× 100
+In our case, the calculated accuracy is
+Accuracy =
+1312 + 986
+1312 + 6 + 31 + 986 × 100 = 98.4%
+As accuracy is not the only measure to evaluate any classification
+model, we further calculate precision, recall and f1 score correspond-
+ing to both the classes as shown in Table 4
+Although, the obtained results from simpler "BNN" can be
+obtained via complex frequentist models, the uniqueness of the
+algorithm is that it agrees to classify only 14% of the unknown
+classes as one of the trained classes as opposed to frequentist
+approaches wherein all those samples are classified as one of these
+classes. Table 5 shows the percentage of data from untrained classes
+Class
+AGN
+Star
+CV
+13.8 %
+0 %
+Pulsars
+2.3 %
+6.3 %
+ULX
+14.9 %
+6.5 %
+LMX
+2 %
+26.5 %
+Total
+9.4 %
+7.8 %
+Table 5. Percentage of misidentified data points
+which are predicted as a Star or a AGN.
+As the algorithm gives significant results on labelled data, we make
+use of it to identify the possible Stars and AGNs in the raw data 2.
+The algorithm almost identifies almost 7.1% of data as AGNs and
+10.04% of data as AGNs. Numerically, the number happens to be
+62807 and 88107 respectively. Although, there’s high probability that
+there exists more Stars and AGNs as compared to the given number
+the algorithm simply refuses to give the prediction as it isn’t enough
+confident with the same.
+4 CONCLUSIONS
+In this study, we propose a Bayesian approach to identify Stars and
+AGNs observed by XMM Newton. The proposed algorithm avoids
+making predictions whenever it is unsure about the predictions. Im-
+plementing such algorithms will help in reducing the number of
+wrong predictions which is one of the major drawbacks of algo-
+rithms making use of the frequentist approach. This is an important
+thing to consider as there always exists a situation wherein the algo-
+rithm receives an input on which it is never trained. The proposed
+algorithm also identifies 62807 Stars and 88107 AGNs in the data
+release 11 by XMM-Newton.
+5 CONFLICT OF INTEREST
+The authors declare that they have no conflict of interest.
+DATA AVAILABILITY
+The raw data used in this study is publicly made available by XMM
+Newton data archive. All the codes corresponding to the algorithm
+and the predicted objects along with the predictions will be publicly
+made available on "Github" and "paperswithcode" by June 2023.
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+MNRAS 000, 1–4 (2022)
+

89AyT4oBgHgl3EQfQ_ZE/content/tmp_files/load_file.txt

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+page_content='MNRAS 000, 1–4 (2022)  Preprint 30 December 2022  Compiled using MNRAS LATEX style file v3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='0  A Bayesian Neural Network Approach to identify Stars and AGNs  observed by XMM Newton ★  Sarvesh Gharat,1† and Bhaskar Bose2  1 Centre for Machine Intelligence and Data Science, Indian Institute of Technology Bombay, 400076, Mumbai, India  2 Smart Mobility Group, Tata Consultancy Services, 560067, Bangalore, India  Accepted XXX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Received YYY;' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' in original form ZZZ  ABSTRACT  In today’s era, a tremendous amount of data is generated by different observatories and manual classification of data is something  which is practically impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Hence, to classify and categorize the objects there are multiple machine and deep learning  techniques used.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' However, these predictions are overconfident and won’t be able to identify if the data actually belongs to the  trained class.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' To solve this major problem of overconfidence, in this study we propose a novel Bayesian Neural Network which  randomly samples weights from a distribution as opposed to the fixed weight vector considered in the frequentist approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The  study involves the classification of Stars and AGNs observed by XMM Newton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' However, for testing purposes, we consider CV,  Pulsars, ULX, and LMX along with Stars and AGNs which the algorithm refuses to predict with higher accuracy as opposed  to the frequentist approaches wherein these objects are predicted as either Stars or AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The proposed algorithm is one of  the first instances wherein the use of Bayesian Neural Networks is done in observational astronomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Additionally, we also make  our algorithm to identify stars and AGNs in the whole XMM-Newton DR11 catalogue.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The algorithm almost identifies 62807  data points as AGNs and 88107 data points as Stars with enough confidence.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' In all other cases, the algorithm refuses to make  predictions due to high uncertainty and hence reduces the error rate.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  Key words: methods: data analysis – methods: observational – methods: miscellaneous  1 INTRODUCTION  Since the last few decades, a large amount of data is regularly  generated by different observatories and surveys.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The classification  of this enormous amount of data by professional astronomers is  time-consuming as well as practically impossible.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' To make the  process simpler, various citizen science projects (Desjardins et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  2021) (Cobb 2021) (Allf et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2022) (Faherty et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2021) are  introduced which has been reducing the required time by some  extent.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' However, there are many instances wherein classifying the  objects won’t be simple and may require domain expertise.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  In this modern era, wherein Machine Learning and Neural Net-  works are widely used in multiple fields, there has been significant  development in the use of these algorithms in Astronomy.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Though  these algorithms are accurate with their predictions there is certainly  some overconfidence (Kristiadi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2020) (Kristiadi et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2021)  associated with it.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Besides that, these algorithms tend to classify  every input as one of the trained classes (Beaumont & Haziza 2022)  irrespective of whether it actually belongs to those trained classes  eg: The algorithm trained to classify stars will also predict AGNs as  one of the stars.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' To solve this major issue, in this study we propose a  Bayesian Neural Network (Jospin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2022) (Charnock et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2022)  ★ Based on observations obtained with XMM-Newton, an ESA science mis-  sion with instruments and contributions directly funded by ESA Member  States and NASA  † E-mail: sarveshgharat19@gmail.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='com  which refuses to make a prediction whenever it isn’t confident about  its predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The proposed algorithm is implemented on the data  collected by XMM-Newton (Jansen et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2001).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' We do a binary  classification to classify Stars and AGNs (Małek et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2013) (Golob  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2021).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Additionally to test our algorithm with the inputs which  don’t belong to the trained class we consider data observed from CV,  Pulsars, ULX, and LMX.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Although, the algorithm doesn’t refuse to  predict all these objects, but the number of objects it predicts for  these 4 classes is way smaller than that of trained classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  For the trained classes, the algorithm gives its predictions for al-  most 64% of the data points and avoids predicting the output when-  ever it is not confident about its predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The achieved accuracy  in this binary classification task whenever the algorithm gives its  prediction is 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='41%.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' On the other hand, only 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='6% of the incor-  rect data points are predicted as one of the classes by the algorithm.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  The percentage decrease from 100% to 14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='6% in the case of different  inputs is what dominates our model over other frequentist algorithms.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  2 METHODOLOGY  In this section, we discuss the methodology used to perform this  study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' This section is divided into the following subsections.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  Data Collection and Feature Extraction  Model Architecture  Training and Testing  © 2022 The Authors  2  S.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Gharat et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  Class  Catalogue  AGN  VERONCAT (Véron-Cetty & Véron 2010)  LMX  NGC3115CXO (Lin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2015)  RITTERLMXB (Ritter & Kolb 2003)  LMXBCAT (Liu et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2007)  INTREFCAT (Ebisawa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2003)  M31XMMXRAY (Stiele et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2008)  M31CFCXO (Hofmann et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2013)  RASS2MASS (Haakonsen & Rutledge 2009)  Pulsars  ATNF (Manchester et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2005)  FERMIL2PSR (Abdo et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2013)  CV  CVC (Drake et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2014)  ULX  XSEG (Drake et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2014)  Stars  CSSC (Skiff 2014)  Table 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Catalogues used to create labeled data  Class  Training Data  Test Data  AGN  8295  2040  LMX  0  49  Pulsars  0  174  CV  0  36  ULX  0  261  Stars  6649  1628  Total  14944  4188  Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Data distribution after cross-matching all the data points with cata-  logs mentioned in Table 1  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='1 Data Collection and Feature Extraction  In this study, we make use of data provided in "XMM-DR11 SEDs"  Webb et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' (2020).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' We further cross-match the collected data with  different vizier (Ochsenbein et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2000) catalogs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Please refer to  Table 1 to view all the catalogs used in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' As the proposed  algorithm is a "supervised Bayesian algorithm", this happens to be  one of the important steps for our algorithm to work.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  The provided data has 336 different features that can increase  computational complexity by a larger extent and also has a lot of  missing data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Therefore in this study, we consider a set of  18 features corresponding to the observed source.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The considered  features for all the sources are available on our Github repository,  more information of which is available on the official webpage 1 of  the observatory.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' After cross-matching and reducing the number of  features, we were left with a total of 19136 data points.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The data  distribution can be seen in Table 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' We further also plot the sources  (Refer Figure1) based on their "Ra" and "Dec" to confirm if the  data coverage of the considered sources matches with the actual data  covered by the telescope.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  1 http://xmmssc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='irap.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='omp.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='eu/Catalogue/4XMM-DR11/col_unsrc.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  html  Figure 1.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Sky map coverage of considered data points  The collected data is further classified into train and test according  to the 80 : 20 splitting condition.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The exact number of data points is  mentioned in Table 2  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='2 Model Architecture  The proposed model has 1 input, hidden and output layers (refer  Figure 2) with 18, 512, and 2 neurons respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The reason for  having 18 neurons in the input layer is the number of input features  considered in this study.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Further, to increase the non-linearity of the  output, we make use of "Relu" (Fukushima 1975) (Agarap 2018) as  an activation function for the first 2 layers.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' On the other hand, the  output layer makes use of "Softmax" to make the predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' This  is done so that the output of the model will be the probability of  image belonging to a particular class (Nwankpa et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2018) (Feng  & Lu 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  The "optimizer" and "loss" used in this study are "Adam" (Kingma  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2020) and "Trace Elbo" (Wingate & Weber 2013) (Ranganath  et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2014) respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The overall idea of BNN (Izmailov et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  2021) (Jospin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2022) (Goan & Fookes 2020) is to have a pos-  terior distribution corresponding to all weights and biases such that,  the output distribution produced by these posterior distributions is  similar to that of the categorical distributions defined in the training  dataset.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Hence, convergence, in this case, can be achieved by min-  imizing the KL divergence between the output and the categorical  distribution or just by maximizing the ELBO (Wingate & Weber  2013) (Ranganath et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2014).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' We make use of normal distributions  which are initialized with random mean and variance as prior (For-  tuin et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2021), along with the likelihood derived from the data to  construct the posterior distribution.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='3 Training and Testing  The proposed model is constructed using Pytorch (Paszke et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  2019) and Pyro (Bingham et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2019).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The training of the model  is conducted on Google Colaboratory, making use of NVIDIA  K80 GPU (Carneiro et al.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' 2018).' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The model is trained over 2500  epochs with a learning rate of 0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='01.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Both these parameters i.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='e  number of epochs and learning rate has to be tuned and are done by  iterating the algorithm multiple times with varying parameter values.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  The algorithm is further asked to make 100 predictions corre-  sponding to every sample in the test set.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Every time it makes the  prediction, the corresponding prediction probability varies.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' This is  due to random sampling of weights and biases from the trained dis-  tributions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Further, the algorithm considers the "mean" and "standard  deviation" corresponding to those probabilities to make a decision  as to proceed with classification or not.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  MNRAS 000, 1–4 (2022)  4  45°  31  15*  15*  30*  45*  60  75"BNN Classifier  3  Figure 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Model Architecture  AGN  Stars  AGN  1312  6  Stars  31  986  Table 3.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Confusion Matrix for classified data points  Class  Precision  Recall  F1 Score  AGN  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='97  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='98  Stars  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='97  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='99  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='98  Average  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='98  0.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='98  Table 4.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Classification report for classified data points  3 RESULTS AND DISCUSSION  The proposed algorithm is one of the initial attempts to implement  "Bayesian Neural Networks" in observational astronomy which  has shown significant results.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The algorithm gives the predictions  with an accuracy of more than 98% whenever it agrees to make  predictions for trained classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  Table 3 represents confusion matrix of classified data.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' To calculate  accuracy, we make use of the given formula.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  Accuracy =  𝑎11 + 𝑎22  𝑎11 + 𝑎12 + 𝑎21 + 𝑎22  × 100  In our case, the calculated accuracy is  Accuracy =  1312 + 986  1312 + 6 + 31 + 986 × 100 = 98.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='4%  As accuracy is not the only measure to evaluate any classification  model,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' we further calculate precision,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' recall and f1 score correspond-  ing to both the classes as shown in Table 4  Although,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' the obtained results from simpler "BNN" can be  obtained via complex frequentist models,' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' the uniqueness of the  algorithm is that it agrees to classify only 14% of the unknown  classes as one of the trained classes as opposed to frequentist  approaches wherein all those samples are classified as one of these  classes.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Table 5 shows the percentage of data from untrained classes  Class  AGN  Star  CV  13.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='8 %  0 %  Pulsars  2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='3 %  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='3 %  ULX  14.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='9 %  6.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='5 %  LMX  2 %  26.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='5 %  Total  9.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='4 %  7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='8 %  Table 5.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Percentage of misidentified data points  which are predicted as a Star or a AGN.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  As the algorithm gives significant results on labelled data, we make  use of it to identify the possible Stars and AGNs in the raw data 2.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  The algorithm almost identifies almost 7.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='1% of data as AGNs and  10.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='04% of data as AGNs.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Numerically, the number happens to be  62807 and 88107 respectively.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Although, there’s high probability that  there exists more Stars and AGNs as compared to the given number  the algorithm simply refuses to give the prediction as it isn’t enough  confident with the same.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  4 CONCLUSIONS  In this study, we propose a Bayesian approach to identify Stars and  AGNs observed by XMM Newton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The proposed algorithm avoids  making predictions whenever it is unsure about the predictions.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' Im-  plementing such algorithms will help in reducing the number of  wrong predictions which is one of the major drawbacks of algo-  rithms making use of the frequentist approach.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' This is an important  thing to consider as there always exists a situation wherein the algo-  rithm receives an input on which it is never trained.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' The proposed  algorithm also identifies 62807 Stars and 88107 AGNs in the data  release 11 by XMM-Newton.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  5 CONFLICT OF INTEREST  The authors declare that they have no conflict of interest.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content='  DATA AVAILABILITY  The raw data used in this study is publicly made available by XMM  Newton data archive.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
+page_content=' All the codes corresponding to the algorithm  and the predicted objects along with the predictions will be publicly  made available on "Github" and "paperswithcode" by June 2023.' metadata={'source': '/home/zjlab/wf/langchain-ChatGLM/knowledge_base/89AyT4oBgHgl3EQfQ_ZE/content/2301.00056v1.pdf'}
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+A Simple Algorithm For Scaling Up Kernel Methods
+Teng Andrea Xu†, Bryan Kelly‡, and Semyon Malamud†
+†Swiss Finance Institute, EPFL
+andrea.xu,[email protected]
+‡Yale School of Management, Yale University
+[email protected]
+Abstract
+The recent discovery of the equivalence between infinitely wide neural networks
+(NNs) in the lazy training regime and Neural Tangent Kernels (NTKs) Jacot et al.
+[2018] has revived interest in kernel methods. However, conventional wisdom suggests
+kernel methods are unsuitable for large samples due to their computational complexity
+and memory requirements. We introduce a novel random feature regression algorithm
+that allows us (when necessary) to scale to virtually infinite numbers of random fea-
+tures. We illustrate the performance of our method on the CIFAR-10 dataset.
+arXiv:2301.11414v1  [cs.LG]  26 Jan 2023
+
+1
+Introduction
+Modern neural networks operate in the over-parametrized regime, which sometimes requires
+orders of magnitude more parameters than training data points. Effectively, they are interpo-
+lators (see, Belkin [2021]) and overfit the data in the training sample, with no consequences
+for the out-of-sample performance. This seemingly counterintuitive phenomenon is some-
+times called “benign overfit” [Bartlett et al., 2020, Tsigler and Bartlett, 2020].
+In the so-called lazy training regime Chizat et al. [2019], wide neural networks (many
+nodes in each layer) are effectively kernel regressions, and “early stopping” commonly used
+in neural network training is closely related to ridge regularization [Ali et al., 2019]. See,
+Jacot et al. [2018], Hastie et al. [2019], Du et al. [2018, 2019a], Allen-Zhu et al. [2019]. Recent
+research also emphasizes the “double descent,” in which expected forecast error drops in the
+high-complexity regime. See, for example, Zhang et al. [2016], Belkin et al. [2019a,b], Spigler
+et al. [2019], Belkin et al. [2020].
+These discoveries made many researchers argue that we need to gain a deeper under-
+standing of kernel methods (and, hence, random feature regressions) and their link to deep
+learning. See, e.g., Belkin et al. [2018]. Several recent papers have developed numerical
+algorithms for scaling kernel-type methods to large datasets and large numbers of random
+features. See, e.g., Zandieh et al. [2021], Ma and Belkin [2017], Arora et al. [2019a], Shankar
+et al. [2020]. In particular, Arora et al. [2019b] show how NTK combined with the support
+vector machines (SVM) (see also Fern´andez-Delgado et al. [2014]) perform well on small
+data tasks relative to many competitors, including the highly over-parametrized ResNet-34.
+In particular, while modern deep neural networks do generalize on small datasets (see, e.g.,
+Olson et al. [2018]), Arora et al. [2019b] show that kernel-based methods achieve superior
+performance in such small data environments. Similarly, Du et al. [2019b] find that the graph
+neural tangent kernel (GNTK) dominates graph neural networks on datasets with up to 5000
+2
+
+samples. Shankar et al. [2020] show that, while NTK is a powerful kernel, it is possible to
+build other classes of kernels (they call Neural Kernels) that are even more powerful and are
+often at par with extremely complex deep neural networks.
+In this paper, we develop a novel form of kernel ridge regression that can be applied to
+any kernel and any way of generating random features. We use a doubly stochastic method
+similar to that in Dai et al. [2014], with an important caveat: We generate (potentially large,
+defined by the RAM constraints) batches of random features and then use linear algebraic
+properties of covariance matrices to recursively update the eigenvalue decomposition of the
+feature covariance matrix, allowing us to perform the optimization in one shot across a large
+grid of ridge parameters.
+The paper is organized as follows. Section 2 discusses related work. In Section 3, we
+provide a novel random feature regression mathematical formulation and algorithm. Then,
+Section 4 and Section 5 present numerical results and conclusions, respectively.
+2
+Related Work
+Before the formal introduction of the NTK in Jacot et al. [2018], numerous papers discussed
+the intriguing connections between infinitely wide neural networks and kernel methods. See,
+e.g., Neal [1996]; Williams [1997]; Le Roux and Bengio [2007]; Hazan and Jaakkola [2015];
+Lee et al. [2018]; Matthews et al. [2018]; Novak et al. [2018]; Garriga-Alonso et al. [2018];
+Cho and Saul [2009]; Daniely et al. [2016]; Daniely [2017].
+As in the standard random
+feature approximation of the kernel ridge regression (see Rahimi and Recht [2007]), only the
+network’s last layer is trained in the standard kernel ridge regression. A surprising discovery
+of Jacot et al. [2018] is that (infinitely) wide neural networks in the lazy training regime
+converge to a kernel even though all network layers are trained. The corresponding kernel,
+the NTK, has a complex structure dependent on the neural network’s architecture. See also
+Lee et al. [2019], Arora et al. [2019a] for more results about the link between NTK and the
+3
+
+underlying neural network, and Novak et al. [2019] for an efficient algorithm for implementing
+the NTK. In a recent paper, Shankar et al. [2020] introduce a new class of kernels and show
+that they perform remarkably well on even very large datasets, achieving a 90% accuracy on
+the CIFAR-10 dataset. While this performance is striking, it comes at a huge computational
+cost. Shankar et al. [2020] write:
+“CIFAR-10/CIFAR-100 consist of 60, 000 32 × 32 × 3 images and MNIST consists of
+70, 000 28 × 28 images. Even with this constraint, the largest compositional kernel matrices
+we study took approximately 1000 GPU hours to compute. Thus, we believe an imperative
+direction of future work is reducing the complexity of each kernel evaluation. Random feature
+methods or other compression schemes could play a significant role here.
+In this paper, we offer one such highly scalable scheme based on random features. How-
+ever, computing the random features underlying the Neural Kernels of Shankar et al. [2020]
+would require developing non-trivial numerical algorithms based on the recursive iteration
+of non-linear functions. We leave this as an important direction for future research.
+As in standard kernel ridge regressions, we train our random feature regression on the
+full sample. This is a key computational limitation for large datasets. After all, one of
+the reasons for the success of modern deep learning is the possibility of training them us-
+ing stochastic gradient descent on mini-batches of data. Ma and Belkin [2017] shows how
+mini-batch training can be applied to kernel ridge regression.
+A key technical difficulty
+arises because kernel matrices (equivalently, covariance matrices of random features) have
+eigenvalues that decay very quickly. Yet, these low eigenvalues contain essential informa-
+tion and cannot be neglected. Our regression method can be easily modified to allow for
+mini-batches. Furthermore, it is known that mini-batch linear regression can even lead to
+performance gains in the high-complexity regime. As LeJeune et al. [2020] show, one can run
+regression on mini-batches and then treat the obtained predictions as an ensemble. LeJeune
+et al. [2020] prove that, under technical conditions, the average of these predictions attains
+4
+
+a lower generalization error than the full-train-sample-based regression. We test this mini-
+batch ensemble approach using our method and show that, indeed, with moderately-sized
+mini-batches, the method’s performance matches that of the full sample regression.
+Moreover, there is an intriguing connection between mini-batch regressions and spectral
+dimensionality reduction. By construction, the feature covariance matrix with a mini-batch
+of size B has at most B non-zero eigenvalues.
+Thus, a mini-batch effectively performs
+a dimensionality reduction on the covariance matrix. Intuitively, we expect that the two
+methods (using a mini-batch of size B or using the full sample but only keeping B largest
+eigenvalues) should achieve comparable performance. We show that this is indeed the case
+for small sample sizes. However, the spectral method for larger-sized samples (N ≥ 10000)
+is superior to the mini-batch method unless we use very large mini-batches. For example,
+on the full CIFAR-10 dataset, the spectral method outperforms the mini-batch approach by
+3% (see Section 4 for details).
+3
+Random Features Ridge Regression and Classifica-
+tion
+Suppose that we have a train sample (X, y)
+=
+(xi, yi)N
+i=1, xi ∈ Rd, yi ∈ R, so that
+X ∈ RN×d, y ∈ RN×1. Following Rahimi and Recht [2007] we construct a large number of
+random features f(x; θp), p = 1, . . . , P, where f is a non-linear function and θp are sampled
+from some distribution, and P is a large number.
+We denote S = f(X; θ) ∈ RN×P as
+the train sample realizations of random features. Following Rahimi and Recht [2007], we
+consider the random features ridge regression,
+β(z) = (S⊤S/N + zI)−1S⊤y/N ,
+(1)
+5
+
+as an approximation for kernel ridge regression when P → ∞. For classification problems,
+it is common to use categorical cross-entropy as the objective. However, as Belkin [2021]
+explains, minimizing the mean-squared error with one-hot encoding often achieves superior
+generalization performance. Here, we follow this approach. Given the K labels, k = 1, . . . , K,
+we build the one-hot encoding matrix Q = (qi,k) where qi,k = 1yi=k. Then, we get
+β(z) = (S⊤S/N + zI)−1S⊤Q/N ∈ RP×K .
+(2)
+Then, for each test feature vector s = f(x; θ) ∈ RP, we get a vector β(z)⊤s ∈ RK. Next,
+define the actual classifier as
+k(x; z) = arg max{β(z)⊤s} ∈ {1, · · · , K} .
+(3)
+3.1
+Dealing with High-Dimensional Features
+A key computational (hardware) limitation of kernel methods comes from the fact that,
+when P is large, computing the matrix S⊤S ∈ RP×P becomes prohibitively expensive, in
+particular, because S cannot even be stored in RAM. We start with a simple observation
+that the following identity implies that storing all these features is not necessary:1
+(S⊤S/N + zI)−1S⊤ = S⊤(SS⊤/N + zI)−1 ,
+(4)
+and therefore we can compute β(z) as
+β(z) = S⊤(SS⊤/N + zI)−1y/N .
+(5)
+Suppose now we split S into multiple blocks, S1, . . . , SK, where Sk ∈ RN×P1 for all
+1This identity follows directly from (S⊤S/N + zI)S⊤ = S⊤(SS⊤/N + zI).
+6
+
+k = 1, . . . , K, for some small P1, with KP1 = P. Then,
+Ψ = SS⊤ =
+K
+�
+k=1
+SkS⊤
+k
+(6)
+can be computed by generating the blocks Sk, one at a time, and recursively adding SkS⊤
+k up.
+Once Ψ has been computed, one can calculate its eigenvalue decomposition, Ψ = V DV ⊤,
+and then evaluate Q(z) = (Ψ/N + zI)−1y/N
+= V (D + zI)−1V ⊤y/N ∈ RN in one go for
+a grid of z. Then, using the same seeds, we can again generate the random features Sk and
+compute βk(z) = S⊤
+k Q(z) ∈ RP1. Then, β(z) = (βk(z))K
+k=1 ∈ RP . The logic described above
+is formalized in Algorithm 1.
+Algorithm 1 FABR
+Require: P1, P, X ∈ RN×d, y ∈ RN, z, voc curve
+blocks ← P//P1
+k ← 0
+Ψ ← 0N×N
+while k < blocks do
+Generate Sk ∈ RN×P1 Use k as seed
+Ψ ← Ψ + SkSk⊤
+if k in voc curve then
+DV ← eigen( Ψ
+N )
+Qk(z) ← V (D + zI)−1V ⊤ y
+N
+▷ Store Qk(z)
+end if
+k = k + 1
+end while
+DV ← eigen( Ψ
+N )
+Q(z) ← V (D + zI)−1V ⊤ y
+N
+k ← 0
+while k < blocks do
+(re-)Generate Sk ∈ RN×P1
+▷ Use k as seed
+βk(z) ← S⊤
+k Q(z)
+ˆy += Skβk
+end while
+7
+
+3.2
+Dealing with Massive Datasets
+The above algorithm relies crucially on the assumption that N is small. Suppose now that
+the sample size N is so large that storing and eigen-decomposing the matrix SS⊤ ∈ RN×N
+becomes prohibitively expensive. In this case, we proceed as follows.
+Define for all k = 1, . . . , K
+Ψk =
+k
+�
+κ=1
+SkS⊤
+k ∈ RN×N, Ψ0 = 0N×N ,
+(7)
+and let λ1(A) ≥ · · · ≥ λN(A) be the eigenvalues of a symmetric matrix A ∈ RN×N. Our
+goal is to design an approximation to (ΨK + zI)−1, based on a simple observation that the
+eigenvalues of the empirically observed Ψk matrices tend to decay very quickly, with only
+a few hundreds of largest eigenvalues being significantly different from zero. In this case,
+we can fix a ν ∈ N and design a simple, rank−ν approximation to ΨK by annihilating all
+eigenvalues below λν(ΨK). As we now show, it is possible to design a recursive algorithm for
+constructing such an approximation to ΨK, dealing with small subsets of random features
+simultaneously. To this end, we proceed as follows.
+Suppose we have constructed an approximation ˆΨk ∈ RN×N to Ψk with rank ν, and
+let Vk ∈ RN×ν be the corresponding matrix of orthogonal eigenvectors for the non-zero
+eigenvalues, and Dk ∈ Rν×ν the diagonal matrix of eigenvalues so that ˆΨk = VkDkV ⊤
+k
+and
+V ⊤
+k Vk = Iν×ν. Instead of storing the full ˆΨk matrix, we only need to store the pair (Vk, Dk).
+For all k = 1, . . . , K, we now define
+˜Ψk+1 = ˆΨk + Sk+1S⊤
+k+1 .
+(8)
+This N × N matrix is a theoretical construct. We never actually compute it (see Algorithm
+8
+
+2). Let Θk = I − VkV ⊤
+k be the orthogonal projection on the kernel of ˆΨk, and
+˜Sk+1 = ΘkSk+1 = Sk+1 − Vk
+����
+N×ν
+(V ⊤
+k Sk+1
+� �� �
+ν×P1
+)
+(9)
+be Sk+1 orthogonalized with respect to the columns of Vk. Then, we define ˜Wk+1 = ˜Sk+1( ˜Sk+1 ˜S⊤
+k+1)−1/2
+to be the orthogonalized columns of ˜Sk+1, and ˆVk+1 = [Vk, ˜Wk+1]. To compute ˜Sk+1( ˜Sk+1 ˜S⊤
+k+1)−1/2,
+we use the following lemma that, once again, uses smart eigenvalue decomposition techniques
+to avoid dealing with the N × N matrix ˜Sk+1 ˜S⊤
+k+1.
+Lemma 1. Let ˜S⊤
+k+1 ˜Sk+1
+�
+��
+�
+ν×ν
+= Wδ ˜W ⊤ be the eigenvalue decomposition of ˜S⊤
+k+1 ˜Sk+1. Then,
+˜W = ˜Sk+1Wδ−1/2 is the matrix of eigenvectors of ˜Sk+1 ˜S⊤
+k+1 for the non-zero eigenvalues.
+Thus,
+˜Sk+1( ˜Sk+1 ˜S⊤
+k+1)−1/2 =
+˜Wk+1 .
+(10)
+By construction, the columns of ˆVk+1 form an orthogonal basis of the span of the columns
+of Vk, Sk+1, and hence
+Ψk+1,∗ = ˆV ⊤
+k+1 ˜Ψk+1 ˆVk+1 ∈ R(P1+ν)×(P1+ν)
+(11)
+has the same non-zero eigenvalues as ˜Ψk+1. We then define ˜Vk+1 ∈ R(P1+ν)×ν to be the
+matrix with eigenvectors of Ψk+1,∗ for the largest ν eigenvalues, and we denote the diagonal
+matrix of these eigenvalues by Dk+1 ∈ Rν×ν, and then we define Vk+1 =
+ˆVk+1 ˜Vk+1 . Then,
+ˆΨk+1
+=
+Vk+1Dk+1Vk+1
+=
+Πk+1 ˜Ψk+1Πk+1 , where Πk+1
+=
+ˆVk+1 ˜Vk+1 ˜V ⊤
+k+1 ˆV ⊤
+k+1 is the
+orthogonal projection onto the eigen-subspace of ˜Ψk+1 for the largest ν eigenvalues.
+Lemma 2. We have ˆΨk ≤ ˜Ψk ≤ ΨK and
+∥Ψk − ˆΨk∥ ≤
+k
+�
+i=1
+λν+1(Ψi) ≤ k λν+1(ΨK) ,
+(12)
+9
+
+and
+∥(Ψk+1 + zI)−1 − (ˆΨk+1 + zI)−1∥ ≤ z−2
+k
+�
+i=1
+λν+1(Ψi) .
+(13)
+There is another important aspect of our algorithm: It allows us to directly compute
+the performance of models with an expanding level of complexity. Indeed, since we load
+random features in batches of size P1, we generate predictions for P ∈ [P1, 2P1, · · · , KP1].
+This is useful because we might use it to calibrate the optimal degree of complexity and
+because we can directly study the double descent-like phenomena, see, e.g., Belkin et al.
+[2019a] and Nakkiran et al. [2021]. That is the effect of complexity on the generalization
+error. In the next section, we do this. As we show, consistent with recent theoretical results
+Kelly et al. [2022], with sufficient shrinkage, the double descent curve disappears, and the
+performance becomes almost monotonic in complexity. Following Kelly et al. [2022], we
+name this phenomenon the virtue of complexity (VoC) and the corresponding performance
+plots the VoC curves. See, Figure 6 below.
+We call this algorithm Fast Annihilating Batch Regression (FABR) as it annihilates all
+eigenvalues below λν(ΨK) and allows to solve the random features ridge regression in one go
+for a grid of z. Algorithm 2 formalizes the logic described above.
+4
+Numerical Results
+This section presents several experimental results on different datasets to evaluate FABR’s
+performance and applications. In contrast to the most recent computational power demand
+in kernel methods, e.g., Shankar et al. [2020], we ran all experiments on a laptop, a MacBook
+Pro model A2485, equipped with an M1 Max with a 10-core CPU and 32 GB RAM.
+10
+
+Algorithm 2 FABR-ν
+Require: ν, P1, P, X ∈ RN×d, y ∈ RN, z, voc curve
+blocks ← P//P1
+k ← 0
+while k < blocks do
+Generate Sk ∈ RN×P1
+▷ Use k as seed to generate the random features
+if k = 0 then
+˜d, ˜V ← eigen(S⊤
+k Sk)
+V ← Sk ˜V diag( ˜d)− 1
+2
+V0 ← V:,min(ν,P1)
+▷ Save V0
+d0 ← ˜d:min(ν,P1)
+▷ Save d0
+if k in voc curve then
+Q0(z) ← V0(diag(d0) + zI)−1V ⊤
+0 y
+▷ Save Q0(z)
+end if
+else if k > 0 then
+˜Sk ← (I − Vk−1V ⊤
+k−1)Sk
+Γk ← ˜
+S⊤
+k ˜Sk
+δk, Wk ← eigen(Γk)
+Keep top min(ν, P1) eigenvalues and eigenvectors from δk, Wk
+˜
+Wk ← ˜SkWkdiag(δk)− 1
+2
+ˆVk ← [Vk−1, ˜
+Wk]
+¯Vk ← ˆ
+V ⊤
+k Vk−1
+¯
+Wk ← ¯Vkdiag(dk−1) ¯
+V ⊤
+k
+¯Sk ← ˆ
+V ⊤
+k Sk
+¯Zk ← ¯SkS⊤
+k
+Ψ∗ ← ¯
+Wk ¯Zk
+dk, Vk ← eigen(Ψ∗)
+Keep top min(ν, P1) eigenvalues and eigenvectors from dk, Vk
+Vk ← ˆVkVk
+▷ Save dk, Vk
+if k in voc curve then
+Qk(z) ← Vk(diag(dk) + zI)−1V ⊤
+k y
+▷ Save Qk(z)
+end if
+end if
+k = k + 1
+end while
+k ← 0
+while k < blocks do
+(re-)Generate Sk ∈ RN×P1
+▷ Use k as seed to generate the random features
+βk(z) ← S⊤
+k Qk(z)
+ˆy += Skβk
+end while
+11
+
+4.1
+A comparison with sklearn
+We now aim to show FABR’s training and prediction time with respect to the number of
+features d. To this end, we do not use any random feature projection or the rank-ν matrix
+approximation described in Section 3.1. We draw N = 5000 i.i.d. samples from ⊗d
+j=1N(0, 1)
+and let
+yi = xiβ + ϵi
+∀i = 1, . . . , N,
+where β ∼ ⊗d
+j=1N(0, 1), and ϵi ∼ N(0, 1) for all i = 1, . . . , N. Then, we define
+yi =
+�
+�
+�
+�
+�
+�
+�
+1
+if yi > median(y),
+0
+otherwise
+∀i = 1, . . . , N.
+Next, we create a set of datasets for classification with varying complexity d and keep the
+first 4000 samples as the training set and the remaining 1000 as the test set. We show in
+Figure 1 the average training and prediction time (in seconds) of FABR with a different
+number of regularizers ( we denote this number by |z|) and sklearn RidgeClassifier with
+an increasing number of features d. The training and prediction time is averaged over five
+independent runs. As one can see, our method is drastically faster when d > 10000. E.g., for
+d = 100000 we outperform sklearn by approximately 5 and 25 times for |z| = 5 and |z| = 50,
+respectively. Moreover, one can notice that the number of different shrinkages |z| does not
+affect FABR. We report a more detailed table with average training and prediction time and
+standard deviation in Appendix B.
+4.2
+Experiments on Real Datasets
+We assess FABR’s performance on both small and big datasets regimes for further evaluation.
+For all experiments, we perform a random features kernel ridge regression for demeaned one-
+12
+
+0
+20000
+40000
+60000
+80000 100000
+d
+0
+200
+400
+600
+800
+Training and Prediction Time (s)
+FABR - |z| = 5
+FABR - |z| = 10
+FABR - |z| = 20
+FABR - |z| = 50
+sklearn - |z| = 5
+sklearn - |z| = 10
+sklearn - |z| = 20
+sklearn - |z| = 50
+Figure 1: The figure above compares FABR training and prediction time, shown on the y-
+axis, in black, against sklearn’s RidgeClassifier, in red, for an increasing amount of features,
+shown on the x-axis, and the number of shrinkages z.
+Here, |z| denotes the number of
+different values of z for which we perform the training.
+hot labels and solve the optimization problem using FABR as described in Section 3.
+4.2.1
+Data Representation
+Table 1: The table below shows the average test accuracy and standard deviation of
+ResNet-34, CNTK, and FABR on the subsampled CIFAR-10 datasets. The test accuracy is
+average over twenty independent runs.
+n
+ResNet-34
+14-layer CNTK
+z=1
+z=100
+z=10000
+z=100000
+10
+14.59% ± 1.99%
+15.33% ± 2.43%
+18.50% ± 2.18%
+18.50% ± 2.18%
+18.42% ± 2.13%
+18.13% ± 2.01%
+20
+17.50% ± 2.47%
+18.79% ± 2.13%
+20.84% ± 2.38%
+20.85% ± 2.38%
+20.78% ± 2.35%
+20.13% ± 2.34%
+40
+19.52% ± 1.39%
+21.34% ± 1.91%
+25.09% ± 1.76%
+25.10% ± 1.76%
+25.14% ± 1.75%
+24.41% ± 1.88%
+80
+23.32% ± 1.61%
+25.48% ± 1.91%
+29.61% ± 1.35%
+29.60% ± 1.35%
+29.62% ± 1.39%
+28.63% ± 1.66%
+160
+28.30% ± 1.38%
+30.48% ± 1.17%
+34.86% ± 1.12%
+34.87% ± 1.12%
+35.02% ± 1.11%
+33.54% ± 1.24%
+320
+33.15% ± 1.20%
+36.57% ± 0.88%
+40.46% ± 0.73%
+40.47% ± 0.73%
+40.66% ± 0.72%
+39.34% ± 0.72%
+640
+41.66% ± 1.09%
+42.63% ± 0.68%
+45.68% ± 0.71%
+45.68% ± 0.72%
+46.17% ± 0.68%
+44.91% ± 0.72%
+1280
+49.14% ± 1.31%
+48.86% ± 0.68%
+50.30% ± 0.57%
+50.32% ± 0.56%
+51.05% ± 0.54%
+49.74% ± 0.42%
+FABR requires, like any standard kernel methods or randomized-feature techniques, a
+good data representation. Usually, we don’t know such a representation a-priori, and learning
+a good kernel is outside the scope of this paper. Therefore, we build a simple Convolutional
+Neural Network (CNN) mapping h : Rd → RD; that extracts image features ˜x ∈ RD for
+some sample x ∈ Rd. The CNN is not optimized; we use it as a simple random feature
+mapping. The CNN architecture, shown in Fig. 2, alternates a 3 × 3 convolution layer with
+13
+
+GlobalAveragePool
+3x3 Convolution
+ReLU
+2x2 Average Pool
+BatchNormalization
+3x3 Convolution
+ReLU
+2x2 Average Pool
+BatchNormalization
+3x3 Convolution
+ReLU
+2x2 Average Pool
+BatchNormalization
+3x3 Convolution
+ReLU
+2x2 Average Pool
+BatchNormalization
+Figure 2: CNN architecture used to extract image features.
+a ReLU activation function, a 2 × 2 Average Pool, and a BatchNormalization layer Ioffe
+and Szegedy [2015]. Convolutional layers weights are initialized using He Uniform He et al.
+[2015]. To vectorize images, we use a global average pooling layer that has proven to enforce
+correspondences between feature maps and to be more robust to spatial translations of the
+input Lin et al. [2013]. We finally obtain the train and test random features realizations
+s = f(˜x, θ). Specifically, we use the following random features mapping
+si = σ(W ˜x),
+(14)
+where W ∈ RP×D with wi,j ∼ N(0, 1) and σ is some elementwise activation function. This
+14
+
+can be described as a one-layer neural network with random weights W.
+To show the
+importance of over-parametrized models, throughout the results, we report the complexity,
+c, of the model as c = P/N, that is, the ratio between the parameters (dimensions) and the
+number of observations. See Belkin et al. [2019a], Hastie et al. [2019], Kelly et al. [2022].
+4.2.2
+Small Datasets
+We now study the performance of FABR on the subsampled CIFAR-10 dataset Krizhevsky
+et al. [2009].
+To this end, we reproduce the same experiment described in Arora et al.
+[2019b]. In particular, we obtain random subsampled training set (y; X) = (yi; xi)n
+i=1 where
+n ∈ {10, 20, 40, 80, 160, 320, 640, 1280} and test on the whole test set of size 10000. We make
+sure that exactly n/10 sample from each image class is in the training sample. We train
+FABR using random features projection of the subsampled training set
+S = σ(Wg(X)) ∈ Rn×P,
+where g is an untrained CNN from Figure 2, randomly initialized using He Uniform distri-
+bution. In this experiment, we push the model complexity c to 100; in other words, FABR’s
+number of parameters equals a hundred times the number of observations in the subsample.
+As n is small, we deliberately do not perform any low-rank covariance matrix approximation.
+Finally, we run our model twenty times and report the mean out-of-sample performance and
+the standard deviation. We report in Table 1 FABR’s performance for different shrinkages
+(z) together with ResNet-34 and the 14-layers CNTK. Without any complicated random fea-
+ture projection, FABR can outperform both ResNet-34 and CNTK. FABR’s test accuracy
+increases with the model’s complexity c on different (n) subsampled CIFAR-10 datasets. We
+show Figure 3 as an example for n = 10. Additionally, we show, to better observe the double
+descent phenomena, truncated curves at c = 25 for all CIFAR-10 subsamples in Figure 4.
+The full curves are shown in Appendix B. To sum up this section findings:
+15
+
+Figure 3: The figures above show FABR’s test accuracy increases with the model’s complexity
+c on the subsampled CIFAR-10 dataset for n = 10. The test accuracy is averaged over five
+independent runs.
+• FABR, with enough complexity together and a simple random feature projection, is
+able to outperform deep neural networks (ResNet-34) and CNTKs.
+• FABR always reaches the maximum accuracy beyond the interpolation threshold.
+• Moreover, if the random feature ridge regression shrinkage z is sufficiently high, the
+double descent phenomenon disappears, and the accuracy does not drop at the inter-
+polation threshold point, i.e., when c = 1 or n = P. Following Kelly et al. [2022], we
+call this phenomenon virtue of complexity (VoC).
+4.2.3
+Big Datasets
+In this section, we repeat the same experiments described in Section 4.2.2, but we extend
+the training set size n up to the full CIFAR-10 dataset. For each n, we train FABR, FABR-ν
+with a rank-ν approximation as described in Algorithm 2, and the min-batch-FABR. We
+use ν = 2000 and batch size = 2000 in the last two algorithms. Following Arora et al.
+[2019b], we train ResNet-34 as the benchmark for 160 epochs, with an initial learning rate
+of 0.001 and a batch size of 32. We decrease the learning rate by ten at epochs 80 and 120.
+ResNet-34 always reaches close to perfect accuracy on the training set, i.e., above 99%. We
+16
+
+0.18
+0.16
+(%)
+Z = 10-5
+Accuracy
+z= 10-1
+0.14
+Z= 100
+z= 101
+0.12
+z= 102
+z= 103
+z= 104
+0.10
+Z= 105
+0
+20
+40
+60
+80
+100
+c(a) n = 10
+(b) n = 20
+(c) n = 40
+(d) n = 80
+(e) n = 160
+(f) n = 320
+(g) n = 640
+(h) n = 1280
+Figure 4: The figures above show FABR’s test accuracy increases with the model’s complexity
+c on different (n) subsampled CIFAR-10 datasets. The expanded dataset follows similar
+patterns. We truncate the curve for c > 25 to better show the double descent phenomena.
+The full curves are shown in Appendix B. Notice that when the shrinkage is sufficiently
+high, the double descent disappears, and the accuracy monotonically increases in complexity.
+Following Kelly et al. [2022], we name this phenomenon the virtue of complexity (VoC). The
+test accuracy is averaged over 20 independent runs.
+run each training five times and report mean out-of-sample performance and its standard
+deviation. As the training sample is sufficiently large already, we set the model complexity
+to only c = 15, meaning that for the full sample, FABR performs a random feature ridge
+regression with P = 7.5 × 105. We report the results in Tables 4.2.3 and 3.
+Table 2: The table below shows the average test accuracy and standard deviation of ResNet-
+34 and FABR on the subsampled and full CIFAR-10 dataset. The test accuracy is average
+over five independent runs.
+n
+ResNet-34
+z=1
+z=100
+z=10000
+z=100000
+2560
+48.12% ± 0.69%
+52.24% ± 0.29%
+52.45% ± 0.21%
+54.29% ± 0.44%
+48.28% ± 0.37%
+5120
+56.03% ± 0.82%
+55.34% ± 0.32%
+55.74% ± 0.34%
+58.29% ± 0.20%
+52.06% ± 0.08%
+10240
+63.21% ± 0.26%
+58.36% ± 0.45%
+58.86% ± 0.54%
+62.17% ± 0.35%
+55.75% ± 0.18%
+20480
+69.24% ± 0.47%
+61.08% ± 0.17%
+61.65% ± 0.27%
+65.12% ± 0.19%
+59.34% ± 0.14%
+50000
+75.34% ± 0.21%
+66.38% ± 0.00%
+66.98% ± 0.00%
+68.62% ± 0.00%
+63.25% ± 0.00%
+The experiment delivers a number of additional conclusions:
+• First, we observe that, while for small train sample sizes of n ≤ 10000, simple kernel
+17
+
+0.45
+0.40
+-
+(%) 
+0.35
+Z = 10-5
+Accuracy
+0.30
+Z= 10-1
+z= 100
+0.25
+z= 101
+0.20
+z = 102
+z= 103
+0.15
+z= 104
+Z= 105
+0.10
+0
+5
+10
+15
+20
+25
+c0.5
+0.4
+%) 
+Z = 10-5
+Accuracy
+Z= 10-1
+0.3
+z=100
+z= 101
+z = 102
+0.2
+Z= 103
+z= 104
+Z= 105
+0.1
+0
+5
+10
+15
+20
+25
+c0.16
+(%)
+Z = 10-5
+cy
+0.14
+Z= 10-1
+Accura
+Z= 100
+z= 101
+0.12
+z = 102
+z= 103
+z= 104
+0.10
+Z= 105
+0
+5
+10
+15
+20
+25
+c-
+0.20
+-
+0.18
+(%)
+0.16
+Z = 10-5
+Accuracy
+Z= 10-1
+z= 100
+0.14
+z= 101
+z = 102
+0.12
+Z= 103
+z= 104
+0.10
+Z= 105
+0
+5
+10
+15
+20
+25
+c-
+0.24
+0.22
+0.20
+Z = 10-5
+Accuracy
+0.18
+Z= 10-1
+z= 100
+0.16
+z= 101
+z = 102
+0.14
+z= 103
+z= 104
+0.12
+Z= 105
+0
+5
+10
+15
+20
+25
+c0.275
+0.250
+(%)
+0.225
+Z = 10-5
+ Accuracy
+Z= 10-1
+0.200
+z= 100
+0.175
+z= 101
+z= 102
+0.150
+z= 103
+z = 104
+0.125
+Z= 105
+0.100
+0
+5
+10
+15
+20
+25
+c1
+0.30
+-
+(%)
+Z = 10-5
+0.25
+Accuracy
+Z = 10-1
+z= 100
+0.20
+z= 101
+z= 102
+z= 103
+0.15
+Z= 104
+Z=105
+0.10
+0
+5
+10
+15
+20
+25
+c0.40
+-
+0.35
+-
+(%)
+0.30
+Z = 10-5
+Accuracy
+Z= 10-1
+0.25
+z= 100
+z= 101
+0.20
+Z= 102
+z= 103
+0.15
+z= 104
+Z= 105
+0.10
+0
+5
+10
+15
+20
+25
+c(a) n = 2560
+(b) n = 50000
+Figure 5: The figures above show FABR’s test accuracy increases with the model’s complexity
+c on the subsampled CIFAR-10 dataset 5a and the full CIFAR-10 dataset 5b. FABR is trained
+using a ν = 2000 low-rank covariance matrix approximation. Notice that we still observe a
+(shifted) double descent when ν ≈ n. The same phenomenon disappears when ν ≪ n. The
+test accuracy is averaged over five independent runs.
+Table 3: The table below shows the average test accuracy and standard deviation of FABR-ν
+and mini-batch FABR on the subsampled and full CIFAR-10 dataset. The test accuracy is
+average over five independent runs.
+z = 1
+z = 100
+z = 10000
+z = 100000
+FABR
+batch = 2000
+ν = 2000
+batch = 2000
+ν = 2000
+batch = 2000
+ν = 2000
+batch = 2000
+ν = 2000
+n
+2560
+53.13% ± 0.38%
+53.48% ± 0.22%
+53.15% ± 0.42%
+53.63% ± 0.24%
+52.01% ± 0.51%
+54.05% ± 0.44%
+46.78% ± 0.52%
+48.23% ± 0.34%
+5120
+57.68% ± 0.18%
+57.63% ± 0.19%
+57.70% ± 0.16%
+57.63% ± 0.18%
+56.83% ± 0.27%
+57.53% ± 0.11%
+51.42% ± 0.22%
+51.75% ± 0.14%
+10240
+59.79% ± 0.35%
+61.20% ± 0.39%
+59.79% ± 0.35%
+61.20% ± 0.38%
+58.63% ± 0.28%
+60.63% ± 0.21%
+53.73% ± 0.37%
+55.16% ± 0.34%
+20480
+61.56% ± 0.35%
+63.50% ± 0.12%
+61.55% ± 0.37%
+63.50% ± 0.13%
+60.90% ± 0.20%
+62.92% ± 0.12%
+57.10% ± 0.19%
+58.40% ± 0.21%
+50000
+62.74% ± 0.10%
+65.45% ± 0.18%
+62.74% ± 0.10%
+65.44% ± 0.18%
+62.35% ± 0.05%
+65.04% ± 0.19%
+59.99% ± 0.02%
+61.71% ± 0.09%
+methods achieve performance comparable with that of DNNs, this is not the case for
+n > 20000. Beating DNNs on big datasets with shallow methods requires more complex
+kernels, such as those in Shankar et al. [2020], Li et al. [2019].
+• Second, we confirm the findings of Ma and Belkin [2017], Lee et al. [2020] suggesting
+that the role of small
+eigenvalues is important. For example, FABR-ν with ν = 2000 loses several percent of
+accuracy on larger datasets.
+18
+
+0.55-
+0.50
+(%)
+0.45
+z = 10-5
+Accuracy
+z= 10-1
+0.40
+z= 100
+z= 101
+0.35
+z= 102
+z= 103
+0.30
+z= 104
+z= 105
+0.0
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+c0.65
+0.60
+z= 10-5
+0.55
+z= 10-1
+z= 100
+0.50
+z= 101
+z= 102
+0.45
+Z= 103
+z= 104
+z= 105
+0.40
+0.0
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+c• Third, surprisingly, both the mini-batch FABR and FABR-ν sometimes achieve higher
+accuracy than the full sample regression on moderately-sized datasets. See Tables 2
+and 3. Understanding these phenomena is an interesting direction for future research.
+• Fourth, the double descent phenomenon naturally appears for both FABR-ν and the
+mini-batch FABR but only when ν ≈ n or batch size ≈ n. However, the double descent
+phenomenon disappears when ν ≪ n. This intriguing finding is shown in Figure 5 for
+FABR-ν, and in Appendix B for the mini-batch FABR.
+• Fifth, on average, FABR-ν outperforms mini-batch FABR on larger datasets.
+5
+Conclusion and Discussion
+The recent discovery of the equivalence between infinitely wide neural networks (NNs) in
+the lazy training regime and neural tangent kernels (NTKs) Jacot et al. [2018] has revived
+interest in kernel methods. However, these kernels are extremely complex and usually re-
+quire running on big and expensive computing clusters Avron et al. [2017], Shankar et al.
+[2020] due to memory (RAM) requirements. This paper proposes a highly scalable random
+features ridge regression that can run on a simple laptop. We name it Fast Annihilating
+Batch Regression (FABR). Thanks to the linear algebraic properties of covariance matrices,
+this tool can be applied to any kernel and any way of generating random features. More-
+over, we provide several experimental results to assess its performance. We show how FABR
+can outperform (in training and prediction speed) the current state-of-the-art ridge classi-
+fier’s implementation. Then, we show how a simple data representation strategy combined
+with a random features ridge regression can outperform complicated kernels (CNTKs) and
+over-parametrized Deep Neural Networks (ResNet-34) in the few-shot learning setting. The
+experiments section concludes by showing additional results on big datasets. In this paper,
+we focus on very simple classes of random features. Recent findings (see, e.g., Shankar et al.
+19
+
+[2020]) suggest that highly complex kernel architectures are necessary to achieve competi-
+tive performance on large datasets. Since each kernel regression can be approximated with
+random features, our method is potentially applicable to these kernels as well. However,
+directly computing the random feature representation of such complex kernels is non-trivial
+and we leave it for future research.
+20
+
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+26
+
+A
+Proofs
+Proof of Lemma 2. We have
+Ψk+1 = Ψk + Sk+1S′
+k+1
+˜Ψk+1 = ˆΨk + Sk+1S′
+k+1
+ˆΨk+1 = Pk+1 ˜Ψk+1Pk+1 .
+(15)
+By the definition of the spectral projection, we have
+∥˜Ψk+1 − ˆΨk+1∥ ≤ λν+1(˜Ψk+1) ≤ λν+1(Ψk+1) ,
+(16)
+and hence
+∥Ψk+1 − ˆΨk+1∥
+≤ ∥Ψk+1 − ˜Ψk+1∥ + ∥˜Ψk+1 − ˆΨk+1∥
+= ∥Ψk − ˆΨk∥ + ∥˜Ψk+1 − ˆΨk+1∥)
+≤ ∥Ψk − ˆΨk∥ + λν+1(Ψk+1) ,
+(17)
+and the claim follows by induction. The last claim follows from the simple inequality
+∥(Ψk+1 + zI)−1 − (ˆΨk+1 + zI)−1∥ ≤ z−2∥Ψk+1 − ˆΨk+1∥ .
+(18)
+B
+Additional Experimental Results
+This section provides additional experiments and findings that may help the community with
+future research.
+First, we dive into more details about our comparison with sklearn. Table 4 shows a more
+27
+
+detailed training and prediction time comparison between FABR and sklearn. In particular,
+we average training and prediction time over five independent runs. The experiment settings
+are explained in Section 4.1. We show how one, depending on the number shrinkages |z|,
+would start considering using FABR when the number of observations in the dataset n ≈
+5000. In this case, we have used the numpy linear algebra library to decompose FABR’s
+covariance matrix, which appears to be faster than the scipy counterpart. We share our
+code in the following repository: https://github.com/tengandreaxu/fabr.
+Second, while Figure 4 shows FABR’s test accuracy on increasing complexity c truncated
+curves, we present here the whole picture; i.e., Figure 6 shows full FABR’s test accuracy
+increases with the model’s complexity c on different (n) subsampled CIFAR-10 datasets
+averaged over twenty independent runs.
+The expanded dataset follows similar patterns.
+Similar to Figure 4, one can notice that when the shrinkage is sufficiently high, the double
+descent disappears, and the accuracy monotonically increases in complexity.
+Third, the double descent phenomenon naturally appears for both FABR-ν and the
+mini-batch FABR but only when ν ≈ n or batch size ≈ n. However, the double descent
+phenomenon disappears when ν ≪ n.
+This intriguing finding is shown in Figure 5 for
+FABR-ν, and here, in Figure 7, we report the same curves for mini-batch FABR.
+28
+
+(a) n = 10
+(b) n = 20
+(c) n = 40
+(d) n = 80
+(e) n = 160
+(f) n = 320
+(g) n = 640
+(h) n = 1280
+Figure 6: The figure above shows the full FABR’s accuracy increase with the model’s com-
+plexity c in the small dataset regime. The expanded dataset follows similar patterns.
+(a) n = 2560
+(b) n = 50000
+Figure 7: Similar to Figure 5, the figures above show FABR’s test accuracy increases with
+the model’s complexity c on the subsampled CIFAR-10 dataset 7a and the full CIFAR-10
+dataset 7b. FABR trains using mini-batches with batch size=2000 in both cases. Notice that
+we still observe a (shifted) double descent when batch size ≈ n, while the same phenomenon
+disappears when batch size ≪ n. The test accuracy is averaged over 5 independent runs.
+29
+
+0.20
+0.18
+(%) 
+Z = 10-5
+Accuracy
+0.16
+z= 10-1
+Z= 100
+0.14
+z= 101
+z= 102
+0.12
+z= 103
+z= 104
+0.10
+Z= 105
+0
+20
+40
+60
+80
+100
+c0.24
+0.22
+(%)
+0.20
+Z = 10-5
+ Accuracy
+Z= 10-1
+0.18
+z=100
+0.16
+z= 101
+z = 102
+0.14
+z= 103
+z= 104
+0.12
+Z= 105
+0
+20
+40
+60
+80
+100
+c0.30
+0.25
+(%) 
+Z = 10-5
+Accuracy
+z= 10-1
+0.20
+z= 100
+z= 101
+z= 102
+0.15
+z= 103
+z= 104
+Z= 105
+0.10
+0
+20
+40
+60
+80
+100
+c0.35
+0.30
+(%) 
+Z = 10-5
+Accuracy
+0.25
+z= 10-1
+z= 100
+0.20
+z= 101
+Z= 102
+z= 103
+0.15
+z= 104
+Z= 105
+0.10
+0
+20
+40
+60
+80
+100
+c0.40
+0.35
+%)
+0.30
+Z = 10-5
+Accuracy
+z= 10-1
+0.25
+z= 100
+z= 101
+0.20
+Z= 102
+z= 103
+0.15
+z= 104
+Z= 105
+0.10
+0
+20
+40
+60
+80
+100
+c0.45
+0.40
+0.35
+Z = 10-5
+Accuracy
+0.30
+Z= 10-1
+z=100
+0.25
+z= 101
+z= 102
+0.20
+z= 103
+0.15
+z= 104
+z= 105
+0.10
+0
+20
+40
+60
+80
+100
+c0.5
+0.4
+[%) 
+Z = 10-5
+Accuracy
+Z= 10-1
+0.3
+Z= 100
+z= 101
+z= 102
+0.2
+Z= 103
+z= 104
+Z= 105
+0.1
+0
+20
+40
+60
+80
+100
+c0.50.
+(%)
+0.45
+z= 10-5
+Accuracy
+0.40
+z= 10-1
+z= 100
+z= 101
+0.35
+z= 102
+z= 103
+0.30
+z= 104
+z= 105
+0.25
+0.0
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+c0.60
+(%)
+0.55
+z= 10-5
+Accuracy
+z= 10-1
+z= 100
+0.50
+Z= 101
+z= 102
+0.45
+z= 103
+z= 104
+z= 105
+0.40
+0.0
+2.5
+5.0
+7.5
+10.0
+12.5
+15.0
+c0.18
+0.16
+(%)
+Z = 10-5
+Accuracy
+z= 10-1
+0.14
+Z= 100
+z= 101
+0.12
+z= 102
+z= 103
+z= 104
+0.10
+Z= 105
+0
+20
+40
+60
+80
+100
+cTable 4: The table below shows FABR and sklearn’s training and prediction time (in sec-
+onds) on a synthetic dataset. We vary the dataset number of features d and the number of
+shrinkages (|z|). We report the average running time and the standard deviation over five
+independent runs.
+|z| = 5
+|z| = 10
+|z| = 20
+|z| = 50
+FABR
+sklearn
+FABR
+sklearn
+FABR
+sklearn
+FABR
+sklearn
+d
+10
+7.72s ± 0.36s
+0.01s ± 0.00s
+6.90s ± 0.77s
+0.02s ± 0.00s
+7.04s ± 0.67s
+0.03s ± 0.00s
+7.44s ± 0.57s
+0.07s ± 0.01s
+100
+7.35s ± 0.36s
+0.06s ± 0.02s
+6.58s ± 0.34s
+0.11s ± 0.01s
+7.61s ± 1.14s
+0.24s ± 0.04s
+7.3s ± 0.49s
+0.53s ± 0.06s
+500
+7.37s ± 0.44s
+0.33s ± 0.16s
+6.81s ± 0.25s
+0.54s ± 0.03s
+7.02s ± 0.35s
+1.01s ± 0.07s
+7.44s ± 0.48s
+2.41s ± 0.21s
+1000
+7.62s ± 0.31s
+0.58s ± 0.21s
+7.38s ± 0.23s
+1.06s ± 0.04s
+7.51s ± 0.24s
+2.04s ± 0.04s
+7.69s ± 0.08s
+4.79s ± 0.36s
+2000
+8.33s ± 0.42s
+1.21s ± 0.03s
+8.09s ± 0.73s
+2.44s ± 0.05s
+8.33s ± 0.24s
+4.87s ± 0.07s
+8.29s ± 0.47s
+12.21s ± 0.15s
+3000
+9.24s ± 0.25s
+2.49s ± 0.05s
+9.18s ± 0.41s
+5.08s ± 0.03s
+9.51s ± 0.20s
+10.06s ± 0.02s
+9.67s ± 0.41s
+25.67s ± 0.23s
+5000
+10.64s ± 0.86s
+5.36s ± 0.05s
+11.01s ± 0.7s
+10.74s ± 0.06s
+11.57s ± 0.81s
+21.31s ± 0.12s
+11.54s ± 0.41s
+54.18s ± 0.73s
+10000
+11.49s ± 0.66s
+17.87s ± 8.58s
+11.81s ± 0.47s
+28.32s ± 10.53s
+11.61s ± 0.49s
+44.72s ± 9.99s
+12.55s ± 0.3s
+101.58s ± 15.66s
+25000
+13.89s ± 0.21s
+27.79s ± 8.75s
+14.50s ± 0.45s
+49.84s ± 9.68s
+14.46s ± 0.96s
+94.08s ± 10.94s
+15.68s ± 0.74s
+224.31s ± 11.75s
+50000
+17.99s ± 0.22s
+50.51s ± 8.99s
+18.27s ± 0.37s
+92.88s ± 10.45s
+19.10s ± 0.37s
+176.24s ± 10.07s
+19.68s ± 0.85s
+422.95s ± 13.22s
+100000
+25.30s ± 0.39s
+95.57s ± 0.25s
+26.16s ± 0.46s
+177.54s ± 3.77s
+27.93s ± 0.35s
+340.32s ± 3.74s
+29.48s ± 1.38s
+816.25s ± 4.35s
+30
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+Draft version January 10, 2023
+Typeset using LATEX default style in AASTeX631
+Pre-merger sky localization of gravitational waves from binary neutron star mergers using deep
+learning
+Chayan Chatterjee
+1 and Linqing Wen
+1
+1Department of Physics, OzGrav-UWA, The University of Western Australia,
+35 Stirling Hwy, Crawley, Western Australia 6009, Australia
+ABSTRACT
+The simultaneous observation of gravitational waves (GW) and prompt electromagnetic counterparts
+from the merger of two neutron stars can help reveal the properties of extreme matter and gravity
+during and immediately after the final plunge. Rapid sky localization of these sources is crucial to
+facilitate such multi-messenger observations. Since GWs from binary neutron star (BNS) mergers can
+spend up to 10-15 mins in the frequency bands of the detectors at design sensitivity, early warning
+alerts and pre-merger sky localization can be achieved for sufficiently bright sources, as demonstrated
+in recent studies. In this work, we present pre-merger BNS sky localization results using CBC-SkyNet,
+a deep learning model capable of inferring sky location posterior distributions of GW sources at orders
+of magnitude faster speeds than standard Markov Chain Monte Carlo methods. We test our model’s
+performance on a catalog of simulated injections from Sachdev et al. (2020), recovered at 0-60 secs
+before merger, and obtain comparable sky localization areas to the rapid localization tool BAYESTAR.
+These results show the feasibility of our model for rapid pre-merger sky localization and the possibility
+of follow-up observations for precursor emissions from BNS mergers.
+1. INTRODUCTION
+The first direct detection of GWs from a merging binary black hole (BBH) system was made in 2015 (Abbott et al.
+(2016)), which heralded a new era in astronomy. Since then the LIGO-Virgo-KAGRA (LVK) Collaboration (Aasi et al.
+(2015); Acernese et al. (2014); Akutsu et al. (2019)) has made more than 90 detections of GWs from merging compact
+binaries (Abbott et al. (2021a)), including two confirmed detections from merging binary neutron stars (BNS) and at
+two from mergers of neutron star-black hole (NSBH) binaries (Abbott et al. (2021a,b)). The first detection of GWs
+from a BNS merger on August 17th, 2017 (GW170817) along with its associated electromagnetic (EM) counterpart
+revolutionized the field of multi-messenger astronomy (Abbott et al. (2017a)). This event involved the joint detection
+of the GW signal by LIGO and Virgo, and the prompt short gamma-ray burst (sGRB) observation by the Fermi-GBM
+and INTEGRAL space telescopes (Abbott et al. (2017b,c)) ∼ 2 secs after the merger. This joint observation of GWs
+and sGRB, along with the observations of EM emissions at all wavelengths for months after the event had a tremendous
+impact on astronomy, leading to – an independent measurement of the Hubble Constant (Abbott et al. (2017d)), new
+constraints on the neutron star equation of state (Abbott et al. (2019)) and confirmation of the speculated connection
+between sGRB and kilonovae with BNS mergers (Abbott et al. (2017b)).
+While more multi-messenger observations involving GWs are certainly desirable, the typical delays between a GW
+detection and the associated GCN alerts, which is of the order of a few minutes (Magee et al. (2021)), makes such joint
+discoveries extremely challenging. This is because the prompt EM emissions lasts for just 1-2 secs after merger, which
+means an advance warning system with pre-merger sky localization of such events is essential to enable joint GW and
+EM observations by ground and space-based telescopes (Haas et al. (2016); Nissanke et al. (2013); Dyer et al. (2022)).
+In recent years, several studies have shown that for a fraction of BNS events, it will be possible to issue alerts
+up to 60 secs before merger (Magee et al. (2021); Sachdev et al. (2020); Kovalam et al. (2022); Nitz et al. (2020)).
+Such early-warning detections, along with pre-merger sky localizations will facilitate rapid EM follow-up of prompt
+emissions. The observations of optical and ultraviolet emissions prior to mergers are necessary for understanding
+r-process nucleosynthesis (Nicholl et al. (2017)) and shock-heated ejecta (Metzger (2017)) post mergers. Prompt X-
+ray emission can reveal the final state of the remnant (Metzger & Piro (2014); Bovard et al. (2017); Siegel & Ciolfi
+(2016)), and early radio observations can reveal pre-merger magnetosphere interactions (Most & Philippov (2020)),
+arXiv:2301.03558v1  [astro-ph.HE]  30 Dec 2022
+
+ID2
+and help test theories connecting BNS mergers with fast radio bursts (Totani (2013); Wang et al. (2016); Dokuchaev
+& Eroshenko (2017)).
+In the last three LVK observation runs, five GW low-latency detection pipelines have processed data and sent out
+alerts in real-time. These pipelines are GstLAL (Sachdev et al. (2019)), SPIIR (Chu et al. (2022)), PyCBC (Usman
+et al. (2016)), MBTA (Aubin et al. (2021)), and cWB (Klimenko et al. (2016)). Of these, the first four pipelines use
+the technique of matched filtering (Hooper (2013)) to identify real GW signals in detector data, while cWB uses a
+coherent analysis to search for burst signals in detector data streams. In 2020, an end-to-end mock data challenge
+(Magee et al. (2021)) was conducted by the GstLAL and SPIIR search pipelines and successfully demonstrated their
+feasibility to send pre-merger alerts (Magee et al. (2021)). This study also estimated the expected rate of BNS mergers
+and their sky localization areas using the rapid localization tool, BAYESTAR (Singer & Price (2016)) using a four detector
+network consisting of LIGO Hanford (H1), LIGO Livingston (L1), Virgo (V1) and KAGRA in O4 detector sensitivity.
+In a previous study, Sachdev et al. (2020) (Sachdev et al. (2020)) showed early warning performance of the GstLAL
+pipeline over a month of simulated data with injections. Their study suggested that alerts could be issued 10s (60 s)
+before merger for 24 (3) BNS systems over the course of one year of observations of a three-detector Advanced network
+operating at design sensitivity. These findings were in broad agreement with the estimates of Cannon et al. (2012)
+(Cannon et al. (2012)) on the rates of early warning detections at design sensitivity. Sky localization was also obtained
+at various number of seconds before merger, using the online rapid sky localization software called BAYESTAR (Singer
+& Price (2016)), with the indication that around one event will be both detected before merger and localized within
+100 deg2, based on current BNS merger rate estimates.
+The online search pipelines, however, experience additional latencies owing to data transfer, calibration and filtering
+processes, which contribute up to 7-8 secs of delay in the publication of early warning alerts (Kovalam et al. (2022);
+Sachdev et al. (2020)). For sky localization, BAYESTAR typically takes 8 secs to produce skymaps, which is expected
+to reduce to 1-2 secs in the third observation run. This latency can, however, be potentially reduced further by the
+application of machine learning techniques, as demonstrated in Chatterjee et al. (2022) (Chatterjee et al. (2022)).
+In this Letter, we report pre-merger sky localization using deep learning for the first time. We obtain our results using
+CBC-SkyNet (Compact Binary Coalescence - Sky Localization Neural Network.), a normalizing flow model (Rezende &
+Mohamed (2015); Kingma et al. (2016); Papamakarios et al. (2017)) for sky localization of all types of compact binary
+coalescence sources (Chatterjee et al. (2022)). We test our model on simulated BNS events from the injection catalog
+in Sachdev et al. (2020) (Sachdev et al. (2020)), that consists of signals detected at 0 to 60 secs before merger using the
+GstLAL search pipeline. We compare our sky localization performance with BAYESTAR and find that our localization
+contours have comparable sky contour areas with BAYESTAR, at an inference speed of just a few milli-seconds using a
+P100 GPU.
+The paper is divided as follows: we briefly describe our normalizing flow model in Section 2. In Section 3, we describe
+the details of the simulations used to generate the training and test sets. In Section 4, we desribe our architecture of
+CBC-SkyNet. In Section 5, we discuss results obtained using our network on the dataset from Sachdev et al. (2020)
+(Sachdev et al. (2020)). Finally, we discuss future directions of this research in Section 6.
+2. METHOD
+Our neural network, CBC-SkyNet is based on a class of deep neural density estimators called normalizing flow,
+the details of which is provided in (Chatterjee et al. (2022)). CBC-SkyNet consists of three main components: (i)
+the normalizing flow, specifically, a Masked Autoregressive Flow (MAF) (Kingma et al. (2016); Papamakarios et al.
+(2017)) network, (ii) a ResNet-34 model (He et al. (2015)) that extracts features from the complex signal-to-noise
+(SNR) time series data which is obtained by matched filtering GW strains with BNS template waveforms, and (iii)
+a fully connected neural network whose inputs are the intrinsic parameters (component masses and z-component of
+spins) of the templates used to generate the SNR time series by matched filtering. The architecture of our model is
+shown in Figure 1. The features extracted by the ResNet-34 and fully connected networks from the SNR time series
+(ρ(t)) and best-matched intrinsic parameters (ˆθin) respectively, are combined into a single feature vector and passed
+as a conditional input to the MAF. The MAF is a normalizing flow with a specific architecture, that transforms a
+simple base distribution (a multi-variate Gaussian) z ∼ p(z) into a more complex target distribution x ∼ p(x) which
+in our case, is the posterior distribution of the right ascension (α) and declination angles (δ) of the GW events, given
+the SNR time series and intrinsic parameters p(α, δ|ρ(t), ˆθin).
+
+3
+Figure 1.
+Architecture of our model, CBC-SkyNet. The input data, consisting of the SNR time series, ρ(t) and intrinsic
+parameters, ˆθin are provided to the network through two separate channels: the ResNet-34 channel (only one ResNet block is
+shown here) and the multi-layered fully connected (Dense) network respectively. The features extracted by ρ(t) and ˆθin are then
+combined and provided as conditional input to the main component of CBC-SkyNet - the Masked Autoregressive Flow (MAF)
+network , denoted by f(z). The MAF draws samples, z, from a multivariate Gaussian, and learns a mapping between z to (α,
+δ), which are the right ascension and declination angles of the GW events.
+This mapping is learnt by the flow during training using the method of maximum likelihood, and can be expressed
+as:
+p(x) = π(z)
+����det∂f(z)
+∂z
+����
+−1
+,
+(1)
+If z is a random sample drawn from the base distribution π(z), and f is the invertible transformation parametrized by
+the normalizing flow, then the new random variable obtained after the transformation is x = f(z). The transformation,
+f can be made more flexible and expressive by stacking a chain of transformations together as follows:
+xk = fk ◦ . . . ◦ f1 (z0)
+(2)
+This helps the normalizing flow learn arbitrarily complex distributions, provided each of the transformations are
+invertible and the Jacobians are easy to evaluate. Neural posterior estimation (NPE) (Papamakarios & Murray (2016);
+Lueckmann et al. (2017); Greenberg et al. (2019)) techniques, including normalizing flows and conditional variational
+autoencoders have been used to estimate posterior distribution of BBH source parameters with high accuracy and
+speed (Dax et al. (2021); Gabbard et al. (2022); Chua & Vallisneri (2020)). Chatterjee et al. (2022) (Chatterjee
+et al. (2022)) used a normalizing flow to demonstrate rapid inference of sky location posteriors for all CBC sources for
+the first time. This work shows the first application of deep learning for pre-merger BNS sky localization and is an
+extension of the model introduced in Chatterjee et al. (2022)
+3.
+DATA GENERATION
+
+Hanford
+Livingston
+Virgo
+Conv 2D
+Dense (64)
+BatchNorm
+ReLU
+Conv2D
+Dense (64)
+Conv 2D
+BatchNorm
+Dense (64)
+BatchNorm
+Dense (64)
+Dense (64)
+ReLU
+90% area: 121 deg
+50% area: 34 deg
+60*
+Pz(z)
+Feature Vector
+f(z)
+30°
+2
+z ~ N(0, 1)D+1
+α, S ~ Pe(α, Slp(t), θin)4
+We train six different versions of CBC-SkyNet with distinct training sets (ρi(t), ˆθi
+in) for each “negative latency",
+i = 0, 10, 14, 28, 44, 58 secs before merger.
+Our training and test set injections parameters were sampled from the
+publicly available injection dataset used in Sachdev et al. (2020) Sachdev et al. (2020). These ˆθi
+in parameters were
+used to first simulate the BNS waveforms using the SpinTaylorT4 approximant (Sturani et al. (2010)) and then
+injected into Gaussian noise with advanced LIGO power spectral density (PSD) at design sensitivity (Littenberg &
+Cornish (2015)) to obtain the desired strains. The SNR time series, ρi(t), was then obtained by matched filtering the
+simulated BNS strains with template waveforms.
+For generating the training sets, the template waveforms for matched filtering were simulated using the optimal
+parameters, which have the exact same values as the injection parameters used to generate the detector strains.
+The SNR time series obtained by matched filtering the strains with the optimal templates, ρi
+opt(t), and the optimal
+intrinsic parameters, ˆθi,opt
+in
+, were then used as input to our network during the training process. For testing, the
+template parameters were sampled from publicly available data by Sachdev et al. (2020) (Sachdev et al. (2020)). These
+parameters correspond to the parameters of the maximum likelihood or ‘best-matched’ signal template recovered by
+the GstLAL matched-filtering search pipeline. Therefore the values of ˆθi
+in used during testing are close to, but is not
+the exact same as ˆθi,opt
+in
+. Similarly, the SNR time series ρi(t) is not exactly similar to the optimal ρi
+opt(t), and has a
+slightly lower peak amplitude than the corresponding ρi
+opt(t) peak because of the small mismatch between the injection
+parameters and the best-matched template waveform parameters.
+While our injections have the same parameter distribution as (Sachdev et al. (2020)), we only choose samples with
+network SNRs lying between 9 and 40, at each negative latency, for this analysis. This is because when the network
+is trained on samples with identical parameter distributions as the dataset from (Sachdev et al. (2020)), our model’s
+predictions on test samples with network SNRs > 40 tend to become spurious, with α and δ samples drawn from
+the predicted posterior distribution for these events having values outside their permissible ranges. This is because
+in the dataset from (Sachdev et al. (2020)), injection samples with SNR > 40 are much fewer in number compared
+to samples between SNR 9 and 40. This means for models trained on data with parameters from (Sachdev et al.
+(2020)), there exists very few training examples for SNR > 40 to learn from. Since Normalizing Flow models are
+known to fail at learning out-of-distribution data, as described in (Kirichenko et al. (2020)), our model fails to make
+accurate predictions at the high SNR limit. Although this can potentially be solved by generating training sets with
+uniform SNR distribution over the entire existing SNR range in (Sachdev et al. (2020)), which corresponds to a uniform
+distribution of sources in comoving volume up to a redshift of z=0.2, this would be require generating an unfeasibly
+large number of training samples for each negative latency. Also, such events detected with SNR > 40 are expected
+to be exceptionally rare, even at design sensitivities of advanced LIGO and Virgo, which is why we choose to ignore
+them for this study. We therefore generate samples with uniformly distributed SNRs between 9 and 40 for training,
+while our test samples have the same SNR distribution as (Sachdev et al. (2020)) between 9 and 40.
+4. NETWORK ARCHITECTURE
+In this section, we describe the architecture of the different components of our model. The MAF is implemented
+using a neural network that is designed to efficiently model conditional probability densities. This network is called
+Masked Autoencoder for Density Estimation (MADE) (Germain et al. (2015)). We stack 10 MADE blocks together
+to make a sufficiently expressive model, with each MADE block consisting of 5 layers with 256 neurons in each layer.
+In between each pair of MADE networks, we use batch normalization to stabilize training. We use a ResNet-34 model
+(He et al. (2015)), that is constructed using 2D convolutional and MaxPooling layers with skip connections, (He et al.
+(2015)) to extract features from the SNR time series data. The real and imaginary parts of the SNR time series are
+stacked vertically to generate a two dimensional input data stream for each training and test sample. The initial
+number of kernels for the convolutional layers of the ResNet model is chosen to be 32, which is doubled progressively
+through the network (He et al. (2015)). The final vector of features obtained by the ResNet are combined with the
+features extracted from the intrinsic parameters, ˆθi
+in, by the fully-connected network, consisting of 5 hidden layers
+with 64 neurons in each hidden layer. The combined feature vector is then passed as a conditional input to the MAF
+which learns the mapping between the base and target distributions during training.
+5. RESULTS
+In this section, we describe the results of the injection runs at each negative latency. Figure 2 (a) to (f) shows
+the histograms of the areas of the 90% credible intervals of the predicted posterior distributions from CBC-SkyNet
+
+5
+(blue) and BAYESTAR (orange), evaluated on the injections in (Sachdev et al. (2020)) with network SNRs between 9
+and 40. We observe that for most of the test sets, our model predicts smaller median 90% credible interval areas than
+BAYESTAR. Also, BAYESTAR shows much broader tails at < 100 deg2, compared to CBC-SkyNet, especially for 0 secs,
+10 secs and 15 secs before merger (Figures 2 (a), (b) and (c)). These injections, with 90% areas < 100 deg2 typically
+have SNR > 25, which shows that although CBC-SkyNet produces smaller 90 % contours on average, it fails to match
+BAYESTAR’s accuracy for high SNR cases. Especially at 0 secs before merger (Figure 2 (a)), the area of the smallest
+90% credible interval by CBC-SkyNet is 13 deg2, whereas for BAYESTAR, it is around 1 deg2. The number of injections
+localized with a 90% credible interval area between 10 - 15 deg2 by CBC-SkyNet is also much lower than BAYESTAR,
+although this effect is much less prominent for the other test sets.
+Similar results are found for the searched area distributions at 0 secs before merger (Figure 3 (a)), although the
+distributions of searched areas from for all other cases (Figure 3 (b) - (f)) from CBC-SkyNet and BAYESTAR are very
+similar. Figures 4 (a) and (b) show box and whisker plots for 90% credible interval areas and searched areas obtained
+by CBC-SkyNet (blue) and BAYESTAR (pink) respectively. We observe that our median 90% areas (white horizontal
+lines) for most of the cases are smaller than BAYESTAR’s.
+A possible explanation for these observations is as follows: BAYESTAR uses an adaptive sampling method (Singer &
+Price (2016)) to evaluate the densities, in which the posterior probability is first evaluated over Nside,0 = 16 HEALPix
+grids (Górski et al. (2005)), corresponding to a single sky grid area of 13.4 deg2. The highest probability grids are
+then adaptively subdivided into smaller grids over which the posterior is evaluated again. This process is repeated
+seven times, with the highest possible resolution at the end of the iteration being Nside = 211, with an area of ∼ 10−3
+deg2 for the smallest grid (Singer & Price (2016)).
+This adaptive sampling process, however, takes much longer to evaluate, compared to conventional evaluation over
+a uniform angular resolution in the sky. This is why for our analysis, we do not adopt the adaptive sampling process,
+since our primary aim is to improve the speed of pre-merger sky localization. Instead, we draw 5000 α and δ posterior
+samples each, from our model’s predicted posterior and then apply a 2-D Kernel Density Estimate (KDE) over these
+samples. We then evaluate the KDE over Nside,0 = 32 HEALPix grids, corresponding to a single grid area of ∼ 3.3
+deg2 to obtain our final result. Therefore, our chosen angular resolution results in sky grids which are much larger
+than BAYESTAR’s smallest sky grids after adaptive refinement. Therefore our approach results in larger 90% contours
+and searched areas than BAYESTAR for high network SNR cases where the angular resolution has a more significant
+impact in the overall result. The sampling process adopted by us may also explain why our median areas are smaller
+compared to BAYESTAR. During inference, after sampling α and δ from the predicted posterior, we evaluate the KDE
+with a fixed bandwidth of 0.03, chosen by cross-validation. This may result in a narrower contour estimate, on average,
+compared to BAYESTAR’s sampling method.
+Figures 5 (a) - (f) show P-P plots for a subset of injections at 0 secs, 10 secs, 15 secs, 28 secs, 44 secs and 58 secs
+before merger respectively. To obtain the P-P plots, we compute the percentile scores of the true right ascension and
+declination parameters within their marginalized posteriors and obtain the cumulative distribution of these scores.
+For accurate posteriors, the distribution of the percentile scores should be uniform, which means the cumulative
+distribution should be diagonal, which is evident from the figures. We also perform Kolmogorov-Smirnoff (KS) tests
+for each dataset to test our hypothesis that the percentile values for each set are uniformly distributed. The p-values
+from the KS tests, shown in the legend, for each parameter have values > 0.05, which means at a 95% level of
+significance, we cannot reject the null hypothesis that the percentile values are uniform, and thereby our posteriors
+are consistent with the expected distribution.
+Because of the low dimensionality of our input data, training our network takes less than an hour on a NVIDIA Tesla
+P100 GPU. Overall the sampling and evaluation step during inference takes a few milli-seconds for each injection on
+the same computational resource. Sample generation and matched filtering was implemented with a modified version
+of the code developed by (Gebhard et al. (2019)) that uses PyCBC software (Nitz et al. (2021)). CBC-SkyNet was written
+in TensorFlow 2.4 (Abadi et al. (2016)) using the Python language.
+6. DISCUSSION
+In summary, we have reported the first deep learning based approach for pre-merger sky localization of BNS sources,
+capable of orders of magnitude faster inference than Bayesian methods. Currently our model’s accuracy is similar to
+BAYESTAR on injections with network SNR between 9 and 40 at design sensitivity. The next step in this research would
+be to perform similar analysis on real detector data which has non-stationary noise and glitches that may corrupt
+
+6
+(a)
+(b)
+(c)
+(d)
+(e)
+(f)
+Figure 2.
+Top panel from (a) to (c): Histograms of the areas of the 90% credible intervals from CBC-SkyNet (blue) and
+BAYESTAR (orange) for 0 secs, 10 secs, 15 secs before merger are shown. Bottom panel from (d) to (f): Similar histograms for 28
+secs, 44 secs and 58 secs before merger are shown.
+the signal and affect detection and sky localization. A possible way to improve our model’s performance at high
+SNRs (> 25) would be to use a finer angular resolution in the sky for evaluating the posteriors. We can also train
+different versions of the model for different luminosity distance (and hence SNR) ranges. Our long-term goal is to
+construct an independent machine learning pipeline for pre-merger detection and localization of GW sources. The
+faster inference speed of machine learning models would be crucial for electromagnetic follow-up and observation of
+prompt and precursor emissions from compact binary mergers. This method is also scalable and can be applied for
+predicting the luminosity distance of the sources pre-merger, which would help obtain volumetric localization of the
+source and potentially identify host galaxies of BNS mergers.
+The authors would like to thank Dr. Foivois Diakogiannis, Kevin Vinsen, Prof. Amitava Datta and Damon Beveridge
+for useful comments on this work. This research was supported in part by the Australian Research Council Centre of
+Excellence for Gravitational Wave Discovery (OzGrav, through Project No. CE170100004). This research was under-
+taken with the support of computational resources from the Pople high-performance computing cluster of the Faculty of
+Science at the University of Western Australia. This work used the computer resources of the OzStar computer cluster
+at Swinburne University of Technology. The OzSTAR program receives funding in part from the Astronomy National
+Collaborative Research Infrastructure Strategy (NCRIS) allocation provided by the Australian Government. This
+research used data obtained from the Gravitational Wave Open Science Center (https://www.gw-openscience.org), a
+service of LIGO Laboratory, the LIGO Scientific Collaboration and the Virgo Collaboration. LIGO is funded by the
+U.S. National Science Foundation. Virgo is funded by the French Centre National de Recherche Scientifique (CNRS),
+the Italian Istituto Nazionale della Fisica Nucleare (INFN) and the Dutch Nikhef, with contributions by Polish and
+Hungarian institutes. This material is based upon work supported by NSF’s LIGO Laboratory which is a major facility
+fully funded by the National Science Foundation.
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+3
+4
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+13
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+Heterogeneous Distributed Systems
+
+CBC-SkyNet
+0.8
+Bayestar
+0.6
+Density
+0.4
+0.2
+0.0
+0
+1
+2
+3
+4
+90% credible interval area in log (deg2)1.2
+CBC-SkyNet
+Bayestar
+1.0
+0.8
+Density
+0.6
+0.4
+0.2
+0.0
+1
+2
+3
+4
+90% credible interval area in log (deg2)CBC-SkyNet
+1.25
+Bayestar
+1.00
+Density
+0.75
+0.50
+0.25
+0.00
+2
+1
+3
+4
+90% credible interval area in log (deg2)CBC-SkyNet
+Bayestar
+1.5
+Density
+1.0
+0.5
+0.0
+1
+2
+3
+4
+90% credible interval area in log (deg2)CBC-SkyNet
+Bayestar
+1.5
+Density
+1.0
+0.5
+0.0
+1
+2
+3
+4
+90% credible interval area in log (deg2)2.0
+CBC-SkyNet
+Bayestar
+1.5
+Density
+1.0
+0.5
+0.0
+1
+2
+3
+4
+90% credible interval area in log (deg2)7
+(a)
+(b)
+(c)
+(d)
+(e)
+(f)
+Figure 3.
+Top panel from (a) to (c): Histograms of the searched areas from CBC-SkyNet (blue) and BAYESTAR (orange) for 0
+secs, 10 secs, 15 secs before merger are shown. Bottom panel from (d) to (f): Similar histograms for 28 secs, 44 secs and 58 secs
+before merger are shown.
+(a)
+(b)
+Figure 4.
+(a) Box and whiskers plots showing the areas of the 90% credible intervals from CBC-SkyNet (blue) and BAYESTAR
+(pink) at 0 secs, 10 secs, 15 secs, 28 secs, 44 secs and 58 secs before merger. The boxes encompass 95% of the events and the
+whiskers extend up to the rest. The white lines within the boxes represent the median values of the respective data sets. (b)
+Similar box and whiskers plot as (a) for comparing searched areas from CBC-SkyNet (blue) and BAYESTAR (pink) at 0 secs, 10
+secs, 15 secs, 28 secs, 44 secs and 58 secs before merger.
+
+0.6
+CBC-SkyNet
+Bayestar
+0.5
+0.4
+Density
+0.3
+0.2
+0.1
+0.0
+-4
+-2
+0
+2
+4
+Searched area in log (deg2)0.6
+CBC-SkyNet
+Bayestar
+0.5
+0.4
+Density
+0.3
+0.2
+0.1
+0.0
+-4
+-2
+0
+2
+4
+Searched area in log (deg2)0.6
+CBC-SkyNet
+Bayestar
+0.5
+0.4
+Density
+0.3
+0.2
+0.1
+0.0
+-4
+-2
+0
+2
+4
+Searched area in log (deg2)CBC-SkyNet
+Bayestar
+0.5
+0.4
+Density
+0.3
+0.2
+0.1
+0.0
+-4
+-2
+0
+2
+4
+Searched area in log (deg2)0.6
+CBC-SkyNet
+Bayestar
+0.5
+0.4
+Density
+0.3
+0.2
+0.1
+0.0
+-4
+-2
+0
+2
+4
+Searched area in log (deg2)104.
+2
+in deg
+area
+103
+90% credible interval
+102
+CBC-SkyNet
+101
+Bayestar
+-10
+-15
+-28
+-44
+-58
+0
+Time from merger (in secs)104
+103.
+2
+6
+p
+Searched area in
+102
+101
+S
+100
+CBC-SkyNet
+Bayestar
+-10
+-15
+-28
+-44
+-58
+0
+Time from merger (in secs)CBC-SkyNet
+0.6
+Bayestar
+0.5
+Density
+0.4
+0.3
+0.2
+0.1
+0.0
+-4
+-2
+0
+2
+4
+Searched area in log (deg2)8
+(a)
+(b)
+(c)
+(d)
+(e)
+(f)
+Figure 5. (a) to (f): P–P plots for a subset of the total number of test samples at 0 secs, 10 secs, 15 secs, 28 secs, 44 secs and
+58 secs before merger. We compute the percentile values (denoted as p) of the true right ascension and declination parameters
+within their 1D posteriors. The figure shows the cumulative distribution function of the percentile values, which should lie close
+to the diagonal if the network is performing properly. The p-values of the KS test for each run is shown in the legend.
+
+1.0
+RA(0.101)
+Dec (0.0571)
+0.8
+Cumulative distribution
+0.6
+0.4
+0.2
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+p1.0
+RA (0.817)
+Dec (0.325)
+0.8
+Cumulative distribution
+0.6
+0.4
+0.2
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+p1.0
+RA (0.829)
+Dec (0.188)
+0.8
+Cumulative distribution
+0.6
+0.4
+0.2
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+p1.0
+RA(0.0891)
+Dec (0.441)
+0.8
+Cumulative distribution
+0.6
+0.4
+0.2
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+p1.0
+RA (0.0745)
+Dec (0.122)
+0.8
+Cumulative distribution
+0.6
+0.4
+0.2
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+p1.0
+RA (0.338)
+Dec (0.147)
+0.8
+Cumulative distribution
+0.6
+0.4
+0.2
+0.0
+0.0
+0.2
+0.4
+0.6
+0.8
+1.0
+p9
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+Chair of Robotics, Artificial Intelligence and Real-Time Systems
+TUM School of Computation, Information and Technology
+Technical University of Munich
+1
+Autonomous Driving Simulator based on Neurorobotics Platform
+Wei Cao, Liguo Zhou �, Yuhong Huang, and Alois Knoll
+Chair of Robotics, Artificial Intelligence and Real-Time Systems, Technical University of Munich
+� [email protected]
+Abstract — There are many artificial intelligence algorithms for autonomous driving in the present market,
+but directly installing these algorithms on vehicles is unrealistic and expensive. At the same time, many of these
+algorithms need an environment to train and optimize. Simulation is a valuable and meaningful solution with
+training and testing functions, and it can say that simulation is a critical link in the autonomous driving world.
+There are also many different applications or systems of simulation from companies or academies such as SVL
+and Carla. These simulators flaunt that they have the closest real-world simulation, but their environment objects,
+such as pedestrians and other vehicles around the agent-vehicle, are already fixed programmed. They can only
+move along the pre-setting trajectory, or random numbers determine their movements. What is the situation
+when all environmental objects are also installed by Artificial Intelligence, or their behaviors are like real people
+or natural reactions of other drivers? This problem is a blind spot for most of the simulation applications, or
+these applications cannot be easy to solve this problem. The Neurorobotics Platform from the TUM team of
+Prof. Alois Knoll has the idea about "Engines" and "Transceiver Functions" to solve the multi-agents problem.
+This report will start with a little research on the Neurorobotics Platform and analyze the potential and possibility
+of developing a new simulator to achieve the true real-world simulation goal. Then based on the NRP-Core
+Platform, this initial development aims to construct an initial demo experiment. The consist of this report
+starts with the basic knowledge of NRP-Core and its installation, then focus on the explanation of the necessary
+components for a simulation experiment, at last, about the details of constructions for the autonomous driving
+system, which is integrated object detection function and autonomous driving control function. At the end will
+discuss the existing disadvantages and improvements of this autonomous driving system.
+Keywords— Simulation, Neurorobotics Platform, NRP-Core, Engines, Transceiver Functions, Autonomous Driving,
+Object Detection, PID Trajectory Control
+1 Introduction
+1.1 Motivation
+At present, there are many different Artificial Intelligence (AI) algorithms used for autonomous driving. Some algorithms
+are used to perceive the environment, such as object detection and semantic/instance segmentation. Some algorithms are
+dedicated to making the best trajectory strategy and control decisions based on the road environment. Others contribute
+to many different applications, e.g. path planning and parking. Simulation is the best cost-performance way to develop
+these algorithms before they are truly deployed to actual vehicles or robots. So, the performance of a simulation platform
+is influencing the performance of the AI algorithms. In the present market or business world, there are already a lot of
+different “real-world” simulation applications such as CARLA [1] for simulating the algorithm for autonomous driving,
+AirSim [2] from Microsoft for autonomous vehicle and quadrotor and PTV Vissim [3] from Germany PTV Group for
+flexible traffic simulation.
+Although these simulators are dedicated to the “real world” simulation, they have more or less “unreal” problems on
+some sides in the process of simulation. For example, besides the problem about the unreal 3-D models and environment,
+these simulators have an obvious feature, these AI algorithms are only deployed to target experimental subjects, vehicles, or
+robots, and the environment such as other vehicles, motorbikes, and pedestrian looks very close to the “real” environment
+but actually these environmental subjects are already in advance pre-programmed and have a fix motion trail. The core
+problem of most of them focuses on basic information transmission. They only transfer the essential or necessary traffic
+information to the agent subject in the simulation. This transmission is one-way direction. Considering this situation, can
+let other subjects in this simulation have their own different AI algorithms at the same time that they can react to the agent’s
+behavior? In the future world, there would be not only one vehicle owning one algorithm from one company, but they
+must also have much interaction with other agents. The interaction between different algorithms can take which influence
+back on these algorithms, and this problem is also a blind point for many simulators.
+This large range of interaction between lots of agents is the main problem that these applications should pay attention
+to and these existing applications do not have an efficient way to solve this problem. A simulation platform that is truly
+arXiv:2301.00089v1  [cs.RO]  31 Dec 2022
+
+2
+like the real world, whose environment is not only a fixed pre-definition program, the objects in the environment can make
+a relative objective interaction with vehicles with the testing autonomous driving algorithms and they can influence each
+other, the goal and concept is an intractable problem for the construction of a simulation platform. There is a platform
+called The Neurorobotics Platform (NRP) from the TUM team of Prof. Alois Knoll that provides a potential idea to solve
+this interaction problem. This research project focuses on preliminary implementation and searches for the possibility of
+solving the previously mentioned interaction problem.
+1.2 Neurorobotics Platform (NRP)
+Figure 1.1 The base model of Neurorobotics Platform (NRP)
+Neurorobotics Platform [4] is an open-source integrative simulation framework platform developed by the group of the
+chair of Robotics, Artificial Intelligence and Real-Time Systems of the Technical University of Munich in the context of
+the Human Brain Project - a FET Flagship funded by the European Commission. The basic starting point of this platform
+enables to choose and test of different brain models (ranging from spiking neural networks to deep networks) for robots.
+This platform builds an efficient information transmission framework to let simulated agents interact with their virtual
+environment.
+The new Version of NRP called NRP Core provides a new idea, which regards all the Participator in the Simulation-
+system as "Engines", just like the object in the programming language C++/python, the properties of the simulation
+participator such as the robot, autonomous-driving car, weather, or pedestrian and their "behaviors" would be completely
+constructed in their own "Engine"-object and let all the participates become a "real" object and can each other influence in
+the simulation world and they would not be a fix definite "Program". And the NRP-Platform is the most important transport
+median between these engines and they are called the Transceiver Function. It transmits the "Information" such as the
+image from the camera and sends the image to an autonomous-driving car and the same time would send other information
+to other engines by different transfer protocols such as JSON or ROS system. That means the transmission of information
+is highly real-time and lets the simulation world very close to the real world and it has high simulation potency, e.g. the
+platform sends the image information to the autonomous-driving car and lets the car computes the situation and makes
+the right strategy and rational decision, and at the same moment the environment-cars or "drivers" also get the location
+information from the autonomous-driving car and make their own decisions such like drive further or change velocity and
+lanes, and the same time these cars are influenced by the situation of the weather, e.g. in raining days the brake time of the
+car would be longer and let the decision making and object detection more significant.
+NRP-core is mostly written in C++, with the Transceiver Function framework relying on Python for better usability.
+It guarantees a fully deterministic execution of the simulation, provided every simulator used is itself deterministic and
+works on the basis of controlled progression through time steps. Users should thus take note that event-based simulators
+may not be suitable for integration in NRP-core (to be analyzed on a case-by-case basis). Communications to and from
+NRP-core are indeed synchronous, and function calls are blocking; as such, the actual execution time of a simulation
+based on NRP-core will critically depend on the slowest simulator integrated therein. The aforementioned feature of the
+NRP-Core platform is significant to build multi-object which interact with other agencies in the simulation progress and
+lets the simulation be close to the real world.
+2 NRP-Core configurations for simulation progress
+NRP-Core has many application scenarios for different demands of simulation situations. For a specific purpose, the
+model of NRP-Core can be widely different. This development for the Autonomous-driving benchmark focuses on the
+actual suggested development progress. It concentrates on the construction of the simulation application, the details of
+
+Close
+Transceiver Functions
+Loop
+Engine3
+the operation mechanism of NRP-Core would not be discussed, and deep research in this development documentation, the
+principle of the operation mechanism can be found on the homepage of NRP-Core.
+2.1 Installation of NRP-Core and setting environment
+For the complete installation, refer to the homepage of the NRP-Core Platform by "Getting Started" under the page
+"Installation Instructions." This section lists only all the requirements for applying the autonomous driving simulator and
+benchmark.
+WARNING: Previous versions of the NRP install forked versions of several libraries, notably NEST and Gazebo.
+Installing NRP-core in a system where a previous version of NRP is installed is known to cause conflicts. That will be
+strongly recommended not to install the last version at the same time.
+Operating System: recommend on Ubuntu 20.04
+Setting the Installation Environment: To properly set the environment to run experiments with NRP-core, please make
+sure that it is added the lines below to your /.bashrc file.
+1 # Start
+setting
+environment
+2 export
+NRP_INSTALL_DIR ="/home/${USER }/. local/nrp" # The
+installation
+directory ,
+which was given
+before
+3 export
+NRP_DEPS_INSTALL_DIR ="/home/${USER }/. local/nrp_deps"
+4 export
+PYTHONPATH="${ NRP_INSTALL_DIR }"/lib/python3 .8/site -packages:"${
+NRP_DEPS_INSTALL_DIR }"/lib/python3 .8/site -packages:$PYTHONPATH
+5 export
+LD_LIBRARY_PATH ="${ NRP_INSTALL_DIR }"/lib:"${ NRP_DEPS_INSTALL_DIR }"/lib:${
+NRP_INSTALL_DIR }/lib/ nrp_gazebo_plugins : $LD_LIBRARY_PATH
+6 export
+PATH=$PATH:"${ NRP_INSTALL_DIR }"/bin:"${ NRP_DEPS_INSTALL_DIR }"/bin
+7 export
+GAZEBO_PLUGIN_PATH =${ NRP_INSTALL_DIR }/lib/ nrp_gazebo_plugins :${
+GAZEBO_PLUGIN_PATH }
+8 . /usr/share/gazebo -11/ setup.sh
+9 . /opt/ros/noetic/setup.bash
+10 . ${CATKIN_WS }/ devel/setup.bash
+11 # End of setting
+environment
+Dependency installation:
+1 # Start of dependencies
+installation
+2 # Pistache
+REST
+Server
+3 sudo add -apt -repository
+ppa:pistache+team/unstable
+4
+5 # Gazebo
+repository
+6 sudo sh -c ’echo "deb http :// packages. osrfoundation .org/gazebo/ubuntu -stable ‘
+lsb_release -cs ‘ main"> /etc/apt/sources.list.d/gazebo -stable.list ’
+7 wget
+https :// packages.osrfoundation .org/gazebo.key -O - | sudo apt -key add -
+8
+9 sudo apt update
+10 sudo apt
+install
+git cmake
+libpistache -dev libboost -python -dev libboost -
+filesystem -dev libboost -numpy -dev libcurl4 -openssl -dev nlohmann -json3 -dev
+libzip -dev cython3
+python3 -numpy
+libgrpc ++-dev protobuf -compiler -grpc
+libprotobuf -dev
+doxygen
+libgsl -dev libopencv -dev python3 -opencv
+python3 -pil
+python3 -pip libgmock -dev
+11
+12 # required by gazebo
+engine
+13 sudo apt
+install
+libgazebo11 -dev
+gazebo11
+gazebo11 -plugin -base
+14
+15 # Remove the flask if it was
+installed to ensure it is installed
+from pip
+16 sudo apt remove
+python3 -flask python3 -flask -cors
+17 # required by Python
+engine
+18 # If you are
+planning to use The
+Virtual
+Brain
+framework , you will most
+likely
+have to use flask
+version
+1.1.4.
+19 # By installing
+flask
+version
+1.1.4
+markupsafe
+library (included
+with
+flask) has
+to be downgraded to version
+2.0.1 to run
+properly
+with
+gunicorn
+20 # You can
+install
+that
+version
+with
+21 # pip install
+flask ==1.1.4
+gunicorn
+markupsafe ==2.0.1
+22 pip install
+flask
+gunicorn
+23
+24 # required by nest -server (which is built and
+installed
+along
+with nrp -core)
+
+4
+25 sudo apt
+install
+python3 - restrictedpython
+uwsgi -core uwsgi -plugin -python3
+26 pip install
+flask_cors
+mpi4py
+docopt
+27
+28 # required by nrp -server , which
+uses gRPC
+python
+bindings
+29 pip install
+grpcio -tools
+pytest
+psutil
+docker
+30
+31 # Required
+for using
+docker
+with ssh
+32 pip install
+paramiko
+33
+34 # ROS , when not needed , can jump to the next step
+35
+36 # Install ROS: follow the
+installation
+instructions: http :// wiki.ros.org/noetic
+Installation/Ubuntu. To enable ros
+support in nrp on ‘ros -noetic -ros -base ‘ is
+required.
+37
+38 #Tell
+nrpcore
+where
+your
+catkin
+workspace is located: export a variable
+CATKIN_WS
+pointing to an existing
+catkin
+workspace
+root
+folder. If the
+variable
+does not exist , a new catkin
+workspace
+will be created at ‘${HOME }/
+catkin_ws ‘.
+39
+40 # MQTT , if needed , see the
+homepage of NRP -Core
+41
+42 # End of dependencies
+installation
+NRP installation:
+1 # Start of installation
+2 git clone
+https :// bitbucket.org/ hbpneurorobotics /nrp -core.git
+3 cd nrp -core
+4 mkdir
+build
+5 cd build
+6 # See the
+section "Common NRP -core
+CMake
+options" in the
+documentation
+for the
+additional
+ways to configure
+the
+project
+with
+CMake
+7 cmake .. -DCMAKE_INSTALL_PREFIX ="${ NRP_INSTALL_DIR }" -
+DNRP_DEP_CMAKE_INSTALL_PREFIX ="${ NRP_DEPS_INSTALL_DIR }"
+8 mkdir -p "${ NRP_INSTALL_DIR }"
+9 # the
+installation
+process
+might
+take some time , as it downloads
+and
+compiles
+Nest as well.
+10 # If you haven ’t installed
+MQTT libraries , add
+ENABLE_MQTT=OFF
+definition to
+cmake (-DENABLE_MQTT=OFF).
+11 make
+12 make
+install
+13 # Just in case of wanting to build the
+documentation . Documentation
+can then be
+found in a new doxygen
+folder
+14 make
+nrp_doxygen
+15 # End of installation
+Common NRP-core CMake options: Here is the list of the CMake options that can help modify the project configu-
+ration (turn on and off the support of some components and features).
+• Developers options:
+– COVERAGE enables the generation of the code coverage reports during the testing
+– BUILD_RST enables the generation of the reStructuredText source files from the Doxygen documentation
+• Communication protocols options:
+– ENABLE_ROS enables compilation with ROS support;
+– ENABLE_MQTT enables compilation with the MQTT support.
+• ENABLE_SIMULATOR and BUILD_SIMULATOR_ENGINE_SERVER options:
+– ENABLE_NEST and BUILD_NEST_ENGINE_SERVER;
+– ENABLE_GAZEBO and BUILD_GAZEBO_ENGINE_SERVER.
+The ENABLE_SIMULATOR and BUILD_SIMULATOR_ENGINE_SERVER flags allow disabling the compilation
+of those parts of nrp-core that depend on or install a specific simulator (eg. gazebo, nest).
+The expected behavior for each of these pairs of flags is as follows:
+
+5
+• the NRPCoreSim is always built regardless of any of the flags values.
+• if ENABLE_SIMULATOR is set to OFF:
+– the related simulator won’t be assumed to be installed in the system, ie. make won’t fail if it isn’t. Also it
+won’t be installed in the compilation process if this possibility is available (as in the case of nest)
+– The engines connected with this simulator won’t be built (nor client nor server components)
+– tests that would fail if the related simulator is not available won’t be built
+• if the ENABLE_SIMULATOR is set to ON and BUILD_SIMULATOR_ENGINE_SERVER is set to OFF: Same
+as above, but:
+– the engine clients connected to this simulator will be built. This means that they should not depend on or link
+to any specific simulator
+– the engine server-side components might or might not be built, depending on if the related simulator is
+required at compilation time
+• if both flags are set to ON the simulator is assumed to be installed or it will be installed from the source if this
+option is available. All targets connected with this simulator will be built.
+This flag system allows configuring the resulting NRP-Core depending on which simulators are available on the system,
+both for avoiding potential dependency conflicts between simulators and enforcing modularity, opening the possibility of
+having specific engine servers running on a different machine or inside containers.
+2.2 Introduction of basic components of simulation by NRP
+Some important elements for constructing a simulation example by the NRP platform are: Engines, Transceiver Function
+(TF) + Preprocessing Function (PF), Simulation Configuration JSON file, Simulation model file and DataPack, which are
+basic components of simulation progress. In this section, list and declare their definition, content and implementation.
+2.2.1 Engine
+Engines are a core aspect of the NRP-core framework. They run the actual simulation software (which can be comprised
+of any number of heterogeneous modules), with the Simulation Loop and TransceiverFunctions merely being a way to
+synchronize and exchange data between them. The data exchange is carried out through an engine client (see paragraph
+below). An Engine can run any type of software, from physics engines to brain simulators. The only requirement is that
+they should be able to manage progressing through time with fixed-duration time steps.
+There are different engines already implemented in NRP-Core:
+• Nest: two different implementations that integrate the NEST Simulator into NRP-core.
+• Gazebo: engine implementation for the Gazebo physics simulator.
+• PySim: engine implementation based on the Python JSON Engine wrapping different simulators (Mujoco, Opensim,
+and OpenAI) with a python API.
+• The Virtual Brain: engine implementation based on the Python JSON Engine and TVB Python API.
+and so on are provided by NRP and as the first user-interested engines for research Spiking neural Networks and the
+like. These applications are distributed to the specific simulator. This platform provides also Python JSON Engine, this
+versatile engine enables users to execute a user-defined python script as an engine server, thus ensuring synchronization
+and enabling DataPack data transfer with the Simulation Loop process. It can be used to integrate any simulator with a
+Python API in an NRP-core experiment. This feature allows users to modular develop experiment agents in constructed
+simulation world and is flexible to manage plural objects with different behaviors and characters.
+2.2.2 DataPack and Construction format
+The carrier of Information which is transported between engines and lets engines with each other communicate is DataPack.
+By NRP are there three types of supported DataPack, all of them are simple objects which wrap around arbitrary data
+structures, one is JSON DataPack, second is Protobuf DataPack and another is ROS msg DataPack. They provide the
+necessary abstract interface, which is understood by all components of NRP-Core, while still allowing the passing of data
+in various formats. DataPack is also an important feature or property of a specific Engine, meaning the parameters and
+form of data of a specific DataPack be declared in the Engine (Example see section 3.4.2).
+A DataPack consists of two parts:
+
+6
+• DataPack ID: which allows unique identify the object.
+• DataPack data: this is the data stored by the DataPack, which can be in the principle of any type.
+DataPacks are mainly used by Transceiver functions to relay data between engines. Each engine type is designed to
+accept only datapacks of a certain type and structure.
+Every DataPack contains a DataPackIdentifier, which uniquely identifies the datapack object and allows for the routing
+of the data between transceiver functions, engine clients and engine servers. A datapack identifier consists of three fields:
+• name - the name of the DataPack. It must be unique.
+• type - string representation of the DataPack data type. This field will most probably be of no concern for the users.
+It is set and used internally and is not in human-readable form.
+• engine name - the name of the engine to which the DataPack is bound.
+DataPack is a template class with a single template parameter, which specifies the type of data contained by the DataPack.
+This DataPack data can be in the principle of any type. In practice, there are some limitations though, since DataPacks,
+which are C++ objects, must be accessible from TransceiverFunctions, which are written in Python. Therefore the only
+DataPack data types which can be actually used in NRP-core are those for which Python bindings are provided. It is
+possible for a DataPack to contain no data. This is useful, for example, when an Engine is asked for a certain DataPack
+but it is not able to provide it. In this case, an Engine can return an empty DataPack. This type of Datapack contains only
+a Datapack identifier and no data. Attempting to retrieve the data from an empty DataPack will result in an exception. A
+method "isEmpty" is provided to check whether a DataPack is empty or not before attempting to access its data:
+1 if(not
+datapack.isEmpty ()):
+2
+# It’s safe to get the data
+3
+print(datapack.data)
+4 else:
+5
+# This will
+raise an exception
+6
+print(datapack.data)
+• The Format of getting DataPack from a particular Engine:
+1 # Declare
+datapack
+with "datapack_name " name from
+engine "engine_name" as
+input
+using the
+@EngineDataPack
+decorator
+2 # The
+transceiver
+function
+must
+accept an argument
+with the same name as "
+keyword" in the
+datapack
+decorator
+3
+4 @EngineDataPack (keyword="datapack", id= DataPackIdentifier (" datapack_name ",
+"engine_name"))
+5 @TransceiverFunction ("engine_name")
+6 def
+transceiver_function (datapack):
+7
+print(datapack.data)
+8
+9 # Multiple
+input
+datapacks
+from
+different
+engines
+can be declared
+10 @EngineDataPack (keyword="datapack1", id= DataPackIdentifier (" datapack_name1 "
+, "engine_name1"))
+11 @EngineDataPack (keyword="datapack2", id= DataPackIdentifier (" datapack_name2 "
+, "engine_name2"))
+12 @TransceiverFunction ("engine_name1 ")
+13 def
+transceiver_function (datapack1 , datapack2):
+14
+print(datapack1.data)
+15
+print(datapack2.data)
+PS: The details of two Decorators of TransceiverFunction see below in section 2.2.3.
+• The Format of setting information in DataPack and sending to particular Engine:
+1 # NRP -Core
+expects
+transceiver
+functions to always
+return a list of
+datapacks
+2 @TransceiverFunction ("engine_name")
+3 def
+transceiver_function ():
+4
+datapack = JsonDataPack(" datapack_name ", "engine_name")
+5
+return [ datapack ]
+6
+
+7
+7 # Multiple
+datapacks
+can be returned
+8
+9 @TransceiverFunction ("engine_name")
+10 def
+transceiver_function ():
+11
+datapack1 = JsonDataPack(" datapack_name1 ", "engine_name")
+12
+datapack2 = JsonDataPack(" datapack_name2 ", "engine_name")
+13
+14
+return [ datapack1 , datapack2 ]
+2.2.3 Transceiver Function and Preprocessing Function
+1. Transceiver Function
+Transceiver Functions are user-defined Python functions that take the role of transmitting DataPacks between engines.
+They are used in the architecture to convert, transform or combine data from one or multiple engines and relay it to another.
+The definition of a Transceiver Function must use Decorator before the user-defined “def” transceiver function, which
+means: Sending the DataPack to the target Engine:
+1 @TransceiverFunction ("engine_name")
+To request datapacks from engines, additional decorators can be prepended to the Transceiver Function, with the form
+(Attention: Receive-Decorator must be in the front of TransceiverFunction):
+1 @EngineDataPack (keyword_datapack , id_datapack)
+• keyword_datapack: user-defined new data name of DataPacks, this keyword is used as Input to Transceiver Function.
+• id_datapack: the id of from particular Engine received DataPack, “DataPack ID” = “DataPack Name” + “Engine
+Name” (Examples see 2.2.2)
+2. Preprocessing Function
+Preprocessing Function is very similar to Transceiver Function but has different usage. Preprocessing Functions are
+introduced to optimize expensive computations on DataPacks attached to a single engine. In some cases, there might be
+necessary to apply the same operations on a particular DataPack in multiple Transceiver Functions. An example of this
+might be applying a filter to a DataPack containing an image from a physics simulator. In order to allow to execute this
+operation just once and let other TFs access the processed DataPack data, PreprocessingFunctions (PFs) are introduced.
+They show two main differences with respect to Transceiver Functions:
+• Their output datapacks are not sent to the corresponding Engines, they are kept in a local datapack cache and can
+be used as input in TransceiverFunctions
+• PFs just can take input DataPacks from the Engine they are linked to
+The format of Preprocessing Function is similar to Transceiver Function:
+1 @PreprocessingFunction ("engine_name")
+2 @PreprocessedDataPack (keyword_datapack , id_datapack)
+These Decorators “@PreprocessingFunction” and “@PreprocessedDataPack” must be used in Preprocessing Functions.
+Since the output of Preprocessing Function is stored in the local cache and does not need to process on the Engine Server
+side, Preprocessing Function can return any type of DataPack without restrictions.
+2.2.4 Simulation Configuration Json file
+The details of configuration information for any simulation with Engines and Transceiver Functions are stored in a single
+JSON file, this file contains the objects of engines, Transceiver functions, and also their important necessary parameters
+to initialize and execute a simulation. This file is usually written in the “example_simlation.json” file.
+The JSON format is here a JSON schema, which is highly readable and offers similar capabilities as XML Schema.
+The advantage of composability and inheritance allows the simulation to use reference keywords to definite the agent and
+to validate inheritance by referring to other schemas. That means that the same basement of an engine can at the same
+time create plural agents or objects with only different identify IDs.
+1. Simulation Parameters
+For details, see appendix Table A.1: Simulation configuration parameter.
+2. Example form
+
+8
+1 {
+2
+" SimulationName": " example_simulation ",
+3
+" SimulationDescription ": "Launch two python
+engines. "
+4
+" SimulationTimeout ": 1,
+5
+" EngineConfigs":
+6
+[
+7
+{
+8
+"EngineType": "python_json",
+9
+"EngineName": "python_1",
+10
+" PythonFileName": "engine_1.py"
+11
+},
+12
+{
+13
+"EngineType": "python_json",
+14
+"EngineName": "python_2",
+15
+" PythonFileName": "engine_2.py"
+16
+}
+17
+],
+18
+" DataPackProcessingFunctions ":
+19
+[
+20
+{
+21
+"Name": "tf_1",
+22
+"FileName": "tf_1.py"
+23
+}
+24
+]
+25 }
+• EngineConfigs: this section list all the engines are participating in the simulation progress.
+There are some
+important parameters should be declared:
+– EngineType: which type of engine is used for this validated engine, e.g., gazebo engine, python JSON engine
+– EngineName: user-defined unit identification name for the validated engine
+– Other Parameters: These Parameters should be declared according to the type of engines (details see appendix
+Table A.2: Engine Base Parameter)
+∗ Python Json engine: “PythonFileName” – reference base python script for validated engine
+∗ Gazebo engine: see in section
+• DataPackProcessingFunctions: this section lists all the Transceiver functions validated in simulation progress.
+Mostly are there two parameters that should be declared:
+– Name: user-defined identification name for validated Transceiver Function
+– FileName: which file as reference base python script to validate Transceiver Function
+• Other Simulation Parameters: see section 2.2.4 – 1. Simulation Parameters
+• Launch a simulation: This simulation configuration JSON file is also the launch file and uses the NRP command to
+start a simulation experiment with the following command:
+1 NRPCoreSim -c user_defined_simulation_config .json
+Tip: In a user-defined simulation, the folder can simultaneously exist many different named configuration JSON files. It
+is very useful to config the target engine or Transceiver Functions that which user wants to launch and test with. To start
+and launch the target simulation experiment, just choose the corresponding configuration file.
+2.2.5 Simulation model file
+In this experiment for Autonomous driving on the NRP platform Gazebo physics simulator [5] is the world description
+simulator. For the construction of the simulation, the world can use the “SDF” file based on XML format to describe all
+the necessary information about 3D models in a file, e.g. sunlight, environment, friction, wind, landform, robots, vehicles,
+and other physics objects. This file can in detail describe the static or dynamic information of the robot, the relative
+position and motion information, the declaration of sensor or control plugins, and so on. And Gazebo is a simulator that
+has a close correlation to the ROS system and provides simulation components for ROS, so the ROS system describes
+many similar details about the construction of SDF file [6].
+According to XML format label to describe components of the simulation world and construct the dependence relation-
+ship of these components:
+
+9
+• World Label
+1 <sdf
+version=’1.7’>
+2
+<world
+name=’default ’>
+3
+........
+4
+</world >
+5 </sdf>
+All the components and their labels should be under <world> label.
+• Model Labels
+1 <model
+name=’model_name ’>
+2
+<pose >0 0 0 0 -0 0</pose >
+3
+<link name=’road map’>
+4
+.........
+5
+</link >
+6
+<plugin
+name=’link_plugin ’ filename=’NRPGazeboGrpcLinkControllerPlugin .
+so’/>
+7
+</plugin >
+8 </model >
+The Description is under label <model>, and importantly if user will use a plugin such as the control-plugin or
+sensor-plugin (camera or lidar), this <plugin> label must be set under the corresponding <model> label. Under
+<link> label describes the model physics features like <collision>, <visual>, <joint>, and so on.
+• 3-D models – mesh files
+Gazebo requires that mesh files be formatted as STL, Collada, or OBJ, with Collada and OBJ being the preferred
+formats. Blow lists the file suffixes to the corresponding mesh file format.
+Collada - .dae
+OBJ - .obj
+STL - .stl
+Tip: Collada and OBJ file formats allow users to attach materials to the meshes. Use this mechanism to improve
+the visual appearance of meshes.
+Mesh file should be declared under a needed label like <visual> or <collision> with layer structure with <geometry>
+- <mesh> - <uri> (Uri can be absolute or relative file path):
+1 <geometry >
+2
+<mesh >
+3
+<uri>xxxx/xxxx.dae</uri>
+4
+</mesh >
+5 </geometry >
+3 Simulation Construction on NRP-Core
+Based on the steps for configuring a simulation on the NRP-Core platform, the autonomous driving benchmark can now be
+implemented with the components mentioned above, from 3D models to communicating mechanisms. This section will
+introduce the requirements of the autonomous driving application, and second will analyze the corresponding components
+and their functions. The third is the concrete implementation of these requirements.
+Second, this project will also research the possibility of achieving modular development for multi-agents on the NRP
+platform, comparing it with other existing and widely used systems, and analyzing the simulation performance according
+to the progress result.
+3.1 Analysis of requirements for autonomous driving application
+An application to achieve the goal of testing the performance of autonomous driving algorithms can refer to different
+aspects. The reason is that autonomous driving can integrate different algorithms such as computer vision, object detection,
+decision-making and trajectory planning, vehicle control, or Simultaneous localization and mapping. The concept and
+final goal of the application are to build a real-world simulation that integrates multi-agents, different algorithms, and
+corresponding evaluation systems to the performance of the autonomous driving vehicle.
+But that first needs many
+available, mature, and feasible algorithms. Second, the construction of world 3D models is a big project. And last, the
+evaluation system is based on the successful operation of the simulation. So the initial construction of the application will
+focus on the base model of the communication mechanism to first achieve the communication between the single agent
+
+10
+and object-detection algorithm under the progress of NRP-Core. And for vehicle control algorithm reacts logically based
+on the object detection and generates feasible control commands, in this project will skip this step and give a specific
+trajectory, that let the vehicle along this trajectory move.
+Requirements of implementation:
+• Construction of the base model frame for communication between the Gazebo simulator, object-detection algorithm,
+and control unit.
+• Selection of feasible object-detection algorithm
+• Simple control system for autonomous movement of high accuracy physical vehicle model
+3.2 Object detection algorithm and YOLO v5 Detector Python Class
+According to the above analysis, the requirements of the application should choose an appropriate existing object detection
+algorithm as the example to verify the communication mechanism of the NRP platform and at the same time to optimize
+performance.
+On the research of existing object detection algorithms from base Alex-Net for image classification [7] and CNN-
+Convolution neural network for image recognition [8], the optimized neural network ResNet [9] and SSD neural network
+for multi-box Detector [10] and in the end the YOLOv5 neural network [11], YOLOv5 has high performance on the object
+detection and its advantage by efficient handling of frame image on real-time let this algorithm also be meaningful as a
+reference to test other object-detection algorithms. Considering the requirements of autonomous driving is YOLOv5 also
+a suitable choice as the experimental object-detection algorithm to integrate into the NRP platform.
+Table Notes:
+• All checkpoints are trained to 300 epochs with default settings and hyperparameters.
+• mAPval values are for single-model single-scale on COCO val2017 dataset. Reproduced by python val.py –data
+coco.yaml –img 640 –conf 0.001 –iou 0.65
+• Speed averaged over COCO val images using a AWS p3.2xlarge instance.
+NMS times ( 1 ms/img) not in-
+cluded.Reproduce by python val.py –data coco.yaml –img 640 –conf 0.25 –iou 0.45
+• TTA Test Time Augmentation includes reflection and scale augmentations.Reproduce by python val.py –data
+coco.yaml –img 1536 –iou 0.7 –augment
+Requirements and Environment for YOLOv5:
+• Quick link for YOLOv5 documentation : YOLOv5 Docs [12]
+• Environment requirements: Python >= 3.7.0 version and PyTorch [13] >= 1.7
+• Integration of original initial trained YOLOv5 neural network parameters, the main backbone has no changes
+compared to the initial version
+Based on the original execute-python file “detect.py” has another python file “Yolov5Detector.py” with a self-defined
+Yolov5Detector class interface written in the “YOLOv5” package. To use YOLO v5 should in main progress validate the
+YOLO v5 class, second use warm-up function “detectorWarmUp()” to initiate the neural network. And “detectImage()”
+is the function that sends the image frame to the main predict detection function and will finally return the detected image
+with bounding boxes in NumPy format.
+3.3 3D-Models for Gazebo simulation world
+According to the performance of the Gazebo is the scope of the base environment world not suitable to use a large map.
+On the basic test of different sizes of the map of Garching-area is the environment world model recommends encircling
+the area of Parkring in Garching-Hochbrück. This map model is based on the high-accuracy satellite generated and is very
+similar to the origin location. And by the simulation progress, the experimental vehicle moves around the main road of
+Parkring.
+The experimental vehicle is also a high detail modeling vehicle model with independently controllable steerings for
+diversion control of two front wheels, free front, and rear wheels, and a high-definition camera. For the rebuilding of
+these models, the belonging relationship for each mode should be declared in the SDF file. In the SDF file are these
+models including base-chassis, steerings, wheels, and camera as “Link” of the car “model” under the <model> label with a
+user-defined unique name. Attention, the name of models or links must be specific and has no same name as other objects.
+The below shows the base architecture frame to describe the physical relationship of the whole vehicle in the SDF file:
+
+11
+(a) Parkring Garching Hochbrueck high accuracy map model
+(b) Experiment vehicle for simulation
+Figure 3.1
+1 <model
+name=’smart_car ’>
+2
+<link name=’base_link ’>
+3
+.......
+4
+</link >
+5
+<link name=’eye_vision_camera ’>
+6
+.......
+7
+</link >
+8
+<joint
+name=’eye_vision_camera_joint ’ type=’revolute ’>
+9
+<parent >base_link </parent >
+10
+<child >eye_vision_camera </child >
+11
+......
+12
+</joint >
+13
+<link name=’front_left_steering_link ’>
+14
+.......
+15
+</link >
+16
+<joint
+name=’front_left_steering_joint ’ type=’revolute ’>
+17
+<parent >base_link </parent >
+18
+<child >front_left_steering_link </child >
+19
+.......
+20
+</joint >
+21
+......
+22 </model >
+1. Description of Labels [6]:
+• <link> — The corresponding model as a component from the entirety model
+• <joint> — Description of relationship between link-components
+• <joint type> — Type of the joint:
+– revolute — a hinge joint that rotates along the axis and has a limited range specified by the upper and lower
+limits.
+– continuous — a continuous hinge joint that rotates around the axis and has no upper and lower limits.
+– prismatic — a sliding joint that slides along the axis, and has a limited range specified by the upper and lower
+limits.
+– fixed — this is not a joint because it cannot move. All degrees of freedom are locked. This type of joint does
+not require the <axis>, <calibration>, <dynamics>, <limits> or <safety_controller>.
+– floating — this joint allows a motion for all 6 degrees of freedom.
+– planar — this joint allows motion in a plane perpendicular to the axis.
+• <parent>/<child> — the secondary label as element of <joint> label
+— declaration for the belonging relationship of referring “links”
+
+12
+The mesh file “vehicle_body.dae” (shown in Fig. 3.1b the blue car body) is used for the base-chassis of the experiment
+vehicle under <link name=‘base_link’> label. And the mesh file “wheel.dae” is used for the rotatable vehicle wheels
+under <link name=’ front_left_wheel_link’> and the other three similar link labels. And for steering models, <cylinder>
+labels are used to simply generate length – 0.01m + height radius 0.1m cylinder as the joint elements between wheels and
+chassis.
+2. Sensor Label:
+In the Gazebo simulator to activate the camera function, the camera model should under the “camera link” label declare
+a new secondary “sensor label” - <sensor> with “name” and “type=camera” elements. And the detailed construction for
+the camera sensor seeing blow scripts:
+1 <sensor
+name=’camera ’ type=’camera ’>
+2
+<pose >0 0 0.132 0
+-0.174 0</pose >
+3
+<topic >/smart/camera </topic >
+4
+<camera >
+5
+<horizontal_fov >1.57 </horizontal_fov >
+6
+<image >
+7
+<width >736</width >
+8
+<height >480</height >
+9
+</image >
+10
+<clip >
+11
+<near >0.1</near >
+12
+<far>100</far>
+13
+</clip >
+14
+<noise >
+15
+<type >gaussian </type >
+16
+<mean >0</mean >
+17
+<stddev >0.007 </stddev >
+18
+</noise >
+19
+</camera >
+20
+<always_on >1</always_on >
+21
+<update_rate >30</update_rate >
+22
+<visualize >1</visualize >
+23 </sensor >
+• <image> — this label defines the camera resolution ratio and this is regarded as the size of the frame-image that
+sends to the Yolo detector engine. According to the requirement of the YOLO detection algorithm, the width and
+height of the camera should be set as integral multiples by 32.
+3.4 Construction of Engines and Transceiver Functions
+Figure 3.2 the system of autonomous driving on NRP
+The construction of the whole project regards as an experiment on the NRP platform, and as an experiment, the
+whole package of the autonomous driving benchmark is under the “nrp-core” path in the examples folder. According
+to bevor announced NRP components for a simulation experiment is the application also modular developed referring
+
+YoloDetectorEngine
+Gazebo Engine
+camera Transeiver
+imageprocess
+function
+Camera frame-image
+Yolo detector class
+OpenCv
+location coordination
+state Transeiver function
+Detected
+camera
+Vehicle control Engine
+motorsettingTranseiver
+coordination transform
+joint control
+function
+trajectorycompute
+controlcommand13
+to requirements of autonomous driving benchmark application. And the whole system frame is shown in Fig. 3.2. The
+construction of simulation would according to primary embrace two branches extend:
+• A close loop from the Gazebo engine to get the location information of the vehicle and sent to the Vehicle control
+engine depending on Gazebo DataPacks (Protobuf DataPack), then send the joint control command back to the
+Gazebo engine.
+• An open loop from Gazebo engine to get camera information and sent to Yolo Detector Engine, final using OpenCV
+to show the detected frame-image as monitor window.
+3.4.1 Gazebo plugins
+Before the steps to acquire the different information must the corresponding plugins in SDF be declared. These plugins label
+are such as recognition-label to let Gazebo know what information and parameters should be sent or received and assigned.
+A set of plugins is provided to integrate the Gazebo in NRP-Core simulation. NRPGazeboCommunicationPlugin registers
+the engine with the SimulationManager and handles control requests for advancing the gazebo simulation or shutting it
+down. Its use is mandatory in order to run the engine. And there are two implementations of the Gazebo engine are
+provided. One is based on JSON over REST and another on Protobuf over gRPC. The latter performs much better and it is
+recommended. The gRPC implementation uses protobuf objects to encapsulate data exchanged between the Engine and
+TFs, whereas the JSON implementation uses nlohmann::json objects. Besides this fact, both engines are very similar in
+their configuration and behavior. The rest of the documentation below is implicitly referred to the gRPC implementation
+even though in most cases the JSON implementation shows no differences. The corresponding plugins are also based on
+Protobuf over the gRPC protocol. There are four plugins that would be applied in the SDF model world file:
+• World communication plugin – NRPGazeboGrpcCommunicationPlugin
+This plugin is the main communication plugin to set up a gRPC server and waits for NRP commands. It must be
+declared under the <world> label in the SDF file.
+1 <world
+name=’default ’>
+2 ...
+3
+<plugin
+name=" nrp_world_plugin " filename=" NRPGazeboGrpcWorldPlugin .so"/
+>
+4 ...
+5 </world >
+• Activation of Camera sensor plugin – NRPGazeboGrpcCameraPlugin
+This plugin is used to add a GazeboCameraDataPack datapack. In the SDF file, the plugin would be named
+“smart_camera” (user-defined). This name can be accessed by TransceiverFunctions and get the corresponding
+information. This plugin must be declared under <sensor> label in the application under the camera sensor label:
+1 <sensor
+name=’camera ’ type=’camera ’>
+2
+...
+3
+<plugin
+name=’smart_camera ’ filename=’
+NRPGazeboGrpcCameraControllerPlugin .so’/>
+4
+...
+5 </sensor >
+• Joint control and message – NRPGazeboGrpcJointPlugin
+This plugin is used to register GazeboJointDataPack DataPack and in this case, only those joints that are explicitly
+named in the plugin will be registered and made available to control under NRP. The joint’s name must be unique
+and once again in the plugin declared. In contrast to the other plugins described above or below, when using
+NRPGazeboGrpcJointPlugin DataPacks can be used to set a target state for the referenced joint, the plugin is
+integrated with the PID controller and can for each of the joint-specific set a better control performance.
+This plugin must be declared under the corresponding <model> label and have the parallel level in contrast to the
+<joint> label, and there are four joints that would be chosen to control: rear left and right wheel joint, front left
+and right steering joint, and according to small tests of the physical model of experiment-vehicle in Gazebo are the
+parameters of PID controller listed in below block:
+1 <model
+name=’smart_car ’>
+2
+...
+3
+<joint
+name=" rear_left_wheel_joint ">...</joint >
+
+14
+4
+<joint
+name=" rear_right_wheel_jointt ">...</joint >
+5
+<joint
+name=" front_left_steering_joint ">...</joint >
+6
+<joint
+name=" front_right_steering_joint ">...</joint >
+7
+...
+8
+<plugin
+name=’smart_car_joint_plugin ’ filename=’
+NRPGazeboGrpcJointControllerPlugin .so’>
+9
+<rear_left_wheel_joint P=’10’ I=’0’ D=’0’ Type=’velocity ’ Target=’0’
+IMax=’0’ IMin=’0’/>
+10
+<rear_right_wheel_joint P=’10’ I=’0’ D=’0’ Type=’velocity ’ Target=’0’
+IMax=’0’ IMin=’0’/>
+11
+<front_left_steering_joint P=’40000.0 ’ I=’200.0 ’ D=’1.0’ Type=’
+position ’ Target=’0’ IMax=’0’ IMin=’0’/>
+12
+<front_right_steering_joint P=’40000.0 ’ I=’200.0 ’ D=’1.0’ Type=’
+position ’ Target=’0’ IMax=’0’ IMin=’0’/>
+13
+</plugin >
+14
+...
+15 </model >
+Attention: There are two target types that can be influenced and supported in Gazebo: Position and Velocity. And
+for the rear left and right wheels of the vehicle are recommended for setting type with “Velocity” and for the front
+left and right steering are recommended setting type with “Position”. Because the actual control of the rear wheels
+is better with velocity and front steering uses angle to describe the turning control.
+• Gazebo link information – NRPGazeboGrpcLinkPlugin
+This plugin is used to register GazebolinkDataPack DataPacks for each link of the experiment vehicle. Similar to
+the sensor plugin, this plugin must be declared under <model> label and has the parallel level of <link> label, and
+only be declared once:
+1 <model
+name=’smart_car ’>
+2
+...
+3
+<plugin
+name=’smart_car_link_plugin ’ filename=’
+NRPGazeboGrpcLinkControllerPlugin .so’/>
+4
+...
+5
+<link name=’base_link ’>...</link >
+6
+<link name=’eye_vision_camera ’>...</link >
+7
+<link name=’front_left_steering_link ’>...</link >
+8
+<link name=’front_left_wheel_link ’>...</link >
+9
+<link name=’front_right_steering_link ’>...</link >
+10
+<link name=’front_right_wheel_link ’>...</link >
+11
+<link name=’rear_left_wheel_link ’>...</link >
+12
+<link name=’rear_right_wheel_link ’>...</link >
+13
+...
+14 </model >
+3.4.2 State Transceiver Function “state_tf.py”
+State Transceiver Function acquires the location information from the Gazebo engine and transmits it to Vehicle Control
+Engine to compute the next control commands. The receiving of location coordinates of the vehicle is based on the
+DataPack from Gazebo, and this DataPack is already encapsulated in NRP, it only needs to in the Decoder indicate which
+link information should be loaded in DataPack.
+1 @EngineDataPack (keyword=’state_gazebo ’, id= DataPackIdentifier (’
+smart_car_link_plugin :: base_link ’, ’gazebo ’))
+2 @TransceiverFunction ("car_ctl_engine ")
+3 def
+car_control(state_gazebo):
+The location coordinates in the experiment would be the coordinate of base-chassis “base_link” chosen and use C++
+inheritance declaration with the name of the plugin that is declared in the SDF file. And the received DataPack with the
+user-defined keyword “state_gazebo” would be sent in Transceiver Function “car_control()”.
+Attention: Guarantee to get link-information from Gazebo it is recommended new declaring on the top of the script
+with the below sentence:
+1 from
+nrp_core.data.nrp_protobuf
+import
+GazeboLinkDataPack
+
+15
+that could let NRP accurately communicate with Gazebo.
+The link-information DataPack in NRP would be called GazeboLinkDataPack. And its Attributes are listed in next
+Table 3.1. In Project are “position” and “rotation” information chosen and set to the “car_ctl_engine” engine defining Json
+DataPack, in the last “return” back to “car_ctl_engine”. Use the “JsonDataPack” function to get in other engine-defined
+DataPack and itself form and assign the corresponding parameter with received information from Gazebo.
+1 car_state = JsonDataPack(" state_location ", " car_ctl_engine ")
+2
+3 car_state.data[’location_x ’] = state_gazebo.data.position [0]
+4 car_state.data[’location_y ’] = state_gazebo.data.position [1]
+5 car_state.data[’qtn_x ’] = state_gazebo.data.rotation [0]
+6 car_state.data[’qtn_y ’] = state_gazebo.data.rotation [1]
+7 car_state.data[’qtn_z ’] = state_gazebo.data.rotation [2]
+8 car_state.data[’qtn_w ’] = state_gazebo.data.rotation [3]
+Tip: The z-direction coordinate is not necessary. So only x- and y-direction coordinates are included in DataPack to
+make the size of JSON DataPack smaller and let the transmission more efficient.
+Attribute
+Description
+Python Type
+C Type
+pos
+Link Position
+numpy.array(3, numpy.float32)
+std::array<float,3>
+rot
+Link Rotation as quaternion
+numpy.array(4, numpy.float32)
+std::array<float,4>
+lin_vel
+Link Linear Velocity
+numpy.array(3, numpy.float32)
+std::array<float,3>
+ang_vel
+Link Angular Velocity
+numpy.array(3, numpy.float32)
+std::array<float,3>
+Table 3.1 GazeboLinkDataPack Attributes.
+Tip: the rotation information from Gazebo is quaternion and its four
+parameters sort sequence is “x, y, z, w”.
+3.4.3 Vehicle Control Engine “car_ctl_engine.py”
+The Vehicle Control Engine would be written according to the form of Python Json Engine. The construction of a Python
+Json Engine is similar to the definition of a python class file that includes the attributes such as parameters or initialization
+and its functions. And a class file should declare that this Python Json Engine inherits the class “EngineScript” to let NRP
+recognize this file as a Python Json Engine to compute and execute. So a Python Json Engine can mostly be divided into
+three main blocks with def functions: def initialize(self), def runLoop(self, timestep_ns), and def shutdown(self).
+• In initialize block is the initial parameters and functions defined for the next simulation. And in this block, should the
+correspondingDataPacksthatbelongtothespecificEngineatthesametimebedefinedwith“self._registerDataPack()”
+and “self._setDataPack()” functions:
+1 self. _registerDataPack ("actors")
+2 self._setDataPack("actors", {"angular_L": 0, "angular_R": 0, "linear_L": 0,
+"linear_R": 0})
+3 self. _registerDataPack ("state_location ")
+4 self._setDataPack("state_location ", { "location_x": 0, "location_y": 0, "
+qtn_x": 0, "qtn_y": 0,"qtn_z": 0,"qtn_w": 0})
+– _registerDataPack(): - given the user-defined DataPack in the corresponding Engine.
+– _setDataPack(): - given the corresponding name of DataPack and set parameters, form, and value of the
+DataPack.
+The generated actors-control-commands and location-coordinate of the vehicle in this project would be as properties
+of the DataPack belonging to the “car_ctl_engine” Engine.
+• runLoop block is the main block that would always be looped during the simulation progress, which means the
+computation that relies on time and always need to update would be written in this block. In the “car_ctl_engine”
+Engine should always get the information from Gazebo Engine with the function “self._getDataPack()”:
+1 state = self._getDataPack(" state_location ")
+– _getDataPack(): - given the user_defined name of the DataPack
+Attention: the name must be same as the name in the Transceiver function that user-chosen DataPack which
+is sent back to Engine.
+
+16
+After the computation of the corresponding command to control the vehicle is the function “_setDataPack()” once
+again called to set the commands information in corresponding “actors” DataPack and waiting for other Transceiver
+Function to call this DataPack:
+1 self._setDataPack("actors", {"angular_L": steerL_angle , "angular_R":
+steerR_angle , "linear_L": rearL_omiga , "linear_R": rearR_omiga })
+• shutdown block is only called when the simulation is shutting down or the Engine arises errors and would run
+under progress.
+3.4.4 Package of Euler-angle-quaternion Transform and Trajectory
+• Euler-angle and quaternion transform
+The received information of rotation from Gazebo is quaternion. That should be converted into Euler-angle to
+conveniently compute the desired steering angle value according to the beforehand setting trajectory. And this
+package is called “euler_from_quaternion.py” and should be in the “car_ctl_engine” Engine imported.
+• Trajectory and Computation of target relative steering angle
+The beforehand setting trajectory consists of many equal proportional divided points-coordinate. And through
+the comparison of the present location coordinate and the target coordinate, the package would get the desired
+distance and steering angle to adjust whether the vehicle arrives at the target. If the vehicle arrives in the radius
+0.8m of the target location points will be decided that the vehicle will reach the present destination, and the
+index will jump to the next destination location coordinate until the final destination.
+This package is called
+“relateAngle_computation.py”.
+3.4.5 Actors “Motor” Setting Transceiver Function “motor_set_tf.py”
+This Transceiver Function is the communication medium similar to the state-Transceiver Function. The direction of data
+is now from the “car_ctl_engine” Engine to the Gazebo engine. The acquired data from the “car_ctl_engine” Engine is
+the DataPack “actors” with the keyword “actors”:
+1 @EngineDataPack (keyword=’actors ’, id= DataPackIdentifier (’actors ’, ’
+car_ctl_engine ’))
+2 @TransceiverFunction ("gazebo")
+3 def
+car_control(actors):
+And the DataPack from the Gazebo joint must be validated in this Transceiver Function with the “GazeboJointDat-
+aPack()” function. This function is specifically provided by Gazebo to control the joint, the given parameters are the
+corresponding joint name (declared with NRPGazeboGrpcJointPlugin plugin name in the SDF file) and target Gazebo
+engine (gazebo) (Attention: each joint should be registered as a new joint DataPack):
+1 rear_left_wheel_joint = GazeboJointDataPack (" smart_car_joint_plugin ::
+rear_left_wheel_joint ", "gazebo")
+2 rear_right_wheel_joint = GazeboJointDataPack (" smart_car_joint_plugin ::
+rear_right_wheel_joint ", "gazebo")
+3 front_left_steering_joint = GazeboJointDataPack (" smart_car_joint_plugin ::
+front_left_steering_joint ", "gazebo")
+4 front_right_steering_joint = GazeboJointDataPack (" smart_car_joint_plugin ::
+front_right_steering_joint ", "gazebo")
+The joint control DataPack is GazeboJointDataPack and its attributes are listed in Table 3.2:
+Attribute
+Description
+Python Type
+C Type
+position
+Joint angle position (in rad)
+float
+float
+velocity
+Joint angle velocity (in rad/s)
+float
+float
+effort
+Joint angle effort (in N)
+float
+float
+Table 3.2 GazeboJointDataPack Attributes.
+Attention: Guarantee to send Joint-information to Gazebo it is recommended new declaring on the top of the script
+with the below sentence:
+1 from
+nrp_core.data.nrp_protobuf
+import
+GazeboJointDataPack
+
+17
+3.4.6 Camera Frame-Image Transceiver Function “camera_tf.py”
+Camera frame-image Transceiver Function acquires the single frame image gathered by Gazebo internally installed camera
+plugin and sends this frame image to YOLO v5 Engine “yolo_detector”. The receiving of the image of the camera is based
+on the camera DataPack from Gazebo called “GazeboCameraDataPack”. To get the data, should the Decorator declare
+the corresponding sensor name with Validation through C++ and indicate the “gazebo” engine and assign a new keyword
+for the next Transceiver Function:
+1 @EngineDataPack (keyword=’camera ’, id= DataPackIdentifier (’smart_camera :: camera ’,
+’gazebo ’))
+2 @TransceiverFunction ("yolo_detector ")
+3 def
+detect_img(camera):
+Attention: Guarantee to acquire camera information from Gazebo it is recommended new declaring on the top of the
+script with the below sentence that confirms import GazeboCameraDataPack:
+1 from
+nrp_core.data.nrp_protobuf
+import
+GazeboCameraDataPack
+And received image Json-information is four parameters: height, width, depth, and image data. The Attributes of the
+GazeboCameraDataPack are listed in Table 3.3:
+Attribute
+Description
+Python Type
+C Type
+image_height
+Camera Image height
+uint32
+uint32
+image_width
+Camera Image width
+uint32
+uint32
+image_depth
+Camera Image depth.
+Number of bytes per pixel
+uint8
+uint32
+image_data
+Camera Image data.
+1-D array of pixel data
+numpy.array(image_height
+* image_width * image_depth,
+numpy.uint8)
+std::vector<unsigned char>
+Table 3.3 GazeboCameraDataPack Attributes.
+The received image data from the gazebo is a 1-D array of pixels with unsigned-int-8 form in a sequence of 3 channels.
+So this Transceiver Function should be pre-processed with NumPy “frombuffer()” function that transforms the 1-D array
+in NumPy form:
+1 imgData = np.frombuffer(trans_imgData_bytes , np.uint8)
+And in the end, validate the Json-DataPack from YOLO v5 Engine and set all information in DataPack, and return to
+YOLO v5 Engine:
+1 processed_image = JsonDataPack("camera_img", " yolo_detector ")
+2
+3 processed_image .data[’c_imageHeight ’] = trans_imgHeight
+4 processed_image .data[’c_imageWidth ’] = trans_imgWidth
+5 processed_image .data[’current_image_frame ’] = imgData
+3.4.7 YOLO v5 Engine for Detection of the Objects “yolo_detector_engine.py”
+YOLO v5 Engine acquires the camera frame image from Gazebo during the camera Transceiver Function and detects
+objects in the current frame image. In the end, through the OpenCV package, the result is shown in another window. And
+the Yolo v5 Engine is also based on the Python Json Engine model and is similar to the vehicle control Engine in section
+3.4.2. The whole structure is divided into three main blocks with another step to import Yolo v5 package.
+• Initialization of Engine with establishing “camera_img” DataPack and validation Yolo v5 object with specific
+pre-preparation by “detectorWarmUp()”:
+1 self. _registerDataPack ("camera_img")
+2 self._setDataPack("camera_img", {" c_imageHeight ": 0, "c_imageWidth": 0, "
+current_image_frame ": [240 , 320 , 3]})
+3 self.image_np = 0
+4
+5 self.detector = Yolov5.Yolov5Detector ()
+
+18
+6 stride , names , pt , jit , onnx , engine , imgsz , device = self.detector.
+detectorInit ()
+7 self.detector.detectorWarmUp ()
+• In the main loop function first step is to acquire the camera image with the “_getDataPack()” function. And the
+extracted image data from Json DataPack during the camera Transceiver Function became already again in 1-D
+“list” data form. There is a necessary step to reform the structure of the image data to fit the form for OpenCV. The
+first is to convert the 1-D array into NumPy ndarray form and, according to acquired height and width information,
+reshape this np-array. And image form for OpenCV is the default in “BGR” form, and the image from Gazebo is
+“RGB”. There is also an extra step to convert the “RGB” shaped NumPy ndarray [14]. In the last, it sends the
+original NumPy array-shaped image and OpenCV-shaped image together into detect-function and finally returns an
+OpenCV-shaped image with an object-bonding box, and this OpenCV-shaped ndarray can directly use the function
+of OpenCV showed in the window:
+1 # Image
+conversion
+2 img_frame = np.array(img_list , dtype=np.uint8)
+3 cv_image = img_frame.reshape (( img_height , img_width , 3))
+4 cv_image = cv_image [:, :, ::-1] - np.zeros_like(cv_image)
+5 np_image = cv_image.transpose (2,0,1)
+6
+7 # Image
+detection by Yolo v5
+8 cv_ImgRet ,detect ,_ = self.detector.detectImage(np_image , cv_image ,
+needProcess=True)
+9
+10 # Show of Detected
+image
+through
+OpenCV
+11 cv2.imshow(’detected
+image ’, cv_ImgRet)
+12 cv2.waitKey (1)
+4 Simulation Result and Analysis of Performance
+(a)
+(b)
+Figure 4.1 Object-detection by Yolo v5 on NRP platform (right: another frame)
+The final goal of the Autonomous driving Benchmark Platform is to build a real-world simulation platform that can
+train, do research, test or validate different AI algorithms integrated into vehicles, and next, according to the performance
+to give benchmark and evaluation to adjust algorithms, in the end to real installed these algorithms on the real vehicle.
+This project “Autonomous Driving Simulator and Benchmark on Neurorobotics Platform” is a basic and tentative concept
+and foundation to research the possibility of the simulator with multi-agents on the NRP-Core platform. And according to
+the above construction of a single vehicle agent, the autonomous driving simulation experiment has been finished. This
+section will discuss the results and suggestions based on the performance of the simulation on the NRP-Core Platform and
+the Gazebo simulator.
+
+detected Image
+traffic light 0.27
+umbrella0.69
+suitcase 0.47 plant 0.25
+truck 0.68person0.93
+person 0.89
+car0.55
+firehydrint 0.87
+x=1273.v=107)
+R:18G-13B:11detectedimage
+suitcase 0.57
+umbrella 0.69
+truck0.72
+person0.81
+firehydrant 0.8719
+4.1 Simulation Result of Object-detection and Autonomous Driving
+4.1.1 Object Detection through YOLOv5 on NRP
+The object detection is based on the visual camera from the Gazebo simulator through the Yolo v5 algorithm. NRP-Core
+is the behind transmit medium between the Gazebo and Yolo v5 detector. The simulation result is shown in Fig. 4.1.
+On the point of objects-detection, the result reaches the standard and performances well, most of the objects in the
+camera frame image has been detected, but in some different frame, the detected objects are not stable and come to
+“undetected.” And in the other hand, although most objects are correctly detected with a high confidence coefficient, e.g.,
+the person is between 80%
+93%, at the same time, there are few detected errors, such as when the flowering shrubs are
+detected as a car or a potted plant, the bush plant is detected as an umbrella and the but in front of the vehicle is detected
+as a suitcase. And last, even though the Yolo works well on the NRP platform, the performance is actually not smooth,
+and in the Gazebo simulator, the running frame rate is very low, perhaps only around 10-13 frames per second, in a more
+complex situation, the frame rate came to only 5 frames per second. That makes the simulation in Gazebo very slow and
+felled the sense of stumble. And when the size and resolution ratio of the camera became bigger, that made the stumble
+situation worse.
+4.1.2 Autonomous Driving along pre-defined Trajectory
+Autonomous driving along a pre-defined trajectory works well, the performance of simulation also runs smoothly and the
+FPS (frame pro second) holds between 20-40 fps. This FPS ratio is also in the tolerance of real-world simulation. The
+part trajectory of the experiment vehicle is shown in Fig. 4.2, and the vehicle could run around Parkring and finish one
+circle. As the first image of the experiment, the vehicle would, according to the detection result, make the corresponding
+decision to control the vehicle to accelerate or to brake down and turn to evade other obstacles. But for this project, there
+is no appropriate autonomous driving algorithm to support presently, so here only use a pre-defined trajectory consisting
+of plenty of point coordinates. The speed of the vehicle is also fixed, and using PID controller to achieve simulated
+autonomous driving.
+And on the other hand, all the 3-D models are equal in proportion to the real size of objects. After many tests of
+different sizes of the world maps, the size of Parkring is almost the limit of the Gazebo, even though the complexity of the
+map is not high. For a bigger scenario of the map, the FPS is obviously reduced, and finally, the simulation would become
+stumble and generate a sense of separation.
+(a)
+(b)
+Figure 4.2 Simulation trajectory of autonomous driving
+4.1.3 Multi-Engines united Simulation
+The final experiment is to start the Yolo v5 Engine and the autonomous driving control Engine. The above experiments
+are loaded with only one Engine, and they actually reacted well and had a relatively good performance. And the goal of
+this project is also to research the possibility of multi-agent simulation.
+The result of multi-Engines simulation actually works in that the Yolo v5 Engine can detect the image and show it
+in a window and at the same time, the vehicle can move along the trajectory automatically drive. But the simulation
+performance is not good, and the FPS can only hold between 9 -11 fps. The driving vehicle in Gazebo moves very slowly
+and not smoothly, and the simulation time has an enormous error compared to the real-time situation.
+
+20
+4.2 Analysis of Simulation Performance and Discussion
+4.2.1 YOLOv5 Detection ratio and Accuracy
+Most of the objects near the vehicle in the field of view of the camera have been detected and have high confidence, but
+there are also some errors appearing during the detection that some objects in as wrong objects are detected, some far
+objects are detected bus some obvious close objects are not detected. The reason can conclude in two aspects:
+1. The employment of the integrated Yolo v5 algorithm is the original version that is not aimed at the specific purpose
+of this autonomous driving project and has not been trained according to the specific usage. Its network parameters and
+arts of objects are original and did not use the specific self-own data set, which makes the result actually have a big error
+between the detected result and expected performance. So that makes the result described in section 4.1.1 that appears
+some detection error.
+2. The accuracy and reality of 3-D models and environment. The object detection algorithm is actually deeply dependent
+on the quality of the sent image. Here the quality is not about the resolution size but refers to the “reality” of the objects in
+the image. The original Yolo v5 algorithm was trained based on real-world images, but the camera images from Gazebo
+actually have enormous distances from real-world images. But the 3-D models and the environment in Gazebo Simulator
+are relatively very rough, and like cartoon style, they have a giant distance to the real-world objects on the side of the light,
+material texture of surface and reflection, the accuracy of objects. For example, in Gazebo, the bus has terrible texture
+and reflection that lets the bus be seen as a black box and not easy to recognize, and Yolo Engine actually detected as a
+suitcase. And the Environment in Gazebo is also not well exquisitely built. For example, the shrub and bushes on the
+roadside have a rough appearance with coarse triangles and obvious polygon shapes. That would make huge mistakes and
+influence the accuracy of desired algorithms.
+(a)
+(b)
+Figure 4.3 Distance between real-world and visual camera image
+3. The property of the Gazebo simulator. The Gazebo simulator is perhaps suitable for small scene simulations like in
+a room, a tank station, or in a factory. Comparing to other simulators on the market like Unity or Unreal, the advantage
+of Gazebo is quickly start-up to the reproduction of a situation and environment. But the upper limit of Gazebo and its
+rendering quality is actually not very close to the real world and can let people at the first time recognize this is a virtual
+simulation, which also has a huge influence on training object-detection algorithms. And the construction of the virtual
+world in Gazebo is very difficult and has to use other supported applications like Blender [15] to help the construction.
+Even in Blender, the world has a very high reality, but after the transfer to Gazebo, the rendering quality becomes terrible
+and awful.
+In fact, although detection has some mistakes and errors, the total result and performance are in line with the forecast
+that the Yolo v5 algorithm has excellent performance.
+4.2.2 Multi-Engines Situation and Non-smooth Simulation Phenomenon
+The simulation of single loaded Yolo Engine and the multi-engine meanwhile operation appear terrible performance by
+the movement of the vehicle and inferior progress FPS of the whole simulation. But simulation for single loaded vehicle
+control engine is actually working well and has smooth performance. After the comparison experiment, the main reason
+for the terrible performance is because of the backstage transmission mechanism of information between Python Json
+
+21
+Engine on the NRP Platform. In the simulation of a single loaded vehicle control Engine, the transmission from Gazebo
+is based on Protobuf-gRPC protocol, and transmission back to Gazebo is JSON protocol, but the size of transmitted
+information is actually very small because the transmitted data consists of only the control commands like “line-velocity”
+and “angular-velocity” that don’t take much transmission capacity and for JSON Protocol is actually has a negligible error
+to Protobuf Protocol. And the image transmission from Gazebo to Transceiver Function is also based on the Protobuf-
+gRPC method. But the transmission of an image from the Transceiver Function to Yolo Engine through JSON Protocol is
+very slow because the information of an image is hundreds of commands, and the according to the simulation loop in NRP,
+would make a block during the process of simulation and let the system “be forced” wait for the finish of transmission
+of the image. The transfer efficiency of JSON Protocol is actually compared to real-time slowness and tardiness, which
+takes the choke point to the transmission and, according to the test, only reduces the resolution rate of the camera to fit the
+simulation speed requirements.
+4.3 Improvement Advice and Prospect
+The autonomous driving simulator and application on NRP-Core achieve the first goal of building a concept and foundation
+for multi-agents, and at the same time, this model is still imperfect and has many disadvantages that would be improved.
+On the NRP-Core platform is also the possibility for a real-world simulator discussed, and the NRP-Core has large potential
+to achieve the complete simulation and online cooperation with other platforms. There are also some directions and advice
+for the improvement of this application presently on NRP for further development.
+4.3.1 Unhindered simulation with other communication protocol
+As mentioned before, the problem that communication with JSON protocol is the simulation at present is not smooth and
+has terrible simulation performance with Yolo Engine. Actually, the transmission of information through the Protobuf
+protocol based on the transmission between Gazebo and Transceiver Functions has an exceeding expectation performance
+than JSON protocol.
+The development Group of NRP-Core has also been developing and integrating the Protobuf-
+gRPC [16] communication backstage mechanism on the NRP-Core platform to solve the big data transmission problem.
+And in order to use Yolo or other object-detection Engines, it is recommended to change the existing communication
+protocol in the Protobuf-gRPC protocol. And the Protobuf protocol is a free and open-source cross-platform data format
+used to serialize structured data and developed by google, and details see on the official website [16].
+4.3.2 Selection of Basic Simulator with better performance
+Because of the limitation of performance and functions of the Gazebo, there are many applications that can not in Gazebo
+easy to realize, such as the weather and itself change, and the accuracy and reality of 3-D models also have limitations.
+The usage of high-accuracy models would make the load became heavier on the Gazebo because of the fall behind the
+optimization of the Gazebo simulator. In fact, there are many excellent simulators, and they also provide many application
+development packages that can shorten the development period, such as Unity3D [17] or Unreal engine simulator [18]. In
+the team of an autonomous driving simulator and the benchmark there is an application demo on Unity3D simulator and
+figure Fig. 4.4 shows the difference between Gazebo and Unity3D.
+The construction and simulation in Unity3D have much better rendering quality close to the real world than Gazebo, and
+the simulation FPS can maintain above 30 or even 60 fps. And for the YoloV5 detection result, according to the analysis
+in section 4.2.1, the result by Unity3D is better than the performance by Gazebo simulator because of more precision
+3-D models and better rendering quality of models (Example see Fig. 4.5). The better choice for the development as
+the basic simulator and world expresser is recommended to develop on Unity3D or other game engines. And actually,
+NRP-Core will push a new version that integrates the interfaces with Unity3D and could use Protobuf protocol to ensure
+better performance for a real-world simulation.
+4.3.3 Comparing to other Communication Systems and frameworks
+There are also many communication transmission frameworks and systems that are widely used in academia or business
+for robot development, especially ROS (Robot Operating System) system already has many applications and development.
+Actually, ROS has already been widely and mainly used for Robot-development with different algorithms: detection
+algorithm and computer vision, SLAM (Simultaneous Localization and Mapping) and Motion-control, and so on. ROS
+has already provided relatively mature and stable methods and schemes to undertake the role of transmitting these necessary
+data from sensors to the robot’s algorithms and sending the corresponding control command codes to the robot body or
+actors. But the reason chosen NRP-Core to be the communication system is based on the concepts of Engines and
+Transceiver Functions. Compared to ROS or other framework NRP platform has many advantages: This platform is very
+easy to build multi-agents in simulation and conveniently load in or delete from the configuration of simulation; The
+
+22
+(a) Sunny
+(b) Foggy
+(c) Raining
+(d) Snowy
+Figure 4.4 Construction of simulation world in Unity3D with weather application
+(a) Detection by YOLOv5 on Gazebo
+(b) Detection by YOLOv5 on Unity3D
+Figure 4.5 Comparing of the detection result by different platforms
+management of information is easier to identify than ROS-topics-system; The transmission of information is theoretically
+more efficient, and modularization and this platform can also let ROS at the same time as parallel transmission method to
+match and adapt to another systems or simulations. From this viewpoint, the NRP platform generalizes the transmission of
+data and extends the boundary of the development of the robot, which makes the development more modular and efficient.
+ROS system can also realize the multi-agents union simulation but is not convenient to manage based on the "topic" system.
+ROS system is now more suitable for a single agent simulation and the simulation environment. As mentioned before,
+the real interacting environment is not easy to realize. But NRP-Core has the potential because that NRP-Core can at the
+same time run the ROS system and let the agent developed based on the ROS system easily join in the simulation. That is
+meaningful to develop further on the NRP-Core platform.
+5 Conclusion and Epilogue
+This project focuses on the first construction of the basic framework on the Neurorobotics Platform for applying the
+Autonomous Driving Simulator and Benchmark. Most of the functions including the template of the autonomous driving
+function and object-detection functions are realized. The part of the benchmark because there are no suitable standards
+and further development is a huge project regarded as further complete development for the application.
+
+umbre
+umbrella 0.69
+suitcase0.57
+truck 0.72
+person 0.85
+00tedpldnt0.4truck0.49
+person 0.81
+fire hydrant 0.87OGGY1
+Burger:Queen
+KSC23
+This project started with researching the basic characters to build a simulation experiment on the NRP-Core Platform.
+Then the requirements of the construction of the simulation are listed and each necessary component and object of the
+NRP-Core is given the basic and key understanding and attention. The next step according to the frame of the NRP-Core
+is the construction of the application of the autonomous driving simulator. Started with establishing the physic model of
+the vehicle and the corresponding environment in the SDF file, then building the “close loop” - autonomous driving based
+on PID control along the pre-defined trajectory and finally the “open loop” – objects-detection based on YoloV5 algorithm
+and successfully achieve the goal to demonstrate the detected current frame image in a window and operated as camera
+monitor. And at last, the current problems and the points of improvement are listed and discussed in this development
+document.
+And at the same time there are also many problems that should be optimized and solved. At present the simulation
+application can only regard as research for the probability of the multi-agent simulation. The performance of the scripts
+has a lot of space to improve, and it is recommended to select a high-performance simulator as the carrier of the real-world
+simulation. In fact the NRP-Core platform has shown enormous potential for the construction of a simulation world with
+each object interacting function and the high efficiency to control and manage the whole simulation project. In conclusion
+the NRP-Core platform has great potential to achieve the multi-agents simulation world.
+References
+[1] Alexey Dosovitskiy, German Ros, Felipe Codevilla, Antonio Lopez, and Vladlen Koltun. CARLA: An open urban
+driving simulator. In Proceedings of the 1st Annual Conference on Robot Learning, pages 1–16, 2017.
+[2] Shital Shah, Debadeepta Dey, Chris Lovett, and Ashish Kapoor. Airsim: High-fidelity visual and physical simulation
+for autonomous vehicles. In Field and Service Robotics, 2017.
+[3] PTV Group. Ptv vissim. https://www.ptvgroup.com/en/solutionsproducts/ptv-vissim/.
+[4] Human Brain Project. Neurorobotics platform. https://neurorobotics.net/.
+[5] Nathan Koenig and Andrew Howard. Design and use paradigms for gazebo, an open-source multi-robot simulator.
+In 2004 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)(IEEE Cat. No. 04CH37566),
+volume 3, pages 2149–2154. IEEE, 2004.
+[6] ROS Wiki. urdf/xml. https://wiki.ros.org/urdf/XML.
+[7] Alex Krizhevsky, Ilya Sutskever, and Geoffrey E Hinton. Imagenet classification with deep convolutional neural
+networks. Communications of the ACM, 60(6):84–90, 2017.
+[8] Karen Simonyan and Andrew Zisserman. Very deep convolutional networks for large-scale image recognition. arXiv
+preprint arXiv:1409.1556, 2014.
+[9] Kaiming He, Xiangyu Zhang, Shaoqing Ren, and Jian Sun. Deep residual learning for image recognition. In
+Proceedings of the IEEE conference on computer vision and pattern recognition, pages 770–778, 2016.
+[10] Wei Liu, Dragomir Anguelov, Dumitru Erhan, Christian Szegedy, Scott Reed, Cheng-Yang Fu, and Alexander C
+Berg. Ssd: Single shot multibox detector. In European conference on computer vision, pages 21–37. Springer, 2016.
+[11] G Jocher, K Nishimura, T Mineeva, and R Vilarino. Yolov5 by ultralytics. Disponıvel em: https://github. com/ultr-
+alytics/yolov5, 2020.
+[12] Yolov5 documentation. https://docs.ultralytics.com/.
+[13] Adam Paszke, Sam Gross, Francisco Massa, Adam Lerer, James Bradbury, Gregory Chanan, Trevor Killeen, Zeming
+Lin, Natalia Gimelshein, Luca Antiga, et al. Pytorch: An imperative style, high-performance deep learning library.
+Advances in neural information processing systems, 32, 2019.
+[14] G. Bradski. The OpenCV Library. Dr. Dobb’s Journal of Software Tools, 2000.
+[15] Blender Online Community. Blender - a 3D modelling and rendering package. Blender Foundation, Stichting
+Blender Foundation, Amsterdam, 2018.
+[16] Kenton Varda. Protocol buffers: Google’s data interchange format. Technical report, Google, 6 2008.
+[17] Unity Technologies. Real-time 3d tools and more. https://unity.com/.
+[18] Epic Games. Unreal engine. https://www.unrealengine.com/.
+A Appendix
+
+24
+Name
+Description
+Type
+Default
+Array
+Values
+SimulationLoop
+Type of simulation loop used in
+the experiment
+enum
+"FTILoop"
+"FTILoop"
+"EventLoop"
+SimulationTimeout
+Experiment Timeout (in
+seconds). It refers to simulation
+time
+integer
+0
+SimulationTimestep
+Time in seconds the simulation
+advances in each Simulation
+Loop. It refers to simulation
+time.
+number
+0.01
+ProcessLauncherType ProcessLauncher type to be used
+for launching engine processes
+string
+Basic
+EngineConfigs
+Engines that will be started in
+the experiment
+EngineBase
+X
+DataPackProcessor
+Framework used to process and
+rely datapack data between
+engines. Available options are
+the TF framework (tf) and
+Computation Graph (cg)
+enum
+"tf"
+"tf", "cg"
+DataPackProcessing-
+Functions
+Transceiver and Preprocessing
+functions that will be used in the
+experiment
+TransceiverFunction
+X
+StatusFunction
+Status Function that can be used
+to exchange data between NRP
+Python Client and Engines
+StatusFunction
+ComputationalGraph
+List of filenames defining
+the ComputationalGraph that
+will be used in the experiment
+string
+X
+EventLoopTimeout
+Event loop timeout (in seconds).
+0 means no timeout. If not
+specified ’SimulationTimeout’
+is used instead
+integer
+0
+EventLoopTimestep
+Time in seconds the event loop
+advances in each loop. If not
+specified ’SimulationTimestep’
+is used instead
+number
+0.01
+ExternalProcesses
+Additional processes that will
+be started in the experiment
+ProcessLauncher
+X
+ConnectROS
+If this parameter is present a
+ROS node is started by
+NRPCoreSim
+ROSNode
+ConnectMQTT
+If this parameter is present an
+MQTT client is instantiated and
+connected
+MQTTClient
+Table A.1 Simulation configuration
+
+25
+Name
+Description
+Type
+Default
+Required Array
+EngineName
+Name of the engine
+string
+X
+EngineType
+Engine type. Used
+by EngineLauncherManager to
+select the correct engine launcher
+string
+X
+EngineProcCmd
+Engine Process Launch command
+string
+EngineProcStartParams
+Engine Process Start Parameters
+string
+[ ]
+X
+EngineEnvParams
+Engine Process Environment
+Parameters
+string
+[ ]
+X
+EngineLaunchCommand
+LaunchCommand with parameters
+that will be used to launch the
+engine process
+object
+"LaunchType":
+"BasicFork"
+EngineTimestep
+Engine Timestep in seconds
+number
+0.01
+EngineCommandTimeout
+Engine Timeout (in seconds). It
+tells how long to wait for the
+completion of the engine runStep.
+0 or negative values are interpreted
+as no timeout
+number
+0.0
+Table A.2 Engine Base Parameter
+

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+Fibrous thermoresponsive Janus membranes for directional 
+vapor transport 
+Anupama Sargur Ranganatha, Avinash Bajia,b, Giuseppino 
+Fortunatoc, René M. Rossic 
+aPillar of Engineering Product Development, Singapore University of Technology and 
+Design, Singapore 487372 
+bManufacturing Engineering, LA TROBE University, Melbourne Victoria 3086, Australia 
+c Empa, Swiss Federal Laboratories for Materials Science and Technology, Laboratory for 
+Biomimetic Membranes and Textiles, CH-9014 St. Gallen, Switzerland 
+Abstract  
+Wearing comfort of apparel is highly dependent on moisture management and the 
+respective transport properties of the textiles. In today’s used textiles, water vapor 
+transmission (WVT) depends primarily on the porosity and the wettability of the clothing 
+layer next to the skin and is not adapting or responsive to environmental conditions. The 
+WVT is inevitably the same from both sides of the membrane. We propose a novel 
+approach in this study by developing a thermoresponsive Janus membrane using 
+electrospinning procedures. We targeted a membrane as a bilayer composite structure using 
+polyvinylidene fluoride (PVDF) as one layer and a blend of PVDF and thermoresponsive 
+poly-n-isopropyl acrylamide (PNIPAM) as the second layer changing wettability 
+properties in the range of physiological temperatures. Tailored electrospinning conditions 
+led to a self-standing membrane incorporating fiber diameters of 400nm and porosities of 
+50% for both layers within the Janus membrane. The WVT studies revealed that the 
+combined effects of the Janus membrane’s directional wettability and the temperature-
+responsive property results in temperature-dependent vapor transport. The results show 
+that the membrane offers minimum resistance to WVT when the PVDF side faces the skin, 
+which depicts the side with high humidity over a range of temperatures. However, the same 
+membrane shows a temperature-dependent WVT behavior when the blend side faces the 
+skin. From a room temperature of 25 °C to an elevated temperature of 35 °C, there is a 
+significant increase in the membrane’s resistance to WVT. This behavior is attributed to 
+the combined effect of the Janus construct and the thermoresponsive property.  
+This temperature-controlled differential vapor transport offers ways to adapt vapor 
+transport independence of environmental conditions leading to enhanced wearing comfort 
+and performance to be applied in fields such as apparel or the packaging industry.  
+Introduction 
+Tailored protective clothing is one of the oldest but actively researched fields for improving 
+textiles' performance and comfort of textiles.1, 2 The practical end-use include firefighter 
+protection clothing, diver’s, and space suit as well as raincoats, etc., drive the research in 
+protective clothing. Typically, a wearer expects the garment to be functional and 
+comfortable for the required end-use. 
+
+Sweat and heat transport of apparel describe the thermal comfort aspect,3 which is a 
+tradeoff between the performance and comfort properties of the clothing4. For example, 
+rain ponchos have one of the best waterproof abilities as they are impermeable to water but 
+uncomfortable to wear as the sweat cannot diffuse. Modern apparels employ a combination 
+of novel chemistry and material structure to attain performance and comfort.5-9 Even 
+though the performance levels have improved from what it was decades ago, the comfort 
+aspect still depends on the surrounding environment. Other than the touch, which is a 
+qualitative factor, sweat transport, measured by water vapor transmission (WVT) across 
+the fabric, is considered a quantitative measure of comfort in apparel. In a practical 
+scenario, sweat transmission combines water and vapor transport, depending on the 
+person’s activity level. Liquid sweat transmission is required during a person’s high 
+activity level. In contrast, vapor transmission is needed during all activity levels of a person 
+and is considered a measure of the fabric’s comfort. It is often reported as a measure of 
+comfort for the new material systems.10-12  
+WVT is primarily driven by the partial vapor pressure difference across the membrane and 
+usually follows Fick’s law of diffusion when a system is in a steady state. The temperature 
+and humidity of the local environment govern the partial vapor pressure as expressed in 
+Eq. 1. Therefore, WVT is achieved much better in arid 13 compared to humid regions. 
+������������������������ =
+������������∗6.11∗ ������������(17.67∗
+������������
+������������+243.6)
+100
+  
+ 
+ 
+ 
+ 
+ 
+ 
+(1) 
+Free water vapor diffusion is often insufficient to increase comfort in humid regions, and 
+forced ventilation is required to pump out the sweat. Attaching devices to circulate the air 
+to remove sweat is cumbersome and practically inconvenient. Therefore, research on a 
+material that can steer, adapt, and respond to environmental changes and pump out liquid 
+sweat without external support is essential. 
+Electrospun fibrous membranes exhibit good water vapor permeability and wind 
+resistance. Gibson et al. reported that the water vapor quickly diffuses out through the 
+electrospun membrane due to the large porosity of the electrospun membrane. On the other 
+side, the large surface area of the nanofibrous layer resists convective wind flow.14 
+Furthermore, to improve the performance, electrospun membranes from selected polymers 
+such as polyacrylonitrile (PAN) and polyurethane (PU) were modified to enhance their 
+tensile stress and breaking elongation %, waterproof ability with tailored vapor 
+permeability.15-17 Selected studies evaluated the vapor permeability of multilayered 
+membranes18, a combination of electrospun and woven textiles19, and electrospinning of 
+hydrophilic/hydrophobic layers.20 Multilayered membrane samples investigated by 
+Mukhopadhyay et al.18 showed that the water vapor transmittance is dependent on the 
+porosity and pore size of the middle layer of polyester fleece/polyester spacer, even when 
+the porosity of the innermost and outermost layers is constant in all the tested samples. 
+Therefore, the multilayer system, which had a highly porous middle layer, exhibited larger 
+WVT due to increased overall porosity. Investigation of the woven fabric coated with an 
+electrospun fibrous mat by Bagherzadeh et al. 19 showed that the electrospun layer did not 
+impede the water vapor permeability of the woven fabric. In another investigation of the 
+multilayer electrospun membrane by Gorji et al.20 they revealed the effect of incorporating 
+graphene oxide in the hydrophilic matrix, which is layered adjacent to a polyurethane 
+
+fibrous membrane. The water vapor permeability reduced with higher hydrophilic layer’s 
+weight. Increasing graphene oxide content from 0.1 to 0.4% in the acrylamide-based 
+hydrophilic polymer, reduced the water solubility of the polymer and consequently 
+increasing the water vapor permeability. However, studies on multi-layer systems did not 
+investigate the direction of the vapor transmission across the thickness of the membranes. 
+As previous studies revealed that the vapor diffusion through the microporous membrane 
+is porosity dependent, the vapor transmission from either side of the membrane along its 
+thickness is assumed to be constant.  
+Introducing heterogeneity in the membrane chemistry across the thickness, without altering 
+the porosity, exhibits directionality in the membrane’s properties. E.g., combining 
+hydrophobic and hydrophilic material in layers within a single membrane exhibits 
+directional water flow. Such membranes, with faces of different chemistry, are termed 
+Janus membranes21, 22. These membranes have attracted high attention from researchers. In 
+one such system, the water drops flow from the hydrophobic side to the hydrophilic side 
+but not from the hydrophilic to the hydrophobic side. The flow from the hydrophobic side 
+is due to the hydrophilic layer underneath the hydrophobic, which pulls the droplet across 
+the membrane. The Laplace pressure difference, along with the thickness of the membrane, 
+explains this  mechanism.23 
+Another class of materials, i.e., environmentally responsive polymers, such as poly N-
+(isopropylacrylamide), are termed ‘smart’ due to their switchable properties in response to 
+environmental cues.24 Figure 1 shows the change in molecular conformation of PNIPAM 
+concerning the environmental temperature. At room temperature, the carbonyl and amide 
+groups of PNIPAM are exposed to form a hydrogen bond with the surrounding water vapor. 
+However, at elevated temperatures, the hydrogen bonds break and cause intramolecular 
+bonding between carbonyl and amide groups from adjacent monomer units. This coil 
+conformation is relatively hydrophobic compared to the extended conformation at room 
+temperature, being hydrophilic.25-27  
+The PNIPAM-based hydrogel can be coated on textiles like cotton or nylon 6 fabrics and 
+exhibit thermoresponsive behavior. The WVT studies by Stular et al., and Verbič et al. 
+show less vapor transmission at ambient temperature in comparison with WVT at an 
+elevated temperature of 40 °C. The swelling of PNIPAM reduces the porosity and, in turn, 
+reduces the vapor transmission at ambient temperature  
+Independent research on responsive materials,24, 28, 29 and Janus constructs30-32 shows high 
+potential for smart and self-sustaining systems with directional liquid transport. Our current 
+study shows the result of combining responsive material such as PNIPAM in a Janus 
+construct. PNIPAM is blended with PVDF in a 25:75 wt% ratio to minimize the effect of 
+swelling and retain the thermoresponsive behavior. The blend and pristine PVDF are 
+electrospun in layers to obtain a Janus construct. Consequently, the electrospun Janus 
+membrane has PVDF on one face and a blend on the other. We use two independent 
+experimental approaches to assess and confirm the WVT performance of the membrane. 
+For the first time in literature, we show that WVT is preferentially more in one direction 
+within a given membrane. The directionality is plausibly due to the ‘passive pumping’ 
+action of the Janus membrane, combined with the thermoresponsive property of the 
+hydrophilic layer. 
+
+ 
+ 
+Figure 1: Shows the change in the molecular conformation of poly N-(isopropyl acrylamide) 
+in response to the change in the environmental temperature. 
+Materials and methods 
+Materials 
+PVDF pellets with a molecular weight of 180000 g/mol and 530000 g/mol powder were 
+procured from Sigma-Aldrich, Switzerland. PNIPAM powder with a molecular weight of 
+300000 g/mol was purchased from Scientific Polymer Products Inc. N, N-
+dimethylformamide (DMF, 99.5 %) from Sigma-Aldrich Switzerland. 
+ 
+Methods 
+Membrane fabrication  
+The PVDF solutions were prepared by dissolving 33 wt% of PVDF (180000 g/mol) pellets 
+in DMF at 60 ºC overnight. The blend solutions were prepared by dissolving 18 wt% of 
+the polymer mixture, i.e., PVDF (530000 g/mol) and PNIPAM (300000 g/mol) in 75/25 
+w/w ratio in DMF, and magnetically stirred at 60 ºC on a hot plate overnight and 
+subsequently cooled to room temperature before electrospinning.  
+ 
+Needle-based electrospinning  
+PVDF solution or the blend solution was loaded in a plastic syringe with a 21G blunt needle 
+(0.8 mm inner diameter). The flow rate of the polymer solution was set to 0.5ml*h-1 using 
+a flow pump. The needle tip was connected to a voltage of 10kV and the collector plate to 
+a voltage of -5kV. The working distance between the needle and the flat plate aluminum 
+collector was 12 cm. The aluminum collector was covered with silicone paper for easy 
+peeling off the electrospun membranes. 
+
+TA2C
+ConLcooo aboe TcsNeedle-less electrospinning (NanospiderTM) 
+NanospiderTM (Elmarco, Czech Republic) is a needle-less electrospinning technology with 
+upscaling capability. Figure 1 shows a schematic of the procedure. The following spinning 
+parameters were used for homogenous spinning: The vertical gap between the two wires 
+was 25 cm, wherein the top wire was applied with a voltage of +60 kV and the bottom wire 
+with -10 kV. The traversing carriage, with a speed of 270 mm/s on the bottom wire, housed 
+a pinhole of 0.5 mm, which controls the volume of polymer solution trailed on the bottom 
+wire. The collector paper moving at a speed of 18 mm/min, is placed right below the top 
+wire 
+After 20 minutes of electrospinning, the paper position is unrolled to the starting point to 
+electrospin in the same area. Five such repetitions build a thick and wide membrane with 
+a surface area of 500 mm2. The fabrication of the blend and PVDF layer followed the same 
+procedure. Four Janus membranes were prepared and tested for water-vapor resistances 
+using the sweating guarded hotplate, elaborated in the following sections. 
+ 
+Figure 2: Needle-less electrospinning setup used to develop sub-micron-sized fibers at 
+the pilot-scale level.  
+A carriage with polymer solution traverses the bottom metallic wire (+60 kV) and leaves 
+a trail of the solution droplets on this wire. The potential difference between the wires 
+draws the fibers from these droplets. The silicone paper collects the fibers placed right 
+below the top metallic wire (-10 kV). 
+ 
+ Material characterization 
+ 
+The viscosity of the polymer solutions was evaluated using a Physica MCR301 Rheometer 
+(Anton P, Graz, Austria) with a plate-cone geometry. The shear viscosity of the polymer 
+solutions was assessed as a function of the shear rate. The spinning solution's electrical 
+
+conductivity was measured using Metrohm 660, Switzerland. The electrospun membranes 
+were visually examined using scanning electron microscopy (SEM) by a Hitachi S-4800, 
+Hitachi High-Technologies, USA & Canada) using 2 kV accelerating voltage and 10 mA 
+current flow. Before the SEM measurements, the samples were sputtered with 8nm of Au-
+Pd to increase the conductivity using a sputter coater, Leica EM ACE600, Leica 
+Microsystems, Germany. 
+ 
+Sweating guarded hotplate 
+ 
+The sweating guarded-hotplate to determine the resistance of the membrane to WVT 
+follows ISO 1109233. It is often referred to as the “skin model” as it simulates the heat and 
+vapor transfer processes next to the skin. Primarily, it consists of an electrically heated 
+porous plate to simulate the thermoregulation model of the skin (Figure 2). Heat loss is 
+avoided by using the guard underneath and on both sides of the hot plate. At the same time, 
+the guards are heated to the same temperature as the porous plate. The water-circulating 
+system feeds the heated plate to produce the vapor by evaporation. The system underneath 
+the plate measures the heating power required to maintain the temperature of the plate. The 
+measurement is carried out in a controlled environment as it involves temperature, relative 
+humidity, and wind speed combinations. 
+ 
+Figure 3: Schematic of the sweating hot plate instrument. a) is the photographic image 
+of the device. b) shows the airflow tangential to the mounted test sample. c) shows the 
+parts in layers. The circulation pump supplies the water to the electrically heated and 
+porous plate for evaporation. Cellophane is a waterproof but vapor permeable layer to 
+transmit the evaporating vapor from the plate. The test membrane lays flat on the 
+cellophane covered heated plate and is held in place by a frame on all sides. 
+The membrane is placed on an electrically heated plate, covered with a saturated 
+cellophane sheet permeable to vapor but impermeable to water. Air is tangentially blown 
+across the membrane surface to maintain a constant vapor pressure gradient. This setup 
+permits only the vapor from the plate to pass through the fibrous membrane and prevents 
+the water from wetting the fibrous membrane. The heat flux required to maintain the 
+saturated vapor pressure is a measure of the membrane’s resistance to vapor permeability. 
+The expression for the resistance to vapor permeability is as follows: 
+������������������������������������ =
+[������������������������−������������������������]
+������������−∆������������������������    
+(2) 
+������������������������������������: Water-vapor resistance in ������������2������������������������ ������������
+⁄
+ 
+
+a)������������������������: The saturation water-vapor partial pressure in Pascal (Pa), at the surface of the heated 
+plate at a temperature in ºC 
+������������������������: The water-vapor partial pressure in Pa of the air in the test enclosure with air 
+temperature in ºC 
+������������: Heating power supplied to the measuring unit in W 
+∆������������������������: Baseline error correction term for heating power for the measurement of water-vapor 
+resistance ������������������������������������, used as a reference value for ambient conditions.  
+The boundary layer resistance of the cellophane layers is the baseline measurement of the 
+system. The software deducts the resistance of the boundary layer from the experiment 
+results for subsequent measurements. Thus, the instrument directly calculates the resistance 
+offered by the fibrous membranes. 
+OptiCal double-chamber method 
+OptiCal from Michell Instruments is a relative humidity (RH) and temperature calibrator 
+that uses an optical sensor for high-precision measurements. It is used to design a setup 
+that determines the WVT of the membrane. Figure 4 shows the setup schematic, which 
+consists of a temperature-controlled chamber with a sealed container for the test membrane. 
+A reservoir draws water from a tube placed on the weighing scale to maintain its level to 
+ensure a controlled RH. A climatic chamber with controlled temperature and RH houses 
+the entire setup. A computer-connected software controls the environmental conditions. In 
+parallel, another software records the weighing scale measurements, i.e., the weight 
+reduction due to water flow into the OptiCal chamber is directly associated with vapor 
+diffusion through the membrane 
+ 
+Figure 4: Schematic of the double chamber setup. 
+Measurement of water vapor permeability started after the stabilization of the 
+environmental conditions. The water vapor passes through the membrane (∅ = 0.06 m) 
+
+Test conditions:
+1. Below LCST
+Climatic chamber
+a.
+Inside: 30 °C & 80% RH
+Outside
+Outside: 30 °C & 40% RH
+b.
+Inside: 20 °C & 80% RH
+Outside: 30 °C & 40% RH
+Inside
+Membrane
+Above LCST
+Inside: 40 °C & 60% RH
+Outside: 30 °C & 40% RH
+Membrane orientation:
+OptiCal calibrator
+ET: External sensor for temperature and RH
+IT: Internal sensor for temperature and RHfrom the OptiCal chamber. As the RH in the OptiCal chamber drops, water from the 
+reservoir is evaporated to maintain the desired RH. The water from the tube on the scale 
+flows to the reservoir to maintain the water level in the reservoir. The reduced amount of 
+water from the tube is weighed by scale, and the weight loss is recorded in real-time. Water 
+vapor permeance is the weight loss over a defined period for a unit partial vapor pressure 
+difference across the membrane. The environmental conditions between the inside and 
+outside instruments govern this partial vapor pressure difference. An external RH and 
+temperature sensor from MSR® with a built-in data logger measured the test conditions 
+outside the membrane surface. 0.05” thermocouple wires were embedded into the fibrous 
+membranes to record the actual temperature at the surface and the interface of two layers 
+of the Janus membrane. The expression for the partial vapor pressure as a function of 
+temperature and humidity is given by following equations34, 35. 
+������������������������ =
+������������∗6.11∗ ������������(17.67∗
+������������
+������������+243.6)
+100
+  
+(3) 
+������������������������ is the partial pressure, H is the humidity in %, and T is the temperature in °C. 
+������������������������������������ =
+������������
+������������ ∗ (������������������������������������− ������������������������������������������������)∗������������ 
+(4) 
+WVP is the water vapor permeability in g/(ℎ ∗ ������������2*mbar), W is the water loss in grams, t 
+is the time in hours, ������������������������������������������������ − ������������������������������������������������������������ is the water vapor partial pressure difference in mbar 
+between inside and outside conditions, A is the membrane area in ������������2. 
+Figure 4 lists the testing condition of the experiments. It was possible to maintain 
+isothermal conditions in the system below the lower critical solution temperature (LCST). 
+As the recommended operating temperature of the OptiCal was less than 30 °C, it was 
+not possible to maintain isothermal conditions above LCST. However, to ensure that the 
+membrane is above LCST and to minimize the thermal gradients, the constant 
+temperature condition of 30 °C and 40 °C are maintained outside and inside the chamber, 
+respectively. 
+ 
+Results and discussion 
+The electrospun membrane with Janus construct was fabricated using a needle-less and 
+needle-based electrospinning setup (see Table 1). The needle-based electrospinning setup 
+allowed us to incorporate the thermocouples between the layers and just below the surface. 
+Therefore, the precise measurement of surface temperature and that between the layers was 
+precisely measured for the double-chamber method. These measured temperatures were 
+used to calculate the vapor pressure gradient across the membrane.  
+The PVDF solution was electrospun on top of the electrospun blend membrane to produce 
+a two-layered Janus construct. The blend solution with a concentration of 16 wt% had a 
+shear viscosity of 2.38 Pa.s under a shear of 1/10 s and a conductivity of 5.16 μs/cm. 
+Similarly, the shear viscosity of the PVDF solution is 1.2 Pa.s and a conductivity of 32 
+μs/cm. The SEM examination shows a smooth fiber morphology with a diameter of 0.2-
+
+0.4 μm for needle-less electrospun fibers and 0.2-0.6 μm for needle based electrospun 
+fibers. These values indicate no dimensional difference between the fibrous web produced 
+by needle based or needle-less electrospinning methods. The specific weight of the Janus 
+membranes is 30-40 GSM, a lightweight fabric category. However, in electrospun or thin-
+film membranes, this weight range indicates a heavyweight membrane suitable for 
+practical applications36. 
+  Table 1: Polymeric solution parameters and their corresponding electrospun membrane 
+properties. 
+ 
+Polymer (MW, Da) 
+Wt% (w/w) 
+Shear 
+viscosity 
+Pa.s, (at 
+1/10 s) 
+Conductivity, 
+μs/cm 
+Duration, 
+no of cycles 
+of 20min 
+each 
+Fiber 
+diameter, 
+nm 
+Thickness, 
+μm 
+Porosity, % 
+PVDF(530K)/PNIPAM 
+(330K)(75/25) 
+18 
+2.4 
+5.16 
+5 
+502 ± 193.8 
+103.3 ± 5.4 
+49.7 ± 1.8 
+PVDF (180K) 
+30 
+1.2 
+32 
+3 
+139.2 ± 76.2 
+67.7 ± 4.7 
+49.6 ± 3.3 
+ 
+ 
+
+um
+5
+um
+5μm
+5μm
+5μm
+5μm
+nS
+5μmFigure 5: SEM micrographs of the four Janus membranes prepared using needle-less 
+electrospinning. Blend fibers are relatively more uniform in comparison to PVDF fibers, which 
+have a bimodal distribution of fiber diameter. GSM refers to the membrane weight in grams 
+per square meter. I to IV are the Janus samples electrospun for measuring WVT 
+Figure 6 shows the surface elemental composition by X-ray photoelectron spectroscopy 
+(XPS) for PNIPAM, PVDF, and their blend. Comparing the blend with respective pristine 
+counterparts reveals that the blend surface is enriched with Nitrogen and Oxygen, which is 
+like PNIPAM fibers. The XPS results confirm the observations from our previous study on 
+the thermoresponsive wettability of PNIPAM/PVDF blends fabricated using needle-based 
+electrospinning29. The Thermal characterization using DSC and TGA suggested the phase 
+separation of PNIPAM and PVDF during electrospinning. At the same time, the wettability 
+switch observed by contact angle measurement at room temperature and elevated 
+temperature suggested PNIPAM enriching the fiber surface29. 
+A comparison of density and solubility parameters in Table 2 favors the dissolution of 
+PNIPAM in DMF over PVDF. Therefore, the evaporation of DMF during the 
+electrospinning process supports the migration of PNIPAM to the fiber surface, lasting 
+longer in solution. Our previous study on this blend suggests miscibility when the PNIPAM 
+content is 50 wt% or above29. However, when the PNIPAM content is 25 wt% or below, 
+PVDF and PNIPAM phases separate, enhancing the migration of PNIPAM to the fiber 
+surface during the electrospinning process.  
+ 
+
+ 
+Elements/transitio
+ns 
+XPS surface composition, at.% 
+PVDF 
+PNIPAM 
+BLEND 
+BLEND after 
+three months 
+in water 
+Carbon C1s 
+51.1 
+75.9 
+71.8 
+71.8 
+Nitrogen N1s 
+- 
+10.9 
+8.7 
+9.4 
+Oxygen O1s 
+3.0 
+13.2 
+11.8 
+9.6 
+Fluorine F1s 
+45.9 
+- 
+7.8 
+9.3 
+ 
+Figure 6: XPS graphs of PNIPAM, PVDF, and the blend of PVDF/PNIPAM (75/25, w/w) 
+ 
+ 
+Table 2: Polymer properties  
+Polymer 
+Density 
+Solubility 
+parameter 
+δ2 
+Solubility 
+parameter 
+DMF δ1 
+Δδ (1-2) 
+
+a) PNIPAM
+b) PVDF
+C-F3
+Measured
+Measured
+Envelope
+C-F4
+Envelope
+C-H3
+C-H2
+C-C, C-H
+C-F2
+N-C=O
+292.5
+290
+287.5
+285
+280
+292.5
+290
+287.5
+285
+282.5 280
+c) Blend
+C-F2
+Measured
+Envelope
+C-H2
+C-C: C-H
+N-C=O
+295
+292.5
+290
+287.5
+285
+282.5
+280
+Binding Energy (ev)PNIPAM 
+1.05 
+23.5 
+24.9 
+1.4 
+PVDF 
+1.68 
+17.5 
+24.9 
+7.4 
+ 
+Before water-vapor transmission experiments were performed, the fabricated membranes 
+were conditioned for a day in an environment-controlled chamber (at test conditions). 
+The skin model (mimicked by the porous hot plate) measures the membrane’s resistance 
+to vapor permeability as a function of temperature, as shown in Figure 7. When the 
+membrane is placed on the hot plate, the water vapor diffuses from the bottom to the top 
+side of the Janus membrane (see Figure 7). The membrane’s resistance to vapor diffusion 
+is measured from both sides of the Janus membrane in a separate set of experiments to 
+assess the influence of the wettability gradient within the membrane. This set of 
+measurements is performed at five different temperatures to plot the membrane’s resistance 
+as a function of temperature. The water vapor resistance measurement removes the 
+temperature bias on the WVT and is expected to be constant for the same fabric at different 
+isothermal conditions. 
+When the membrane is placed on the hot plate with the blend side facing down, i.e., when 
+vapor transmits from the blend to the PVDF side of the Janus membrane, there is an 
+increased water vapor resistance at higher temperatures (see Figure 7). As the blend is 
+thermoresponsive, it is hydrophilic (CA=10⁰) at a lower temperature range (<32 ⁰C) and 
+hydrophobic (CA=120⁰) at a temperature higher than 32 ⁰C. As a result, the lower resistance 
+is attributed to the blend’s affinity to water vapor at a lower temperature. Similarly, the 
+reduced affinity at elevated temperatures causes more significant resistance to vapor 
+transmission. As the vapor transmits from the blend to the PVDF side, the hydrophobicity 
+increases the membrane’s thickness and consequently increases the membrane’s resistance 
+to vapor transmission. 
+The hydrophilic layer next to the PVDF layer supports the vapor transmission when the 
+PVDF side faces the hot plate. At elevated temperatures, the resistance increases but is 
+significantly lower than the resistance the membrane offers, with the blend facing the hot 
+plate (Figure 7). Even though the blend is hydrophobic at elevated temperatures, it is less 
+hydrophobic than PVDF. Therefore, when the vapor transmits from the PVDF to the blend 
+side, the hydrophobicity reduces along with the thickness of the membrane, which favors 
+the vapor transmission. 
+Based on the examination of the results, the Janus construct with PVDF facing the hot plate 
+favors the vapor transmission at all investigated temperatures. This behavior is due to 
+unchanging hygroscopic properties of the PVDF with temperature. Therefore, the 
+thermoresponsive Janus membrane makes it possible to maintain active vapor transport 
+irrespective of the outside temperature. 
+
+ 
+Figure 7: Effect of Janus directionality on the resistance to water-vapor permeability 
+through the membranes. The thermoresponsive property of the blend combined with 
+the Janus structure offers higher resistance to WVT. The behavior is attributed to the 
+moisture released by the blend layer at a higher temperature. As a result, when the 
+blend faces the hot plate, it increases the boundary layer gap and consequently 
+increases the resistance to water-vapor permeability. 
+ 
+We measured the water vapor permeability using a double chamber method to verify the 
+observed behavior. Needle-based electrospinning was used to fabricate the Janus 
+membrane to incorporate the thermocouples between the layers and almost at the surface 
+of the Blend layer (approximately 5sec of electrospinning). Figure 8 shows the Janus 
+membrane with thermocouples on the sample holder to fit the mouth of the OptiCal 
+chamber. The figure also shows the SEM micrographs of the blend and PVDF side of the 
+Janus membrane incorporating a fiber diameter of 0.2-0.6 μm.  
+The sample holder plugs the mouth of the chamber such that one of the sides of the 
+membrane faces outside the chamber and the other faces the inside chamber of the OptiCal 
+chamber. The entire system and the membranes were conditioned at 20°C and 40% RH 
+before carrying out below LCST. Before measurements above LCST, membranes were 
+conditioned at 30°C and 40% RH, as mentioned in Figure 4.  
+
+3.5
+PVDFtoBlend
+Blend to PVDF
+3
+2.5
+, m’Pa/W
+PVDF
+2
+RET,
+H
+Blend
+1.5
+0.5
+20
+25
+30
+35
+40
+Temperature, °C 
+Figure 8: The top part shows the membrane with the thermocouples mounted (red arrow) 
+on the sample holder that fits the mouth of the OptiCal instrument. The bottom section 
+shows the SEM micrographs of the fibers from the PVDF and the blend side, respectively 
+ 
+ 
+Figure 9 shows the membranes' water vapor permeability as a temperature function. At a 
+lower temperature of 20 °C, the permeabilities are comparable for both samples. However, 
+the increasing vapor permeability with increasing temperature is predominantly due to 
+increasing partial vapor pressure difference across the membrane37. Figure 10 plots the 
+vapor permeability as a function of partial vapor pressure across the membrane.  
+PVDF being hydrophobic is expected to adsorb less moisture and transmit less than the 
+unswelling hydrophilic membrane (Blend). However, interestingly, the vapor permeability 
+from the PVDF to the blend side is significantly higher than from the blend to the PVDF 
+side. Further, to isolate the membrane effects from the vapor pressure, Figure 10B shows 
+the water vapor permeability per unit of partial pressure across the membrane. When the 
+vapor transmits from the blend side, the permeability is constant, suggesting the vapor 
+pressure difference is the primary driving force. However, vapor permeates significantly 
+more (P-value =0.003, n=4) from the PVDF side, suggesting that the membrane’s influence 
+on vapor transmission increases with temperature. Therefore, the combined effect of the 
+Janus constructs and the temperature-responsive property drives more vapor through the 
+membrane from one direction over the other. 
+ 
+
+Sum
+10um 
+Figure 9: a) shows the Janus membrane's water vapor permeability as a temperature 
+function and compares the effect of the membrane’s directionality. b) shows the partial 
+vapor pressure difference across the membrane as a function of temperature. The water 
+vapor permeability for PVDF to blend direction is significantly higher due to the 
+additional partial pressure drop caused by the wettability gradient in the membrane. 
+ 
+ 
+ 
+
+300
+250
+Blend to PVDF
+PVDF to Blend
+200
+150
+100
+b)
+30
+Blend to PVDF
+25
+PVDF to Blend
+20
+10
+20
+25
+30
+35
+40
+Temperature, 'C 
+a)
+ 
+b)
+ 
+Figure 10: a) Water vapor permeability as a function of the partial vapor pressure 
+difference across the Janus membrane. Vapor permeability from the PVDF side is 
+significantly higher than from the blend side due to the Janus structure favoring the 
+vapor transmission from the PVDF to the blend side.  
+b) Water vapor permeability per unit of the partial vapor pressure difference across the 
+Janus membrane as a function of temperature. The differences in the vapor permeability 
+from the blend side to PVDF are statistically insignificant at all tested temperatures. The 
+partial vapor pressure difference across the membrane is the primary driving force for 
+transmitting the water vapor from the blend side. However, this permeability per unit of 
+the pressure from the PVDF side increases significantly with temperature due to the 
+Janus construct's combined effect and the blend's thermoresponsive property. 
+ 
+Figure 10 shows the possible mechanism based on the obtained experimental results. Based 
+on the prior hygroscopic measurements, pristine PNIPAM adsorbs 19 wt% of vapor at a 
+temperature of 40 °C38. As the blend contains 25 wt% of PNIPAM and adsorbs water vapor 
+in proportion to the PNIPAM content29, which is at least 4 wt% of vapor at 40 °C. However, 
+PVDF being hydrophobic, adsorbs less than 1% of vapor via Van der Waal’s forces29. 
+Therefore, at any given time during the experiment, the blend surface layer will hold more 
+moisture (vapor molecules) (C������������), when compared with the PVDF surface layer (C������������).  
+When the PVDF side faces outside, the vapor transmits from the blend to the PVDF side 
+of the membrane. The amount of vapor molecules available for evaporation is C������������ on the 
+PVDF surface. Therefore, the vapor pressure gradient drives C������������ molecules through the 
+membrane. As this concentration of vapor C������������ does not change with temperature, we have 
+almost the same vapor permeability when transmitting from the blend to the PVDF side. 
+In the other scenario, with the blend side facing outside, the vapor transmits from the PVDF 
+side to the blend side of the membrane. At equilibrium, the blend surface holds more vapor 
+
+PVDFtoBlend
+250
+BlendtoPVDF
+200
+Water vapor
+100
+50
+5
+10
+15
+20
+25
+30
+Partialvaporpressuredifference,mbar12
+PVDFtoBlend
+BlendtoPVDF
+"mbar
+HHHH
+Blend
+PVDF
+10
+9
+PVDF
+Blend
+8
+20
+25
+30
+35
+40
+Temperature,Cthan the PVDF side. However, at 20 °C, most vapor molecules form hydrogen bonds with 
+the amide (-N-H) and carbonyl (-C=O-) groups from PNIPAM. As a result, the 
+concentration of vapor molecules (C������������) is a combination of bound vapor (T) and free vapor 
+molecules (F). The vapor pressure gradient drives the free vapor molecules (F) through the 
+membrane, which is comparable with C������������. Therefore, vapor permeability at temperatures 
+below LCST is similar irrespective of the transmission direction.  
+Above LCST, due to the coil conformation of PNIPAM, all the bound vapor molecules are 
+released and become free vapor molecules. When the vapor molecule C������������ evaporates, the 
+vapor pressure gradient drives C������������ through the membrane. As C������������≫C������������, the vapor 
+permeability from PVDF to the blend side is higher than that from the flipped direction. 
+ 
+ 
+Figure 11: Illustrates the mechanism of water vapor permeability from the blend side to 
+the PVDF side and vice-versa when driven by the partial vapor pressure difference. 
+Conclusion 
+Electrospun thermoresponsive Janus membranes exhibit directional WVT. Herein, the 
+vapor transmitted from the hydrophobic (PVDF) side to the hydrophilic (blend) is faster 
+than in the opposite direction (hydrophilic to hydrophobic). The results from the indirect 
+approach, i.e., via the sweating hot plate method, and from the direct approach, i.e., via a 
+double-chamber method, complement each other. Based on the physical reasoning, we 
+postulate that this mechanism is due to the combined effect of the temperature-responsive 
+behavior of the Janus construct on vapor transmission. By complementing the experiment, 
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+:8:8:8:
+Cp is exposed
+CB is all FreeThese new results open pathways in membrane research and development, which is unique 
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+  
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+1
+Skeletal Video Anomaly Detection using Deep
+Learning: Survey, Challenges and Future Directions
+Pratik K. Mishra, Alex Mihailidis, Shehroz S. Khan
+Abstract—The existing methods for video anomaly detec-
+tion mostly utilize videos containing identifiable facial and
+appearance-based features. The use of videos with identifiable
+faces raises privacy concerns, especially when used in a hospital
+or community-based setting. Appearance-based features can also
+be sensitive to pixel-based noise, straining the anomaly detection
+methods to model the changes in the background and making
+it difficult to focus on the actions of humans in the foreground.
+Structural information in the form of skeletons describing the
+human motion in the videos is privacy-protecting and can over-
+come some of the problems posed by appearance-based features.
+In this paper, we present a survey of privacy-protecting deep
+learning anomaly detection methods using skeletons extracted
+from videos. We present a novel taxonomy of algorithms based on
+the various learning approaches. We conclude that skeleton-based
+approaches for anomaly detection can be a plausible privacy-
+protecting alternative for video anomaly detection. Lastly, we
+identify major open research questions and provide guidelines to
+address them.
+Index Terms—skeleton, body joint, human pose, anomaly
+detection, video.
+I. INTRODUCTION
+Anomalous events pertain to unusual or abnormal actions,
+behaviours or situations that can lead to health, safety and
+economical risks [1]. Anomalous events, by definition, are
+largely unseen and not much is known about them in advance
+[2]. Due to their rarity, diversity and infrequency, collecting
+labeled data for anomalous events can be very difficult or
+costly [1], [3]. With the lack of predetermined classes and
+a few labelled data for anomalous events, it can be very hard
+to train supervised machine learning models [1]. Therefore, a
+general approach in majority of anomaly detection algorithms
+is to train a model that can best represent the ’normal’ events
+or actions, and any deviations from it can be flagged as an
+unseen anomaly [4]. Anomalous behaviours among humans
+can be attributed at an individual level (e.g., falls [5]) or
+multiple people in a scene (e.g., pedestrian crossing [6],
+violence in a crowded mall [7]). In the context of video-
+based anomaly detection, the general approach is to train
+a model to learn the patterns of actions or behaviours of
+individual(s), background and other semantic information in
+the normal activities videos, and identify significant deviations
+in the test videos as anomalies. However, anomaly detection
+is a challenging task due to the lack of labels and often times
+the unclear definition of an anomaly [2].
+Pratik K. Mishra, Alex Mihailidis, and Shehroz S. Khan are with the
+Institute of Biomedical Engineering, University of Toronto, Toronto, Canada,
+and also with the KITE – Toronto Rehabilitation Institute, University
+Health Network, Toronto, Canada (e-mail: [email protected];
+[email protected]; [email protected]).
+The majority of video-based anomaly detection approaches
+use RGB videos where the people in the scene are identifiable.
+While using RGB camera-based systems in public places (e.g.,
+malls, airports) is generally acceptable, the situation can be
+very different in personal dwelling, community, residential or
+clinical settings [8]. In a home or residential setting (e.g.,
+nursing homes), individuals or patients can be monitored in
+their personal space that may breach their privacy. The lack
+of measures to deal with the privacy of individuals can be
+a bottleneck in the adoption and deployment of the anomaly
+detection-based systems [9]. However, monitoring of people
+with physical, cognitive or aging issues is also important to
+improve their quality of life and care. Therefore, as a trade-
+off, privacy-protecting video modalities can fill that gap and
+be used in these settings to save lives and improve patient
+care. Wearable devices face compliance issues among certain
+populations, where people may forget or in some cases refuse
+to wear them [10]. Some of the privacy-protecting camera
+modalities that has been used in the past for anomaly detection
+involving humans include depth cameras [5], [11], thermal
+cameras [12], and infrared cameras [13], [14]. While these
+modalities can partially or fully obfuscate an individual’s
+identity, they require specialized hardware or cameras and
+can be expensive to be used by general population. Skeletons
+extracted from RGB camera streams using pose estimation al-
+gorithms [15] provide a suitable solution of privacy protection
+over RGB and other types of cameras. Skeleton tracking only
+focuses on body joints and ignores facial identity, full body
+scan or background information. The pixel-based features in
+RGB videos that mask important information about the scene
+are sensitive to noise resulting from illumination, viewing
+direction and background clutter, resulting in false positives
+when detecting anomalies [16]. Furthermore, due to redundant
+information present in these features (e.g., background), there
+is an increased burden on methods to model the change in
+those areas of the scene rather than focus on the actions of
+humans in the foreground. Extracting information specific to
+human actions can not only provide a privacy-protecting solu-
+tion, but can also help to filter out the background-related noise
+in the videos and aid the model to focus on key information
+for detecting abnormal events related to human behaviour.
+The skeletons represent an efficient way to model the human
+body joint positions over time and are robust to the complex
+background, illumination changes, and dynamic camera scenes
+[17]. In addition to being privacy-protecting, skeleton features
+are compact, well-structured, semantically rich, and highly
+descriptive about human actions and motion [17]. Anomaly
+detection using skeleton tracking is an emerging area of
+research as awareness around privacy of individuals and their
+arXiv:2301.00114v1  [cs.CV]  31 Dec 2022
+
+2
+data grows. However, skeleton-based approaches may not be
+sufficient for situations that explicitly need facial information
+for analysis, including emotion recognition [18], [19], pain
+detection [20] or remote heart monitoring [21], to name a few.
+In recent years, deep learning methods have been developed
+to use skeletons for different applications, such as action
+recognition [40], medical diagnosis [24], and sports analytics
+[41]. The use of skeletons for anomaly detection in videos
+is an under-explored area, and concerted research is needed
+[24]. The human skeletons can help in developing privacy-
+preserving solutions for private dwellings, crowded/public
+areas, medical settings, rehabilitation centers and long-term
+care homes to detect anomalous events that impacts health
+and safety of individuals. Use of this type of approach could
+improve the adoption of video-based monitoring systems in
+the homes and residential settings. However, there is a paucity
+of literature on understanding the existing techniques that use
+skeleton-based anomaly detection approaches. We identify this
+gap in the literature and present one of the first survey on the
+recent advancements in using skeletons for anomaly detection
+in videos. We identified the major themes in existing work
+and present a novel taxonomy that is based on how these
+methods learn to detect anomalous events. We also discuss the
+applications where these approaches were used to understand
+their potential in bringing these algorithms in a personal
+dwelling, or long-term care scenario.
+II. LITERATURE SURVEY
+We adopted a narrative literature review for this work.
+The following keywords (and their combinations) were used
+to search for relevant papers – skeleton, human pose, body
+pose, body joint, trajectory, anomaly detection, abnormal and
+video. These keywords were searched on scholarly databases,
+including Google Scholar, IEEE Xplore, Elsevier and Springer.
+We mostly reviewed papers between year 2016 to year 2022;
+therefore, the list may not be comprehensive. In this review,
+we only focus on the recent deep learning-based algorithms
+for skeletal video anomaly detection and did not include
+traditional machine learning based approaches. We did not
+adopt the systematic or scoping review search protocol for this
+work; therefore, our literature review may not be exhaustive.
+However, we tried our best to include the latest development
+in the field to be able to summarize their potential and identify
+challenges. In this section, we provide a survey of skeletal deep
+learning video anomaly detection methods. We present a novel
+taxonomy to study the skeletal video anomaly approaches
+based on learning approaches into four broad categories,
+i.e., reconstruction, prediction, their combinations and other
+specific approaches. Table I provides a summary of 21 relevant
+papers, based on the taxonomy, found in our literature search.
+Unless otherwise specified, the values in the last column of
+the table refer to AUC(ROC) values corresponding to each
+dataset in the reviewed paper. Five papers use reconstruction
+approach, five papers use prediction approach, five papers use
+a combination of reconstruction and prediction approaches,
+three papers use a combination of reconstruction and clustering
+approaches, and three papers use other specific approaches.
+A. Reconstruction Approaches
+In the reconstruction approaches, generally, an autoencoder
+(AE) or its variant model is trained on the skeleton information
+of only normal human activities. During training, the model
+learns to reconstruct the samples representing normal activ-
+ities with low reconstruction error. Hence, when the model
+encounters an anomalous sample at test time, it is expected to
+give high reconstruction error.
+Gatt et al. [22] used Long Short-Term Memory (LSTM)
+and 1-Dimensional Convolution (1DConv)-based AE models
+to detect abnormal human activities, including, but not limited
+to falls, using skeletons estimated from videos of a publicly
+available dataset. Temuroglu et al. [23] proposed a skeleton
+trajectory representation that handled occlusions and an AE
+framework for pedestrian abnormal behaviour detection. The
+pedestrian video dataset used in this work was collected by the
+authors, where the training dataset was composed of normal
+walking, and the test dataset was composed of normal and
+drunk walking. The pose skeletons were treated to handle
+occlusions using the proposed representation and combined
+into a sequence to train an AE. They compared the results
+of occlusion-aware skeleton keypoints input with keypoints
+without occlusion flags, keypoint image heatmaps and raw
+pedestrian image inputs. The authors used average of recall
+and specificity to evaluate the models due to the unbalanced
+dataset and found that occlusion-aware input achieved the
+highest results. Suzuki et al. [24] trained a Convolutional
+AE (CAE) on good gross motor movements in children and
+detected poor limb motion as an anomaly. Motion time-series
+images [42] were obtained from skeletons estimated from
+the videos of kindergarten children participants. The motion
+time-series images were fed as input to a CAE, which was
+trained on only the normal data. The difference between
+the input and reconstructed pixels was used to localize the
+poor body movements in anomalous frames. Jiang et al. [25]
+presented a message passing Gated Recurrent Unit (GRU)
+encoder-decoder network to detect and localize the anomalous
+pedestrian behaviours in videos captured at the grade crossing.
+The field-collected dataset consisted of over 50 hours of
+video recordings at two selected grade crossings with different
+camera angles. The skeletons were estimated and decomposed
+into global and local components before being fed as input to
+the encoder-decoder network. The localization of the anoma-
+lous pedestrians within a frame was done by identifying the
+skeletons with reconstruction error higher than the empirical
+threshold. They manually removed wrongly detected false
+skeletons as they claim that the wrong detection issue was
+observed at only one grade crossing. However, an approach
+of manual removal of false skeletons is impractical in many
+real world applications where the data is very large, making
+the need of an automated false skeleton identification and
+removal step imperative. Fan et al. [26] proposed an anomaly
+detection framework which consisted of two pairs of generator
+and discriminator. The generators were trained to reconstruct
+the normal video frames and the corresponding skeletons,
+respectively. The discriminators were trained to distinguish
+the original and reconstructed video frames and the original
+
+3
+TABLE I
+SUMMARY OF REVIEWED PAPERS.
+Learning
+approach
+Paper
+Datasets used
+Experimental
+Setting
+Number of
+people in
+scene
+Type of anomalies
+Pose
+estimation
+algorithm
+Model input
+Model type
+Anomaly score
+Eval. metric
+AUC(ROC)
+(or other)
+Reconstruction
+Gatt et al. [22]
+UTD-MHAD
+Indoor
+Single
+Irregular body
+postures
+Openpose,
+Posenet
+Skeleton
+keypoints
+1DConv-AE,
+LSTM-AE
+Reconstruction
+error
+AUC(PR)=0.91,
+F score=0.98
+Temuroglu et al. [23]
+Custom
+Outdoor
+Multiple
+Drunk walking
+Openpose
+Skeleton
+keypoints
+AE
+Reconstruction
+error
+Average of
+recall and
+specificity=0.91
+Suzuki et al. [24]
+Custom
+—
+Single
+Poor body
+movements in
+children
+Openpose
+Motion time-
+series images
+CAE
+Reconstruction
+error
+Accuracy=99.3,
+F score=0.99
+Jiang et al. [25]
+Custom
+Outdoor
+Multiple
+Abnormal pedestrian
+behaviours at
+grade crossings
+Alphapose
+Skeleton
+keypoints
+GRU Encoder-
+Decoder
+Reconstruction
+error
+0.82
+Fan et al. [26]
+CUHK Avenue,
+UMN
+Indoor and
+Outdoor
+Multiple
+Anomalous human
+behaviours
+Alphapose
+Video frame,
+Skeleton
+keypoints
+Generative
+adversarial network
+Reconstruction
+error of
+video frame
+0.88
+0.99
+Prediction
+Rodrigues et al. [27]
+IITB-Corridor,
+ShanghaiTech,
+CUHK Avenue
+Outdoor
+Multiple
+Abnormal human
+activities
+Openpose
+Skeleton
+keypoints
+Multi-timescale
+1DConv
+encoder-decoder
+Prediction error
+from different
+timescales
+0.67
+0.76
+0.83
+Luo et al. [16]
+ShanghaiTech,
+CUHK Avenue
+Outdoor
+Multiple
+Irregular body
+postures
+Alphapose
+Skeleton
+joints graph
+Spatio-Temporal
+GCN
+Prediction error
+0.74
+0.87
+Zeng et al. [28]
+UCSD Pedestrian,
+ShanghaiTech,
+CUHK Avenue,
+IITB-Corridor
+Outdoor
+Multiple
+Anomalous human
+behaviours
+HRNet
+Skeleton
+joints graph
+Hierarchical
+Spatio-Temporal
+GCN
+Weighted sum of
+prediction errors
+from different
+levels
+0.98
+0.82
+0.87
+0.7
+Fan et al. [29]
+ShanghaiTech,
+CUHK Avenue
+Outdoor
+Multiple
+Anomalous human
+actions
+Alphapose
+Skeleton
+keypoints
+GRU feed forward
+network
+Prediction error
+0.83
+0.92
+Pang et al. [30]
+ShanghaiTech,
+CUHK Avenue
+Outdoor
+Multiple
+Anomalous human
+actions
+Alphapose
+Skeleton
+keypoints
+Transformer
+Prediction error
+0.77
+0.87
+Reconstruction+
+Prediction
+Morais et al. [17]
+ShanghaiTech,
+CUHK Avenue
+Outdoor
+Multiple
+Anomalous human
+actions
+Alphapose
+Skeleton
+keypoints
+GRU Encoder-
+Decoder
+Weighted sum of
+reconstruction and
+prediction errors
+0.73
+0.86
+Boekhoudt et al. [7]
+ShanghaiTech,
+HR Crime
+Indoor and
+Outdoor
+Multiple
+Human and Crime
+related anomalies
+Alphapose
+Skeleton
+keypoints
+GRU Encoder-
+Decoder
+Weighted sum of
+reconstruction and
+prediction errors
+0.73
+0.6
+Li and Zhang [31]
+ShanghaiTech
+Outdoor
+Multiple
+Abnormal pedestrian
+behaviours
+Alphapose
+Skeleton
+keypoints
+GRU Encoder-
+Decoder
+Weighted sum of
+reconstruction and
+prediction errors
+0.75
+Li et al. [32]
+ShanghaiTech,
+CUHK Avenue
+Outdoor
+Multiple
+Human-related
+anomalous events
+Alphapose
+Skeleton
+joints graph
+GCAE with
+embedded LSTM
+Sum of max
+reconstruction and
+prediction errors
+0.76, EER=30.7
+0.84, EER=20.7
+Wu et al. [33]
+ShanghaiTech,
+CUHK Avenue
+Outdoor
+Multiple
+Abnormal human
+actions
+Alphapose
+Skeleton
+joints graph,
+Confidence
+scores
+GCN
+Confidence score
+weighted sum of
+reconstruction,
+prediction and
+SVDD errors
+0.77
+0.85
+Reconstruction+
+Clustering
+Markovitz et al. [34]
+ShanghaiTech,
+NTU-RGB+D,
+Kinetics-250
+Indoor and
+Outdoor
+Multiple
+Anomalous human
+actions
+Alphapose,
+Openpose
+Skeleton
+joints graph
+GCAE,
+Deep clustering
+Dirichlet process
+mixture model
+score
+0.75
+0.85
+0.74
+Cui et al. [35]
+ShanghaiTech
+Outdoor
+Multiple
+Human pose
+anomalies
+—
+Skeleton
+joints graph
+GCAE,
+Deep clustering
+Dirichlet process
+mixture model
+score
+0.77
+Liu et al. [36]
+ShanghaiTech,
+CUHK Avenue
+Outdoor
+Multiple
+Anomalous human
+behaviours
+Alphapose
+Skeleton
+joints graph
+GCAE,
+Deep clustering
+Dirichlet process
+mixture model
+score
+0.79
+0.88
+Clustering
+Yang et al. [37]
+UCSD Pedestrian 2,
+ShanghaiTech
+Outdoor
+Multiple
+Anomalous human
+behaviours and
+objects
+Alphapose
+Skeleton
+joints graph,
+Numerical
+features
+GCN
+Skeleton cluster +
+Object anomaly
+score
+0.93
+0.82
+Iterative self-
+training
+Nanjun et al. [38]
+ShanghaiTech,
+CUHK Avenue
+Outdoor
+Multiple
+Human-related
+anomalous events
+Alphapose
+Skeleton
+joints graph,
+Numerical
+features
+GCN
+Self-trained fully
+connected layers
+output
+0.72, EER=34.1
+0.82, EER=23.9
+Multivariate
+gaussian
+distribution
+Tani and Shibata [39]
+ShanghaiTech
+Outdoor
+Multiple
+Anomalous human
+behaviours
+Openpose
+Skeleton
+joints graph
+GCN, Multivariate
+gaussian distribution
+Mahalanobis
+distance
+0.77
+
+4
+and reconstructed skeletons, respectively. The video frames
+and corresponding extracted skeletons served as input to the
+framework during training; however, at test time, decision was
+made based on only reconstruction error of video frames.
+Challenges: AEs or their variants are widely used in
+many video-based anomaly detection methods [5]. The choice
+of the right architecture to model the skeletons is very
+important. Further, being trained on the normal data, they
+are expected to produce higher reconstruction error for the
+abnormal inputs than the normal inputs, which has been
+adopted as a criterion for identifying anomalies. However, this
+assumption does not always hold in practice, that is, the AEs
+can generalize well that it can also reconstruct anomalies well,
+leading to false negatives [43].
+B. Prediction Approaches
+In prediction approaches, a network is generally trained to
+learn the normal human behaviour by predicting the skeletons
+at the next time step(s) using the skeletons representing normal
+human actions at past time steps. During testing, the test sam-
+ples with high prediction errors are flagged as anomalies as the
+network is trained to predict only the skeletons representing
+normal actions.
+Rodrigues et al. [27] suggested that abnormal human activ-
+ities can take place at different timescales, and the methods
+that operate at a fixed timescale (frame-based or video-clip-
+based) are not enough to capture the wide range of anomalies
+occurring with different time duration. They proposed a multi-
+timescale 1DConv encoder-decoder network where the inter-
+mediate layers were responsible to generate future and past
+predictions corresponding to different timescales. The network
+was trained to make predictions on normal activity skeletons
+input. The prediction errors from all timescales were combined
+to get an anomaly score to detect abnormal activities. Luo
+et al. [16] proposed a spatio-temporal Graph Convolutional
+Network (GCN)-based prediction method for skeleton-based
+video anomaly detection. The body joints were estimated and
+built into skeleton graphs, where the body joints formed the
+nodes of the graph. The spatial edges connected different joints
+of a skeleton, and temporal edges connected the same joints
+across time. A fully connected layer was used at the end
+of the network to predict future skeletons. Zeng et al. [28]
+proposed a hierarchical spatio-temporal GCN, where high-
+level representations encoded the trajectories of people and the
+interactions among multiple identities while low-level skeleton
+graph representations encoded the local body posture of each
+person. The method was proposed to detect anomalous human
+behaviours in both sparse and dense scenes. The inputs were
+organized into spatio-temporal skeleton graphs whose nodes
+were human body joints from multiple frames and fed to
+the network. The network was trained on the input skeleton
+graph representations of normal activities. Optical flow fields
+and size of skeleton bounding boxes were used to determine
+sparse and dense scenes. For dense scenes with crowds, higher
+weights were assigned to high-level representations while for
+sparse scenes, the weights of low-level graph representations
+were increased. During testing, the prediction errors from
+different branches were weighted and combined to obtain the
+final anomaly score. Fan et al. [29] proposed a GRU feed-
+forward network that was trained to predict the next skeleton
+using past skeleton sequences and a loss function that incorpo-
+rated the range and speed of the predicted skeletons. Pang et
+al. [30] proposed a skeleton transformer to predict future pose
+components in video frames and considered error between
+predicted pose components and corresponding expected values
+as anomaly score. They applied a multi-head self-attention
+module to capture long-range dependencies between arbitrary
+pairwise pose components and the temporal convolutional
+layer to concentrate on local temporal information.
+Challenges: In these methods, it is difficult to choose
+how far in future (or past) the prediction should be made to
+achieve optimum results. This could potentially be determined
+empirically; however, in the absence of a validation set such
+solutions remain elusive. The future prediction-based methods
+can be sensitive to noise in the past data [44]. Any small
+changes in the past can result in significant variation in
+prediction, and not all of these changes signify anomalous
+situations.
+C. Combinations of learning approaches
+In this section, we discuss the existing methods that uti-
+lize a combination of different learning approaches, namely,
+reconstruction and prediction approaches, and reconstruction
+and clustering approaches.
+1) Combination
+of
+reconstruction
+and
+prediction
+ap-
+proaches: Some skeletal video anomaly detection methods
+utilize a multi-objective loss function consisting of both recon-
+struction and prediction errors to learn the characteristics of
+skeletons signifying normal behaviour and identify skeletons
+with large errors as anomalies. Morais et al. [17] proposed a
+method to model the normal human movements in surveillance
+videos using human skeletons and their relative positions
+in the scene. The human skeletons were decomposed into
+two sub-components: global body movement and local body
+posture. The global movement tracked the dynamics of the
+whole body in the scene, while the local posture described the
+skeleton configuration. The two components were passed as
+input to different branches of a message passing GRU single-
+encoder-dual-decoder-based network. The branches processed
+their data separately and interacted via cross-branch message
+passing at each time step. Each branch had an encoder, a
+reconstruction-based decoder and a prediction-based decoder.
+The network was trained using normal data, and during testing,
+a frame-level anomaly score was generated by aggregating
+the anomaly scores of all the skeletons in a frame to identify
+anomalous frames. In order to avoid the inaccuracy caused by
+incorrect detection of skeletons in video frames, the authors
+leave out video frames where the skeletons cannot be estimated
+by the pose estimation algorithm. Hence, the results in this
+work was not a good representation of a real-world scenario,
+which often consists of complex-scenes with occluding objects
+and overlapping movement of people. Boekhoudt et al. [7]
+utilized the network proposed by Morais et al. [17] for de-
+tecting human crime-based anomalies in videos using a newly
+
+5
+proposed crime-based video surveillance dataset. Similar to
+the work by Morais et al. [17], Li and Zhang [31] proposed
+a dual branch single-encoder-dual-decoder GRU network that
+was trained on normal behaviour skeletons estimated from
+pedestrian videos. The two decoders were responsible for
+reconstructing the input skeletons and predicting future skele-
+tons, respectively. However, unlike the work by Morais et al.
+[17], there was no provision of message passing between the
+branches. Li et al. [32] proposed a single-encoder-dual-decoder
+architecture established on a spatio-temporal Graph CAE
+(GCAE) embedded with a LSTM network in hidden layers.
+The two decoders were used to reconstruct the input skeleton
+sequences and predict the unseen future sequences, respec-
+tively, from the latent vectors projected via the encoder. The
+sum of maximum reconstruction and prediction errors among
+all the skeletons within a frame was used as anomaly score for
+detecting anomalous frames. Wu et al. [33] proposed a GCN-
+based encoder-decoder architecture that was trained using
+normal action skeleton graphs and keypoint confidence scores
+as input to detect anomalous human actions in surveillance
+videos. The skeleton graph input was decomposed into global
+and local components. The network consisted of three encoder-
+decoder pipelines: the global pipeline, the local pipeline and
+the confidence score pipeline. The global and local encoder-
+decoder-based pipelines learned to reconstruct and predict the
+global and local components, respectively. The confidence
+score pipeline learned to reconstruct the confidence scores.
+Further, a Support Vector Data Description (SVDD)-based loss
+was employed to learn the boundary of the normal action
+global and local pipeline encoder output in latent feature space.
+The network was trained using a multi-objective loss function,
+composed of a weighted sum of skeleton graph reconstruction
+and prediction losses, confidence score reconstruction loss and
+multi-center SVDD loss.
+2) Combination
+of
+reconstruction
+and
+clustering
+ap-
+proaches: Some skeletal video anomaly detection methods
+utilize a two-stage approach to identify anomalous human
+actions using spatio-temporal skeleton graphs. In the first
+pre-training stage, a GCAE-based model is trained to min-
+imize the reconstruction loss on input skeleton graphs. In
+the second fine-tuning stage, the latent features generated by
+the pre-trained GCAE encoder is fed to a clustering layer
+and a Dirichlet Process Mixture model is used to estimate
+the distribution of the soft assignment of feature vectors
+to clusters. Finally at the test time, the Dirichlet normality
+score is used to identify the anomalous samples. Markovitz
+et al. [34] identified that anomalous actions can be broadly
+classified in two categories, fine and coarse-grained anomalies.
+Fine-grained anomaly detection refers to detecting abnormal
+variations of an action, e.g., abnormal type of walking. Coarse-
+grained anomaly detection refers to defining particular normal
+actions and regarding other actions as abnormal, such as
+determining dancing as normal and gymnastics as abnormal.
+They utilized a spatio-temporal GCAE to map the skeleton
+graphs representing normal actions to a latent space, which
+was soft assigned to clusters using a deep clustering layer. The
+soft-assignment representation abstracted the type of data (fine
+or coarse-grained) from the Dirichlet model. After pre-training
+of GCAE, the latent feature output of the encoder and clusters
+were fine-tuned by minimizing a multi-objective loss function
+consisting of both the reconstruction loss and clustering loss.
+They leveraged ShanghaiTech [45] dataset to test the perfor-
+mance of their proposed method on fine-grained anomalies,
+and NTU-RGB+D [46] and Kinetics-250 [47] datasets for
+coarse-grained anomaly detection performance evaluation. Cui
+et al. [35] proposed a semi-supervised prototype generation-
+based method for video anomaly detection to reduce the
+computational cost associated with graph-embedded networks.
+Skeleton graphs for normal actions were estimated from the
+videos and fed as input to a shift spatio-temporal GCAE to
+generate features. It was not clear which pose estimation algo-
+rithm was used to estimate the skeletons from video frames.
+The generated features were fed to the proposed prototype gen-
+eration module designed to map the features to prototypes and
+update them during the training phase. In the pre-training step,
+the GCAE and prototype generation module were optimized
+using a loss function composed of reconstruction loss and
+generation loss of prototypes. In the fine-tuning step, the entire
+network was fine-tuned using a multi-objective loss function,
+composed of reconstruction loss, prototype generation loss and
+cluster loss. Later, Liu et al. [36] used self-attention augmented
+graph convolutions for detecting abnormal human behaviours
+based on skeleton graphs. Skeleton graphs were fed as input to
+a spatio-temporal self-attention augmented GCAE and latent
+features were extracted from the encoder part of the trained
+GCAE. After pre-training of GCAE, the entire network was
+fine-tuned using a multi-objective loss function consisting of
+both the reconstruction loss and clustering loss.
+Challenges: The combination-based methods can carry
+the limitations of the individual learning approaches, as de-
+scribed in Section II-A and II-B. Further, in the absence of a
+validation set, it is difficult to determine the optimum value
+of combination coefficients in a multi-objective loss function.
+D. Other Approaches
+This section discusses the methods that leveraged a pre-
+trained deep learning model to encode latent features from the
+input skeletons and used approaches such as, clustering and
+multivariate gaussian distribution, in conjunction for detecting
+human action-based anomalies in videos.
+Yang et al. [37] proposed a two-stream fusion method to
+detect anomalies pertaining to body movement and object
+positions. YOLOv3 [48] was used to detect people and objects
+in the video frames. Subsequently, skeletons were estimated
+from the video frames and passed as input to a spatio-temporal
+GCN, followed by a clustering-based fully connected layer to
+generate anomaly scores for skeletons. The information per-
+taining to the bounding box coordinates and confidence score
+of the detected objects was used to generate object anomaly
+scores. Finally, the skeleton and object normality scores were
+combined to generate the final anomaly score for a frame.
+Nanjun et al. [38] used the skeleton features estimated from
+the videos for pedestrian anomaly detection using an iterative
+self-training strategy. The training set consisted of unlabelled
+normal and anomalous video sequences. The skeletons were
+
+6
+decomposed into global and local components, which were fed
+as input to an unsupervised anomaly detector, iForest [49], to
+yield the pseudo anomalous and normal skeleton sets. The
+pseudo sets were used to train an anomaly scoring module,
+consisting of a spatial GCN and fully connected layers with
+a single output unit. As part of the self-training strategy,
+new anomaly scores were generated using previously trained
+anomaly scoring module to update the membership of skeleton
+samples in the skeleton sets. The scoring module was then
+retrained using updated skeleton sets, until the best scoring
+model was obtained. However, the paper doesn’t discuss the
+criteria to decide the best scoring model. Tani and Shibata
+[39] proposed a framework for training a frame-wise Adap-
+tive GCN (AGCN) for action recognition using single frame
+skeletons and used the features extracted from the AGCN to
+train an anomaly detection model. As part of the proposed
+framework, a pretrained action recognition model [50] was
+used to identify the frames with large temporal attention in
+the Kinetics-skeleton dataset [51] as the action frames to train
+the AGCN. Further, the trained AGCN was used to extract
+features from the normal behaviour skeletons identified in the
+ShanghaiTech Campus dataset [17] to model a multivariate
+gaussian distribution. During testing, the Mahalanobis distance
+was used to calculate the anomaly score under the multivariate
+gaussian distribution.
+Challenges: The performance of these methods rely on
+the pre-training strategy of the deep learning models used to
+learn the latent features and the choice of training parameters
+for the subsequent machine learning models.
+III. DISCUSSION
+This section leverages Table I and synthesizes the informa-
+tion and trends that can be inferred from the existing work on
+skeletal video anomaly detection.
+• ShanghaiTech [45] and CUHK Avenue [52] were the
+most frequently used video datasets to evaluate the perfor-
+mance of the skeletal video anomaly detection methods.
+The ShanghaiTech dataset has videos of people walking
+along a sidewalk of the ShanghaiTech university. Anoma-
+lous activities include bikers, skateboarders and people
+fighting. It has 330 training videos and 107 test videos.
+However, not all the anomalous activities are related
+to humans. A subset of the ShanghaiTech dataset that
+contained anomalous activities only related to humans
+was termed as HR ShanghaiTech and was used in many
+papers. The CUHK Avenue dataset consists of short video
+clips looking at the side of a building with pedestrian
+walking by it. Concrete columns that are part of the
+building cause some occlusion. The dataset contains 16
+training videos and 21 testing videos. The anomalous
+events comprise of actions such as “throwing papers”,
+“throwing bag”, “child skipping”, “wrong direction” and
+“bag on grass”. Similarly, a subset of the CUHK Avenue
+dataset containing anomalous activities only related to
+humans, called HR Avenue, has been used to evaluate
+the methods. Other video datasets that have been used
+include UTD-MHAD [53], UMN [54], UCSD Pedestrian
+[6], IITB-Corridor [27], HR Crime [7], NTU-RGB+D
+[46], and Kinetics-250 [47]. From the type of anomalies
+present in these datasets, it can be inferred that the
+existing skeletal video anomaly detection methods have
+been evaluated mostly on individual human action-based
+anomalies. Hence, it is not clear how well can they
+detect anomalies that involve interactions among multiple
+individuals or interaction among people and objects.
+• Most of the papers (19 out of 21), detected anomalous
+human actions for multiple people in the video scene.
+The usual approach was to estimate the skeletons for the
+people in the scene using a pose estimation algorithm,
+and calculate anomaly scores for each of the skeletons.
+The maximum anomaly score among all the skeletons
+within a frame was used to identify the anomalous
+frames. A single video frame could contain multiple
+people, among which not all of them were performing
+anomalous actions. Hence, taking the maximum anomaly
+score of all the skeletons helped to nullify the effect of
+people with normal actions on the final decision for the
+frame. Further, calculating anomaly scores for individual
+skeletons helped to localize the source of anomaly within
+a frame.
+• The definition of anomalous human behaviours can differ
+across applications. While most of the existing papers
+focused on detecting anomalous human behaviours in
+general, four papers focused on detecting anomalous be-
+haviours for specific applications, that is, drunk walking
+[23], poor body movements in children [24], abnormal
+pedestrian behaviours at grade crossings [25] and crime-
+based anomalies [7]. Further, the nature of anomalous
+behaviours can vary depending upon various factors,
+like span of time, crowded scenes, and specific action-
+based anomalies. Some papers identified and addressed
+the need to detect specific types of anomalies, namely,
+multi-timescale anomalies occurring over different time
+duration [27], anomalies in both sparse and crowded
+scenes [28], fine and coarse-grained anomalies [34] and
+body movement and object position anomalies [37].
+• Alphapose [15] and Openpose [55] were the most com-
+mon choice of pose estimation algorithm for extraction
+of skeletons for the people in the scene. Other pose
+estimation methods that have been used were Posenet
+[56] and HRNet [57]. However, in general, the papers
+did not provide any rationale behind their choice of the
+pose estimation algorithm.
+• The type of models used in the papers can broadly
+be divided into two types, sequence-based and graph-
+based models. The sequence-based models that have
+been used include 1DConv-AE, LSTM-AE, GRU, and
+Transformer. These models treated skeleton keypoints for
+individual people across multiple frames as time series
+input. The graph-based models that have been used in-
+volve GCAE and GCN. The graph-based models received
+spatio-temporal skeleton graphs for individual people as
+input. The spatio-temporal graphs were constructed by
+considering body joints as the nodes of the graph. The
+spatial edges connected different joints of a skeleton, and
+
+7
+temporal edges connected the same joints across time.
+• Area Under Curve (AUC) of Receiver Operating Charac-
+teristic (ROC) curve was the most common metric used
+to evaluate the performance among the existing skeletal
+video anomaly detection methods. Other performance
+evaluation metrics include F score, accuracy, Equal Error
+Rate (EER) and AUC of Precision-Recall (PR) Curve.
+EER signifies the percentage of misclassified frames
+when the false positive rate equals to the miss rate on
+the ROC curve. While AUC(ROC) can provide a good
+estimate of the classifier’s performance over different
+thresholds, it can be misleading in case the data is
+imbalanced [58]. In anomaly detection scenario, it is
+common to have imbalance in the test data, as the anoma-
+lous behaviours occur infrequently, particularly in many
+medical applications [59], [60]. The AUC(PR) value
+provides a good estimate of the classifier’s performance
+on imbalanced datasets [58]; however, only one of the
+papers used AUC(PR) as an evaluation metric.
+• The highest AUC(ROC) values reported for the Shang-
+haiTech [45] and CUHK Avenue [52] datasets across
+different methods in Table I were 0.83 and 0.92, re-
+spectively. A direct comparison may not be possible due
+to the difference in the experimental setup and train-
+test splits across the reviewed methods; however, it gives
+some confidence on the viability of these approaches for
+skeletal video anomaly detection.
+IV. CHALLENGES AND FUTURE DIRECTIONS
+In general, the efficiency of the skeletal video anomaly
+detection algorithms depends upon the accuracy of the skele-
+tons estimated by the pose-estimation algorithm. If the pose
+estimation algorithm misses certain joints or produces ar-
+tifacts in the scene, then it can increase the number of
+false alarms. There are various challenges associated with
+estimating skeletons from video frames [61]: (i) complex
+body configuration causing self-occlusions and complex poses,
+(ii) diverse appearance, including clothing, and (iii) complex
+environment with occlusion from other people in the scene,
+various viewing angles, distance from camera and trunca-
+tion of parts in the camera view. This can lead to a poor
+approximation of skeletons and can negatively impact the
+performance of the anomaly detection algorithms. Methods
+have been proposed to address some of these challenges [62],
+[63]; however, extracting skeletons in complex environments
+remains a difficult problem. Some of the existing methods
+manually remove inaccurate and false skeletons [17], [25]
+to train the model, which is impractical in many real-world
+applications where the amount of available data is very large.
+There is a need of an automated false skeleton identification
+and removal step, when estimating skeletons from videos.
+The skeletons collected using Microsoft Kinect (depth)
+camera has been used in the past studies [64], [65]. However,
+the defunct production of the Microsoft Kinect camera [66]
+has lead to hardware constraints in the further development
+of skeletal anomaly detection approaches. Other commer-
+cial products include Vicon [67] with optical sensors and
+TheCaptury [68] with multiple cameras. But they function
+in very constrained environments or require special markers
+on the human body. New cameras, such as ‘Sentinare 2’
+from AltumView [69], circumvent such hardware requirements
+by directly processing videos on regular RGB cameras and
+transmitting skeletons information in real-time. The exist-
+ing approaches for skeletal video anomaly detection involve
+spatio-temporal skeleton graphs [16] or temporal sequences
+[17], which are constructed by tracking an individual across
+multiple frames. However, this is challenging in scenarios
+where there are multiple people within a scene. The entry
+and exit of people in the scene, overlapping of people during
+movement and presence of occluding objects make tracking
+people across frames a very challenging task. There can be
+deployment issues in these methods because the choice of
+threshold is not clear. In the absence of any validation set
+(containing both normal and unseen anomalies) in an anomaly
+detection setting, it is very hard to fine-tune an operating
+threshold using just the training data (comprising of normal
+activities only). To handle these situations, outliers within the
+normal activities can be used as a proxy for unseen anomalies
+[70]; however, inappropriate choices can lead to increased false
+alarms or missed alarms. Domain expertise can be utilized to
+adjust a threshold, which may not be available in many cases.
+The anomalous human behaviours of interest and their
+difficulty of detection can vary depending upon the definition
+of anomaly, application, time span of the anomalous actions,
+and presence of single/multiple people in the scenes. For
+example, in the case of driver anomaly detection application,
+the anomalous behaviours can include talking on the phone,
+dozing off or drinking [14]. The anomalous actions can span
+over different time lengths, ranging from few seconds to hours
+or days, e.g., jumping and falls [70] are short-term anomalies,
+while loitering and social isolation [71] are long-term events.
+More focus is needed on developing methods that can identify
+both short and long-term anomalies.
+Sparse scene anomalies can be described as anomalies
+in scenes with less number of humans, while dense scene
+anomalies can be described as anomalies in crowded scenes
+with large number of humans [28]. It is comparatively difficult
+to identify anomalous behaviours in dense scenes than sparse
+scenes due to tracking multiple people and finding their
+individual anomaly scores [17]. Thus, there is a need to
+develop methods that can effectively identify both sparse and
+dense scene anomalies. Further, there is a need to address the
+challenges associated with the granularity and the decision
+making time of the skeletal video anomaly detection methods
+for real time applications. The existing methods mostly output
+decision on a frame level, which becomes an issue when the
+input to the method is a real-time continuous video stream
+at multiple frames per second. This can lead to alarms going
+off multiple times a second, which can be counter-productive.
+One solution is for the methods to make decisions on a time-
+window basis, each window of length of a specified duration.
+However, this brings in the question about the optimal length
+of each decision window. A short window is impractical as
+it can lead to frequent and repetitive alarms, while a long
+window can lead to missed alarms, and delayed response
+
+8
+and intervention. Domain knowledge can be used to make a
+decision about the length of decision windows.
+Skeletons can be used in conjunction with optical flow
+[72] to develop privacy-protecting approaches to jointly learn
+from temporal and structural modalities. Approaches based
+on federated learning (that do not combine individual data,
+but only the models) can further improve the privacy of these
+methods [73]. Segmentation masks [74] can be leveraged in
+conjunction with skeletons to occlude humans while capturing
+the information pertaining to scene and human motion to
+develop privacy-protecting anomaly detection approaches.
+The skeletons signify motion and posture information for
+the individual humans in the video; however, they lack in-
+formation regarding human-human and human-object interac-
+tions. Information pertaining to interaction of the people with
+each other and the objects in the environment is important for
+applications such as, violence detection [7], theft detection [7]
+and agitation detection [60] in care home settings. Skeletons
+can be used to replace the bodies of the participants, while
+keeping the background information in video frames [75]
+to analyze both human-human and human-object interaction
+anomalies. Further, object bounding boxes can be used in
+conjunction with human skeletons to model human-object in-
+teraction while preserving the privacy of humans in the scene.
+The information from other modalities (e.g. wearable devices)
+along with skeleton features can be used to develop multi-
+modal anomaly detection methods to improve the detection
+performance.
+As can be seen in Table I, the existing skeletal video
+anomaly detection methods and available datasets focus to-
+wards detecting irregular body postures [16], and anomalous
+human actions [30] in mostly outdoor settings, and not in
+proper healthcare settings, such as personal homes and long-
+term care homes. This a gap towards real world deployment,
+as there is a need to extend the scope of detecting anomalous
+behaviours using skeletons to in-home and care home settings,
+where privacy is a very important concern. This can be utilized
+to address important applications, such as fall detection [76],
+agitation detection [60], [75], and independent assistive living.
+This will help to develop supportive homes and communi-
+ties and encourage autonomy and independence among the
+increasing older population and dementia residents in care
+homes. While leveraging skeletons helps to get rid of facial
+identity and appearance-based information, it is important to
+ask the question if skeletons can be considered private enough
+[77], [78] and what steps can be taken to further anonymize
+the skeletons.
+V. CONCLUSION
+In this paper, we provided a survey of recent works that
+leverage the skeletons or body joints estimated from videos
+for the anomaly detection task. The skeletons hide the facial
+identity and overall appearance of people and can provide
+vital information about joint angles [79], speed of walking
+[80], and interaction with other people in the scene [17].
+Our literature review showed that many deep learning-based
+approaches leverage reconstruction, prediction error and their
+other combinations to successfully detect anomalies in a
+privacy protecting manner. This review suggests the first
+steps towards increasing adoption of devices (and algorithms)
+focused on improving privacy in a residential or communal
+setting. It will further improve the deployment of anomaly
+detection systems to improve the safety and care of people.
+The skeleton-based anomaly detection methods can be used to
+design privacy-preserving technologies for the assisted living
+of older adults in a care environment [81] or enable older
+adults to live independently in their own homes to cope with
+the increasing cost of long-term care demands [82]. Privacy-
+preserving methods using skeleton features can be employed
+to assist with skeleton-based rehab exercise monitoring [83]
+or in social robots for robot-human interaction [84] that assist
+older people in their activities of daily living.
+VI. ACKNOWLEDGEMENTS
+This work was supported by AGE-WELL NCE Inc,
+Alzheimer’s Association, Natural Sciences and Engineering
+Research Council and UAE Strategic Research Grant.
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+Pratik K. Mishra obtained his Masters in Computer
+Science and Engineering from the Indian Institute
+of Technology (IIT) Indore, India, in 2020. He
+is currently pursuing his Ph.D. from the Institute
+of Biomedical Engineering, University of Toronto
+(UofT). He is currently working towards the appli-
+cation of computer vision for detecting behaviours of
+risk in people with dementia. Previously, he worked
+as a research volunteer at the Toronto Rehabilitation
+Institute, Canada and as a Data Management Support
+Specialist at IBM India Private Limited.
+Alex Mihailidis , PhD, PEng, is the Barbara G.
+Stymiest Research Chair in Rehabilitation Technol-
+ogy at KITE Research Institute at University Health
+Network/University of Toronto. He is the Scientific
+Director of the AGE-WELL Network of Centres of
+Excellence, which focuses on the development of
+new technologies and services for older adults. He
+is a Professor in the Department of Occupational
+Science and Occupational Therapy and in the In-
+stitute of Biomedical Engineering at the University
+of Toronto (U of T), as well as holds a cross
+appointment in the Department of Computer Science at the U of T.
+Mihailidis is very active in the rehabilitation engineering profession and
+is the Immediate Past President for the Rehabilitation Engineering and
+Assistive Technology Society for North America (RESNA) and was named a
+Fellow of RESNA in 2014, which is one of the highest honours within this
+field of research and practice. His research disciplines include biomedical
+and biochemical engineering, computer science, geriatrics and occupational
+therapy. Alex is an internationally recognized researcher in the field of
+technology and aging. He has published over 150 journal and conference
+papers in this field and co-edited two books: Pervasive computing in healthcare
+and Technology and Aging.
+Shehroz S. Khan obtained his B.Sc Engineering,
+Masters and Phd degrees in computer science in
+1997, 2010 and 2016. He is currently working as a
+Scientist at KITE – Toronto Rehabilitation Institute
+(TRI), University Health Network, Canada. He is
+also cross appointed as an Assistant Professor at the
+Institute of Biomedical Engineering, University of
+Toronto (UofT). Previously, he worked as a post-
+doctoral researcher at the UofT and TRI. Prior to
+joining academics, he worked in various scientific
+and researcher roles in the industry and government
+jobs. He is an associate editor of the Journal of Rehabilitation and Assistive
+Technologies. He has organized four editions of the peer-reviewed workshop
+on AI in Aging, Rehabilitation and Intelligent Assisted Living held with
+top AI conferences (ICDM and IJCAI) from 2017-2021. His research is
+funded through several granting agencies in Canada and abroad, including
+NSERC, CIHR, AGEWELL, SSHRC, CABHI, AMS Healthcare, JP Bickell
+Foundation, United Arab Emirates University and LG Electronics. He has
+published 49 peer-reviewed research papers and his research focus is the
+development of AI algorithms for solving aging related health problems.
+