Daily Papers

The impressive capabilities in Large Language Models (LLMs) provide a powerful approach to reimagine users' typing experience. This paper demonstrates Proofread, a novel Gboard feature powered by a server-side LLM in Gboard, enabling seamless sentence-level and paragraph-level corrections with a single tap. We describe the complete system in this paper, from data generation, metrics design to model tuning and deployment. To obtain models with sufficient quality, we implement a careful data synthetic pipeline tailored to online use cases, design multifaceted metrics, employ a two-stage tuning approach to acquire the dedicated LLM for the feature: the Supervised Fine Tuning (SFT) for foundational quality, followed by the Reinforcement Learning (RL) tuning approach for targeted refinement. Specifically, we find sequential tuning on Rewrite and proofread tasks yields the best quality in SFT stage, and propose global and direct rewards in the RL tuning stage to seek further improvement. Extensive experiments on a human-labeled golden set showed our tuned PaLM2-XS model achieved 85.56\% good ratio. We launched the feature to Pixel 8 devices by serving the model on TPU v5 in Google Cloud, with thousands of daily active users. Serving latency was significantly reduced by quantization, bucket inference, text segmentation, and speculative decoding. Our demo could be seen in https://youtu.be/4ZdcuiwFU7I{Youtube}.

Data-driven research on the automated discovery and repair of security vulnerabilities in source code requires comprehensive datasets of real-life vulnerable code and their fixes. To assist in such research, we propose a method to automatically collect and curate a comprehensive vulnerability dataset from Common Vulnerabilities and Exposures (CVE) records in the public National Vulnerability Database (NVD). We implement our approach in a fully automated dataset collection tool and share an initial release of the resulting vulnerability dataset named CVEfixes. The CVEfixes collection tool automatically fetches all available CVE records from the NVD, gathers the vulnerable code and corresponding fixes from associated open-source repositories, and organizes the collected information in a relational database. Moreover, the dataset is enriched with meta-data such as programming language, and detailed code and security metrics at five levels of abstraction. The collection can easily be repeated to keep up-to-date with newly discovered or patched vulnerabilities. The initial release of CVEfixes spans all published CVEs up to 9 June 2021, covering 5365 CVE records for 1754 open-source projects that were addressed in a total of 5495 vulnerability fixing commits. CVEfixes supports various types of data-driven software security research, such as vulnerability prediction, vulnerability classification, vulnerability severity prediction, analysis of vulnerability-related code changes, and automated vulnerability repair.

Modern recommender systems may output considerably different recommendations due to small perturbations in the training data. Changes in the data from a single user will alter the recommendations as well as the recommendations of other users. In applications like healthcare, housing, and finance, this sensitivity can have adverse effects on user experience. We propose a method to stabilize a given recommender system against such perturbations. This is a challenging task due to (1) the lack of a ``reference'' rank list that can be used to anchor the outputs; and (2) the computational challenges in ensuring the stability of rank lists with respect to all possible perturbations of training data. Our method, FINEST, overcomes these challenges by obtaining reference rank lists from a given recommendation model and then fine-tuning the model under simulated perturbation scenarios with rank-preserving regularization on sampled items. Our experiments on real-world datasets demonstrate that FINEST can ensure that recommender models output stable recommendations under a wide range of different perturbations without compromising next-item prediction accuracy.

We study best arm identification (BAI) in linear bandits in the fixed-budget regime under differential privacy constraints, when the arm rewards are supported on the unit interval. Given a finite budget T and a privacy parameter varepsilon>0, the goal is to minimise the error probability in finding the arm with the largest mean after T sampling rounds, subject to the constraint that the policy of the decision maker satisfies a certain {\em varepsilon-differential privacy} (varepsilon-DP) constraint. We construct a policy satisfying the varepsilon-DP constraint (called {\sc DP-BAI}) by proposing the principle of {\em maximum absolute determinants}, and derive an upper bound on its error probability. Furthermore, we derive a minimax lower bound on the error probability, and demonstrate that the lower and the upper bounds decay exponentially in T, with exponents in the two bounds matching order-wise in (a) the sub-optimality gaps of the arms, (b) varepsilon, and (c) the problem complexity that is expressible as the sum of two terms, one characterising the complexity of standard fixed-budget BAI (without privacy constraints), and the other accounting for the varepsilon-DP constraint. Additionally, we present some auxiliary results that contribute to the derivation of the lower bound on the error probability. These results, we posit, may be of independent interest and could prove instrumental in proving lower bounds on error probabilities in several other bandit problems. Whereas prior works provide results for BAI in the fixed-budget regime without privacy constraints or in the fixed-confidence regime with privacy constraints, our work fills the gap in the literature by providing the results for BAI in the fixed-budget regime under the varepsilon-DP constraint.

We introduce the Fixed Point Diffusion Model (FPDM), a novel approach to image generation that integrates the concept of fixed point solving into the framework of diffusion-based generative modeling. Our approach embeds an implicit fixed point solving layer into the denoising network of a diffusion model, transforming the diffusion process into a sequence of closely-related fixed point problems. Combined with a new stochastic training method, this approach significantly reduces model size, reduces memory usage, and accelerates training. Moreover, it enables the development of two new techniques to improve sampling efficiency: reallocating computation across timesteps and reusing fixed point solutions between timesteps. We conduct extensive experiments with state-of-the-art models on ImageNet, FFHQ, CelebA-HQ, and LSUN-Church, demonstrating substantial improvements in performance and efficiency. Compared to the state-of-the-art DiT model, FPDM contains 87% fewer parameters, consumes 60% less memory during training, and improves image generation quality in situations where sampling computation or time is limited. Our code and pretrained models are available at https://lukemelas.github.io/fixed-point-diffusion-models.

In the setting of finite groups, suppose J acts on N via automorphisms so that the induced semidirect product Nrtimes J acts on some non-empty set Omega, with N acting transitively. Glauberman proved that if the orders of J and N are coprime, then J fixes a point in Omega. We consider the non-coprime case and show that if N is abelian and a Sylow p-subgroup of J fixes a point in Omega for each prime p, then J fixes a point in Omega. We also show that if N is nilpotent, Nrtimes J is supersoluble, and a Sylow p-subgroup of J fixes a point in Omega for each prime p, then J fixes a point in Omega.

Large pretrained masked language models have become state-of-the-art solutions for many NLP problems. The research has been mostly focused on English language, though. While massively multilingual models exist, studies have shown that monolingual models produce much better results. We train two trilingual BERT-like models, one for Finnish, Estonian, and English, the other for Croatian, Slovenian, and English. We evaluate their performance on several downstream tasks, NER, POS-tagging, and dependency parsing, using the multilingual BERT and XLM-R as baselines. The newly created FinEst BERT and CroSloEngual BERT improve the results on all tasks in most monolingual and cross-lingual situations

Large Language Models (LLMs) have demonstrated remarkable proficiency across a variety of complex tasks. One significant application of LLMs is in tackling software engineering challenges, particularly in resolving real-world tasks on GitHub by fixing code based on the issues reported by the users. However, many current approaches rely on proprietary LLMs, which limits reproducibility, accessibility, and transparency. The critical components of LLMs for addressing software engineering issues and how their capabilities can be effectively enhanced remain unclear. To address these challenges, we introduce SWE-Fixer, a novel open-source LLM designed to effectively and efficiently resolve GitHub issues. SWE-Fixer comprises two essential modules: a code file retrieval module and a code editing module. The retrieval module employs BM25 along with a lightweight LLM model to achieve coarse-to-fine file retrieval. Subsequently, the code editing module utilizes the other LLM model to generate patches for the identified files. Then, to mitigate the lack of publicly available datasets, we compile an extensive dataset that includes 110K GitHub issues along with their corresponding patches, and train the two modules of SWE-Fixer separately. We assess our approach on the SWE-Bench Lite and Verified benchmarks, achieving state-of-the-art performance among open-source models with scores of 23.3% and 30.2%, respectively. These outcomes highlight the efficacy of our approach. We will make our model, dataset, and code publicly available at https://github.com/InternLM/SWE-Fixer.

Quantization is a crucial technique for deploying deep learning models on resource-constrained devices, such as embedded FPGAs. Prior efforts mostly focus on quantizing matrix multiplications, leaving other layers like BatchNorm or shortcuts in floating-point form, even though fixed-point arithmetic is more efficient on FPGAs. A common practice is to fine-tune a pre-trained model to fixed-point for FPGA deployment, but potentially degrading accuracy. This work presents QFX, a novel trainable fixed-point quantization approach that automatically learns the binary-point position during model training. Additionally, we introduce a multiplier-free quantization strategy within QFX to minimize DSP usage. QFX is implemented as a PyTorch-based library that efficiently emulates fixed-point arithmetic, supported by FPGA HLS, in a differentiable manner during backpropagation. With minimal effort, models trained with QFX can readily be deployed through HLS, producing the same numerical results as their software counterparts. Our evaluation shows that compared to post-training quantization, QFX can quantize models trained with element-wise layers quantized to fewer bits and achieve higher accuracy on both CIFAR-10 and ImageNet datasets. We further demonstrate the efficacy of multiplier-free quantization using a state-of-the-art binarized neural network accelerator designed for an embedded FPGA (AMD Xilinx Ultra96 v2). We plan to release QFX in open-source format.

Fine-grained few-shot entity extraction in the chemical domain faces two unique challenges. First, compared with entity extraction tasks in the general domain, sentences from chemical papers usually contain more entities. Moreover, entity extraction models usually have difficulty extracting entities of long-tailed types. In this paper, we propose Chem-FINESE, a novel sequence-to-sequence (seq2seq) based few-shot entity extraction approach, to address these two challenges. Our Chem-FINESE has two components: a seq2seq entity extractor to extract named entities from the input sentence and a seq2seq self-validation module to reconstruct the original input sentence from extracted entities. Inspired by the fact that a good entity extraction system needs to extract entities faithfully, our new self-validation module leverages entity extraction results to reconstruct the original input sentence. Besides, we design a new contrastive loss to reduce excessive copying during the extraction process. Finally, we release ChemNER+, a new fine-grained chemical entity extraction dataset that is annotated by domain experts with the ChemNER schema. Experiments in few-shot settings with both ChemNER+ and CHEMET datasets show that our newly proposed framework has contributed up to 8.26% and 6.84% absolute F1-score gains respectively.

The original Grover's algorithm suffers from the souffle problem, which means that the success probability of quantum search decreases dramatically if the iteration time is too small or too large from the right time. To overcome the souffle problem, the fixed-point quantum search with an optimal number of queries was proposed [Phys. Rev. Lett. 113, 210501 (2014)], which always finds a marked state with a high probability when a lower bound of the proportion of marked states is given. The fixed-point quantum search relies on a key lemma regarding the explicit formula of recursive quasi-Chebyshev polynomials, but its proof is not given explicitly. In this work, we give a detailed proof of this lemma, thus providing a sound foundation for the correctness of the fixed-point quantum search. This lemma may be of independent interest as well, since it expands the mathematical form of the recursive relation of Chebyshev polynomials of the first kind, and it also constitutes a key component in overcoming the souffle problem of quantum walk-based search algorithms, for example, robust quantum walk search on complete bipartite graphs [Phys. Rev. A 106, 052207 (2022)]. Hopefully, more applications of the lemma will be found in the future.

The privacy in classical federated learning can be breached through the use of local gradient results along with engineered queries to the clients. However, quantum communication channels are considered more secure because a measurement on the channel causes a loss of information, which can be detected by the sender. Therefore, the quantum version of federated learning can be used to provide more privacy. Additionally, sending an N dimensional data vector through a quantum channel requires sending log N entangled qubits, which can potentially provide exponential efficiency if the data vector is utilized as quantum states. In this paper, we propose a quantum federated learning model where fixed design quantum chips are operated based on the quantum states sent by a centralized server. Based on the coming superposition states, the clients compute and then send their local gradients as quantum states to the server, where they are aggregated to update parameters. Since the server does not send model parameters, but instead sends the operator as a quantum state, the clients are not required to share the model. This allows for the creation of asynchronous learning models. In addition, the model as a quantum state is fed into client-side chips directly; therefore, it does not require measurements on the upcoming quantum state to obtain model parameters in order to compute gradients. This can provide efficiency over the models where the parameter vector is sent via classical or quantum channels and local gradients are obtained through the obtained values of these parameters.

During typical gradient-based training of deep neural networks, all of the model's parameters are updated at each iteration. Recent work has shown that it is possible to update only a small subset of the model's parameters during training, which can alleviate storage and communication requirements. In this paper, we show that it is possible to induce a fixed sparse mask on the model's parameters that selects a subset to update over many iterations. Our method constructs the mask out of the k parameters with the largest Fisher information as a simple approximation as to which parameters are most important for the task at hand. In experiments on parameter-efficient transfer learning and distributed training, we show that our approach matches or exceeds the performance of other methods for training with sparse updates while being more efficient in terms of memory usage and communication costs. We release our code publicly to promote further applications of our approach.

Network quantization generally converts full-precision weights and/or activations into low-bit fixed-point values in order to accelerate an inference process. Recent approaches to network quantization further discretize the gradients into low-bit fixed-point values, enabling an efficient training. They typically set a quantization interval using a min-max range of the gradients or adjust the interval such that the quantization error for entire gradients is minimized. In this paper, we analyze the quantization error of gradients for the low-bit fixed-point training, and show that lowering the error for large-magnitude gradients boosts the quantization performance significantly. Based on this, we derive an upper bound of quantization error for the large gradients in terms of the quantization interval, and obtain an optimal condition for the interval minimizing the quantization error for large gradients. We also introduce an interval update algorithm that adjusts the quantization interval adaptively to maintain a small quantization error for large gradients. Experimental results demonstrate the effectiveness of our quantization method for various combinations of network architectures and bit-widths on various tasks, including image classification, object detection, and super-resolution.

Neural embedding models have become a fundamental component of modern information retrieval (IR) pipelines. These models produce a single embedding x in R^d per data-point, allowing for fast retrieval via highly optimized maximum inner product search (MIPS) algorithms. Recently, beginning with the landmark ColBERT paper, multi-vector models, which produce a set of embedding per data point, have achieved markedly superior performance for IR tasks. Unfortunately, using these models for IR is computationally expensive due to the increased complexity of multi-vector retrieval and scoring. In this paper, we introduce MUVERA (MUlti-VEctor Retrieval Algorithm), a retrieval mechanism which reduces multi-vector similarity search to single-vector similarity search. This enables the usage of off-the-shelf MIPS solvers for multi-vector retrieval. MUVERA asymmetrically generates Fixed Dimensional Encodings (FDEs) of queries and documents, which are vectors whose inner product approximates multi-vector similarity. We prove that FDEs give high-quality epsilon-approximations, thus providing the first single-vector proxy for multi-vector similarity with theoretical guarantees. Empirically, we find that FDEs achieve the same recall as prior state-of-the-art heuristics while retrieving 2-5times fewer candidates. Compared to prior state of the art implementations, MUVERA achieves consistently good end-to-end recall and latency across a diverse set of the BEIR retrieval datasets, achieving an average of 10% improved recall with 90% lower latency.

We study differentially private (DP) machine learning algorithms as instances of noisy fixed-point iterations, in order to derive privacy and utility results from this well-studied framework. We show that this new perspective recovers popular private gradient-based methods like DP-SGD and provides a principled way to design and analyze new private optimization algorithms in a flexible manner. Focusing on the widely-used Alternating Directions Method of Multipliers (ADMM) method, we use our general framework to derive novel private ADMM algorithms for centralized, federated and fully decentralized learning. For these three algorithms, we establish strong privacy guarantees leveraging privacy amplification by iteration and by subsampling. Finally, we provide utility guarantees using a unified analysis that exploits a recent linear convergence result for noisy fixed-point iterations.

Scale has become a main ingredient in obtaining strong machine learning models. As a result, understanding a model's scaling properties is key to effectively designing both the right training setup as well as future generations of architectures. In this work, we argue that scale and training research has been needlessly complex due to reliance on the cosine schedule, which prevents training across different lengths for the same model size. We investigate the training behavior of a direct alternative - constant learning rate and cooldowns - and find that it scales predictably and reliably similar to cosine. Additionally, we show that stochastic weight averaging yields improved performance along the training trajectory, without additional training costs, across different scales. Importantly, with these findings we demonstrate that scaling experiments can be performed with significantly reduced compute and GPU hours by utilizing fewer but reusable training runs.

Transformers have a potential of learning longer-term dependency, but are limited by a fixed-length context in the setting of language modeling. We propose a novel neural architecture Transformer-XL that enables learning dependency beyond a fixed length without disrupting temporal coherence. It consists of a segment-level recurrence mechanism and a novel positional encoding scheme. Our method not only enables capturing longer-term dependency, but also resolves the context fragmentation problem. As a result, Transformer-XL learns dependency that is 80% longer than RNNs and 450% longer than vanilla Transformers, achieves better performance on both short and long sequences, and is up to 1,800+ times faster than vanilla Transformers during evaluation. Notably, we improve the state-of-the-art results of bpc/perplexity to 0.99 on enwiki8, 1.08 on text8, 18.3 on WikiText-103, 21.8 on One Billion Word, and 54.5 on Penn Treebank (without finetuning). When trained only on WikiText-103, Transformer-XL manages to generate reasonably coherent, novel text articles with thousands of tokens. Our code, pretrained models, and hyperparameters are available in both Tensorflow and PyTorch.

Quantization is a technique for reducing deep neural networks (DNNs) training and inference times, which is crucial for training in resource constrained environments or applications where inference is time critical. State-of-the-art (SOTA) quantization approaches focus on post-training quantization, i.e., quantization of pre-trained DNNs for speeding up inference. While work on quantized training exists, most approaches require refinement in full precision (usually single precision) in the final training phase or enforce a global word length across the entire DNN. This leads to suboptimal assignments of bit-widths to layers and, consequently, suboptimal resource usage. In an attempt to overcome such limitations, we introduce AdaPT, a new fixed-point quantized sparsifying training strategy. AdaPT decides about precision switches between training epochs based on information theoretic conditions. The goal is to determine on a per-layer basis the lowest precision that causes no quantization-induced information loss while keeping the precision high enough such that future learning steps do not suffer from vanishing gradients. The benefits of the resulting fully quantized DNN are evaluated based on an analytical performance model which we develop. We illustrate that an average speedup of 1.27 compared to standard training in float32 with an average accuracy increase of 0.98% can be achieved for AlexNet/ResNet on CIFAR10/100 and we further demonstrate these AdaPT trained models achieve an average inference speedup of 2.33 with a model size reduction of 0.52.

We present a new regular grid search algorithm for quick fixed-radius nearest-neighbor lookup developed in Python. This module indexes a set of k-dimensional points in a regular grid, with optional periodic conditions, providing a fast approach for nearest neighbors queries. In this first installment we provide three types of queries: bubble, shell and the nth-nearest; as well as three different metrics of interest in astronomy: the euclidean and two distance functions in spherical coordinates of varying precision, haversine and Vincenty; and the possibility of providing a custom distance function. This package results particularly useful for large datasets where a brute-force search turns impractical.

As first-order optimization methods become the method of choice for solving large-scale optimization problems, optimization solvers based on first-order algorithms are being built. Such general-purpose solvers must robustly detect infeasible or misspecified problem instances, but the computational complexity of first-order methods for doing so has yet to be formally studied. In this work, we characterize the optimal accelerated rate of infeasibility detection. We show that the standard fixed-point iteration achieves a O(1/k^2) and O(1/k) rates, respectively, on the normalized iterates and the fixed-point residual converging to the infimal displacement vector, while the accelerated fixed-point iteration achieves O(1/k^2) and mathcal{O}(1/k^2) rates. We then provide a matching complexity lower bound to establish that Theta(1/k^2) is indeed the optimal accelerated rate.

There is a recently discovered and intriguing phenomenon called Neural Collapse: at the terminal phase of training a deep neural network for classification, the within-class penultimate feature means and the associated classifier vectors of all flat classes collapse to the vertices of a simplex Equiangular Tight Frame (ETF). Recent work has tried to exploit this phenomenon by fixing the related classifier weights to a pre-computed ETF to induce neural collapse and maximize the separation of the learned features when training with imbalanced data. In this work, we propose to fix the linear classifier of a deep neural network to a Hierarchy-Aware Frame (HAFrame), instead of an ETF, and use a cosine similarity-based auxiliary loss to learn hierarchy-aware penultimate features that collapse to the HAFrame. We demonstrate that our approach reduces the mistake severity of the model's predictions while maintaining its top-1 accuracy on several datasets of varying scales with hierarchies of heights ranging from 3 to 12. Code: https://github.com/ltong1130ztr/HAFrame

We study the problem of classification with a reject option for a fixed predictor, applicable in natural language processing. We introduce a new problem formulation for this scenario, and an algorithm minimizing a new surrogate loss function. We provide a complete theoretical analysis of the surrogate loss function with a strong H-consistency guarantee. For evaluation, we choose the decontextualization task, and provide a manually-labelled dataset of 2mathord,000 examples. Our algorithm significantly outperforms the baselines considered, with a sim!!25% improvement in coverage when halving the error rate, which is only sim!! 3 % away from the theoretical limit.

The performance of a large language model (LLM) depends heavily on the quality and size of its pretraining dataset. However, the pretraining datasets for state-of-the-art open LLMs like Llama 3 and Mixtral are not publicly available and very little is known about how they were created. In this work, we introduce FineWeb, a 15-trillion token dataset derived from 96 Common Crawl snapshots that produces better-performing LLMs than other open pretraining datasets. To advance the understanding of how best to curate high-quality pretraining datasets, we carefully document and ablate all of the design choices used in FineWeb, including in-depth investigations of deduplication and filtering strategies. In addition, we introduce FineWeb-Edu, a 1.3-trillion token collection of educational text filtered from FineWeb. LLMs pretrained on FineWeb-Edu exhibit dramatically better performance on knowledge- and reasoning-intensive benchmarks like MMLU and ARC. Along with our datasets, we publicly release our data curation codebase and all of the models trained during our ablation experiments.

Denoising diffusion probabilistic models (DDPMs) and generative adversarial networks (GANs) are popular generative models for neural vocoders. The DDPMs and GANs can be characterized by the iterative denoising framework and adversarial training, respectively. This study proposes a fast and high-quality neural vocoder called WaveFit, which integrates the essence of GANs into a DDPM-like iterative framework based on fixed-point iteration. WaveFit iteratively denoises an input signal, and trains a deep neural network (DNN) for minimizing an adversarial loss calculated from intermediate outputs at all iterations. Subjective (side-by-side) listening tests showed no statistically significant differences in naturalness between human natural speech and those synthesized by WaveFit with five iterations. Furthermore, the inference speed of WaveFit was more than 240 times faster than WaveRNN. Audio demos are available at google.github.io/df-conformer/wavefit/.

NVDLA is an open-source deep neural network (DNN) accelerator which has received a lot of attention by the community since its introduction by Nvidia. It is a full-featured hardware IP and can serve as a good reference for conducting research and development of SoCs with integrated accelerators. However, an expensive FPGA board is required to do experiments with this IP in a real SoC. Moreover, since NVDLA is clocked at a lower frequency on an FPGA, it would be hard to do accurate performance analysis with such a setup. To overcome these limitations, we integrate NVDLA into a real RISC-V SoC on the Amazon cloud FPGA using FireSim, a cycle-exact FPGA-accelerated simulator. We then evaluate the performance of NVDLA by running YOLOv3 object-detection algorithm. Our results show that NVDLA can sustain 7.5 fps when running YOLOv3. We further analyze the performance by showing that sharing the last-level cache with NVDLA can result in up to 1.56x speedup. We then identify that sharing the memory system with the accelerator can result in unpredictable execution time for the real-time tasks running on this platform. We believe this is an important issue that must be addressed in order for on-chip DNN accelerators to be incorporated in real-time embedded systems.

In this paper, we realize automatic visual recognition and direction estimation of pointing. We introduce the first neural pointing understanding method based on two key contributions. The first is the introduction of a first-of-its-kind large-scale dataset for pointing recognition and direction estimation, which we refer to as the DP Dataset. DP Dataset consists of more than 2 million frames of over 33 people pointing in various styles annotated for each frame with pointing timings and 3D directions. The second is DeePoint, a novel deep network model for joint recognition and 3D direction estimation of pointing. DeePoint is a Transformer-based network which fully leverages the spatio-temporal coordination of the body parts, not just the hands. Through extensive experiments, we demonstrate the accuracy and efficiency of DeePoint. We believe DP Dataset and DeePoint will serve as a sound foundation for visual human intention understanding.

This paper explores the expressive power of deep neural networks through the framework of function compositions. We demonstrate that the repeated compositions of a single fixed-size ReLU network exhibit surprising expressive power, despite the limited expressive capabilities of the individual network itself. Specifically, we prove by construction that L_2circ g^{circ r}circ mathcal{L}_1 can approximate 1-Lipschitz continuous functions on [0,1]^d with an error O(r^{-1/d}), where g is realized by a fixed-size ReLU network, mathcal{L}_1 and L_2 are two affine linear maps matching the dimensions, and g^{circ r} denotes the r-times composition of g. Furthermore, we extend such a result to generic continuous functions on [0,1]^d with the approximation error characterized by the modulus of continuity. Our results reveal that a continuous-depth network generated via a dynamical system has immense approximation power even if its dynamics function is time-independent and realized by a fixed-size ReLU network.

This paper provides a non-asymptotic analysis of linear stochastic approximation (LSA) algorithms with fixed stepsize. This family of methods arises in many machine learning tasks and is used to obtain approximate solutions of a linear system Atheta = b for which A and b can only be accessed through random estimates {({bf A}_n, {bf b}_n): n in N^*}. Our analysis is based on new results regarding moments and high probability bounds for products of matrices which are shown to be tight. We derive high probability bounds on the performance of LSA under weaker conditions on the sequence {({bf A}_n, {bf b}_n): n in N^*} than previous works. However, in contrast, we establish polynomial concentration bounds with order depending on the stepsize. We show that our conclusions cannot be improved without additional assumptions on the sequence of random matrices {{bf A}_n: n in N^*}, and in particular that no Gaussian or exponential high probability bounds can hold. Finally, we pay a particular attention to establishing bounds with sharp order with respect to the number of iterations and the stepsize and whose leading terms contain the covariance matrices appearing in the central limit theorems.

Data heterogeneity is an inherent challenge that hinders the performance of federated learning (FL). Recent studies have identified the biased classifiers of local models as the key bottleneck. Previous attempts have used classifier calibration after FL training, but this approach falls short in improving the poor feature representations caused by training-time classifier biases. Resolving the classifier bias dilemma in FL requires a full understanding of the mechanisms behind the classifier. Recent advances in neural collapse have shown that the classifiers and feature prototypes under perfect training scenarios collapse into an optimal structure called simplex equiangular tight frame (ETF). Building on this neural collapse insight, we propose a solution to the FL's classifier bias problem by utilizing a synthetic and fixed ETF classifier during training. The optimal classifier structure enables all clients to learn unified and optimal feature representations even under extremely heterogeneous data. We devise several effective modules to better adapt the ETF structure in FL, achieving both high generalization and personalization. Extensive experiments demonstrate that our method achieves state-of-the-art performances on CIFAR-10, CIFAR-100, and Tiny-ImageNet.

Security vulnerability repair is a difficult task that is in dire need of automation. Two groups of techniques have shown promise: (1) large code language models (LLMs) that have been pre-trained on source code for tasks such as code completion, and (2) automated program repair (APR) techniques that use deep learning (DL) models to automatically fix software bugs. This paper is the first to study and compare Java vulnerability repair capabilities of LLMs and DL-based APR models. The contributions include that we (1) apply and evaluate five LLMs (Codex, CodeGen, CodeT5, PLBART and InCoder), four fine-tuned LLMs, and four DL-based APR techniques on two real-world Java vulnerability benchmarks (Vul4J and VJBench), (2) design code transformations to address the training and test data overlapping threat to Codex, (3) create a new Java vulnerability repair benchmark VJBench, and its transformed version VJBench-trans and (4) evaluate LLMs and APR techniques on the transformed vulnerabilities in VJBench-trans. Our findings include that (1) existing LLMs and APR models fix very few Java vulnerabilities. Codex fixes 10.2 (20.4%), the most number of vulnerabilities. (2) Fine-tuning with general APR data improves LLMs' vulnerability-fixing capabilities. (3) Our new VJBench reveals that LLMs and APR models fail to fix many Common Weakness Enumeration (CWE) types, such as CWE-325 Missing cryptographic step and CWE-444 HTTP request smuggling. (4) Codex still fixes 8.3 transformed vulnerabilities, outperforming all the other LLMs and APR models on transformed vulnerabilities. The results call for innovations to enhance automated Java vulnerability repair such as creating larger vulnerability repair training data, tuning LLMs with such data, and applying code simplification transformation to facilitate vulnerability repair.

Automated Program Repair (APR) improves software reliability by generating patches for a buggy program automatically. Recent APR techniques leverage deep learning (DL) to build models to learn to generate patches from existing patches and code corpora. While promising, DL-based APR techniques suffer from the abundant syntactically or semantically incorrect patches in the patch space. These patches often disobey the syntactic and semantic domain knowledge of source code and thus cannot be the correct patches to fix a bug. We propose a DL-based APR approach KNOD, which incorporates domain knowledge to guide patch generation in a direct and comprehensive way. KNOD has two major novelties, including (1) a novel three-stage tree decoder, which directly generates Abstract Syntax Trees of patched code according to the inherent tree structure, and (2) a novel domain-rule distillation, which leverages syntactic and semantic rules and teacher-student distributions to explicitly inject the domain knowledge into the decoding procedure during both the training and inference phases. We evaluate KNOD on three widely-used benchmarks. KNOD fixes 72 bugs on the Defects4J v1.2, 25 bugs on the QuixBugs, and 50 bugs on the additional Defects4J v2.0 benchmarks, outperforming all existing APR tools.