Daily Papers

Large Language Models (LLMs) have recently gained popularity due to their impressive few-shot performance across various downstream tasks. However, fine-tuning all parameters and storing a unique model for each downstream task or domain becomes impractical because of the massive size of checkpoints (e.g., 350GB in GPT-3). Current literature, such as LoRA, showcases the potential of low-rank modifications to the original weights of an LLM, enabling efficient adaptation and storage for task-specific models. These methods can reduce the number of parameters needed to fine-tune an LLM by several orders of magnitude. Yet, these methods face two primary limitations: 1) the parameter reduction is lower-bounded by the rank one decomposition, and 2) the extent of reduction is heavily influenced by both the model architecture and the chosen rank. For instance, in larger models, even a rank one decomposition might exceed the number of parameters truly needed for adaptation. In this paper, we introduce NOLA, which overcomes the rank one lower bound present in LoRA. It achieves this by re-parameterizing the low-rank matrices in LoRA using linear combinations of randomly generated matrices (basis) and optimizing the linear mixture coefficients only. This approach allows us to decouple the number of trainable parameters from both the choice of rank and the network architecture. We present adaptation results using GPT-2 and ViT in natural language and computer vision tasks. NOLA performs as well as, or better than models with equivalent parameter counts. Furthermore, we demonstrate that we can halve the parameters in larger models compared to LoRA with rank one, without sacrificing performance.

Following the traditional paradigm of convolutional neural networks (CNNs), modern CNNs manage to keep pace with more recent, for example transformer-based, models by not only increasing model depth and width but also the kernel size. This results in large amounts of learnable model parameters that need to be handled during training. While following the convolutional paradigm with the according spatial inductive bias, we question the significance of learned convolution filters. In fact, our findings demonstrate that many contemporary CNN architectures can achieve high test accuracies without ever updating randomly initialized (spatial) convolution filters. Instead, simple linear combinations (implemented through efficient 1times 1 convolutions) suffice to effectively recombine even random filters into expressive network operators. Furthermore, these combinations of random filters can implicitly regularize the resulting operations, mitigating overfitting and enhancing overall performance and robustness. Conversely, retaining the ability to learn filter updates can impair network performance. Lastly, although we only observe relatively small gains from learning 3times 3 convolutions, the learning gains increase proportionally with kernel size, owing to the non-idealities of the independent and identically distributed (i.i.d.) nature of default initialization techniques.

Model order reduction has been extensively studied over the last two decades. Projection-based methods such as the Proper Orthogonal Decomposition and the Reduced Basis Method enjoy the important advantages of Galerkin methods in the derivation of the reduced problem, but are limited to linear data compression for which the reduced solution is sought as a linear combination of spatial modes. Nonlinear data compression must be used when the solution manifold is not embedded in a low-dimensional subspace. Early methods involve piecewise linear data compression, by constructing a dictionary of reduced-order models tailored to a partition of the solution manifold. In this work, we introduce the concept of optimal partition of the solution manifold in terms of normalized Kolmogorov widths, and prove that the optimal partitions can be found by means of a representative-based clustering algorithm using the sine dissimilarity measure on the solution manifold.

We study reward-free reinforcement learning (RL) with linear function approximation, where the agent works in two phases: (1) in the exploration phase, the agent interacts with the environment but cannot access the reward; and (2) in the planning phase, the agent is given a reward function and is expected to find a near-optimal policy based on samples collected in the exploration phase. The sample complexities of existing reward-free algorithms have a polynomial dependence on the planning horizon, which makes them intractable for long planning horizon RL problems. In this paper, we propose a new reward-free algorithm for learning linear mixture Markov decision processes (MDPs), where the transition probability can be parameterized as a linear combination of known feature mappings. At the core of our algorithm is uncertainty-weighted value-targeted regression with exploration-driven pseudo-reward and a high-order moment estimator for the aleatoric and epistemic uncertainties. When the total reward is bounded by 1, we show that our algorithm only needs to explore tilde O( d^2varepsilon^{-2}) episodes to find an varepsilon-optimal policy, where d is the dimension of the feature mapping. The sample complexity of our algorithm only has a polylogarithmic dependence on the planning horizon and therefore is ``horizon-free''. In addition, we provide an Omega(d^2varepsilon^{-2}) sample complexity lower bound, which matches the sample complexity of our algorithm up to logarithmic factors, suggesting that our algorithm is optimal.

Domain specific question answering is an evolving field that requires specialized solutions to address unique challenges. In this paper, we show that a hybrid approach combining a fine-tuned dense retriever with keyword based sparse search methods significantly enhances performance. Our system leverages a linear combination of relevance signals, including cosine similarity from dense retrieval, BM25 scores, and URL host matching, each with tunable boost parameters. Experimental results indicate that this hybrid method outperforms our single-retriever system, achieving improved accuracy while maintaining robust contextual grounding. These findings suggest that integrating multiple retrieval methodologies with weighted scoring effectively addresses the complexities of domain specific question answering in enterprise settings.

We propose BERMo, an architectural modification to BERT, which makes predictions based on a hierarchy of surface, syntactic and semantic language features. We use linear combination scheme proposed in Embeddings from Language Models (ELMo) to combine the scaled internal representations from different network depths. Our approach has two-fold benefits: (1) improved gradient flow for the downstream task as every layer has a direct connection to the gradients of the loss function and (2) increased representative power as the model no longer needs to copy the features learned in the shallower layer which are necessary for the downstream task. Further, our model has a negligible parameter overhead as there is a single scalar parameter associated with each layer in the network. Experiments on the probing task from SentEval dataset show that our model performs up to 4.65% better in accuracy than the baseline with an average improvement of 2.67% on the semantic tasks. When subject to compression techniques, we find that our model enables stable pruning for compressing small datasets like SST-2, where the BERT model commonly diverges. We observe that our approach converges 1.67times and 1.15times faster than the baseline on MNLI and QQP tasks from GLUE dataset. Moreover, our results show that our approach can obtain better parameter efficiency for penalty based pruning approaches on QQP task.

Motion modeling is critical in flow-based Video Frame Interpolation (VFI). Existing paradigms either consider linear combinations of bidirectional flows or directly predict bilateral flows for given timestamps without exploring favorable motion priors, thus lacking the capability of effectively modeling spatiotemporal dynamics in real-world videos. To address this limitation, in this study, we introduce Generalizable Implicit Motion Modeling (GIMM), a novel and effective approach to motion modeling for VFI. Specifically, to enable GIMM as an effective motion modeling paradigm, we design a motion encoding pipeline to model spatiotemporal motion latent from bidirectional flows extracted from pre-trained flow estimators, effectively representing input-specific motion priors. Then, we implicitly predict arbitrary-timestep optical flows within two adjacent input frames via an adaptive coordinate-based neural network, with spatiotemporal coordinates and motion latent as inputs. Our GIMM can be smoothly integrated with existing flow-based VFI works without further modifications. We show that GIMM performs better than the current state of the art on the VFI benchmarks.

Pre-trained models produce strong generic representations that can be adapted via fine-tuning. The learned weight difference relative to the pre-trained model, known as a task vector, characterises the direction and stride of fine-tuning. The significance of task vectors is such that simple arithmetic operations on them can be used to combine diverse representations from different domains. This paper builds on these properties of task vectors and aims to answer (1) whether components of task vectors, particularly parameter blocks, exhibit similar characteristics, and (2) how such blocks can be used to enhance knowledge composition and transfer. To this end, we introduce aTLAS, an algorithm that linearly combines parameter blocks with different learned coefficients, resulting in anisotropic scaling at the task vector level. We show that such linear combinations explicitly exploit the low intrinsic dimensionality of pre-trained models, with only a few coefficients being the learnable parameters. Furthermore, composition of parameter blocks leverages the already learned representations, thereby reducing the dependency on large amounts of data. We demonstrate the effectiveness of our method in task arithmetic, few-shot recognition and test-time adaptation, with supervised or unsupervised objectives. In particular, we show that (1) learned anisotropic scaling allows task vectors to be more disentangled, causing less interference in composition; (2) task vector composition excels with scarce or no labeled data and is less prone to domain shift, thus leading to better generalisability; (3) mixing the most informative parameter blocks across different task vectors prior to training can reduce the memory footprint and improve the flexibility of knowledge transfer. Moreover, we show the potential of aTLAS as a PEFT method, particularly with less data, and demonstrate that its scalibility.

Direct Preference Optimization (DPO) improves the alignment of large language models (LLMs) with human values by training directly on human preference datasets, eliminating the need for reward models. However, due to the presence of cross-domain human preferences, direct continual training can lead to catastrophic forgetting, limiting DPO's performance and efficiency. Inspired by intraspecific competition driving species evolution, we propose a Online Fast-Slow chasing DPO (OFS-DPO) for preference alignment, simulating competition through fast and slow chasing among models to facilitate rapid adaptation. Specifically, we first derive the regret upper bound for online learning, validating our motivation with a min-max optimization pattern. Based on this, we introduce two identical modules using Low-rank Adaptive (LoRA) with different optimization speeds to simulate intraspecific competition, and propose a new regularization term to guide their learning. To further mitigate catastrophic forgetting in cross-domain scenarios, we extend the OFS-DPO with LoRA modules combination strategy, resulting in the Cross domain Online Fast-Slow chasing DPO (COFS-DPO). This method leverages linear combinations of fast modules parameters from different task domains, fully utilizing historical information to achive continual value alignment. Experimental results show that OFS-DPO outperforms DPO in in-domain alignment, while COFS-DPO excels in cross-domain continual learning scenarios.

Reinforcement learning from human feedback (RLHF) is a key driver of quality and safety in state-of-the-art large language models. Yet, a surprisingly simple and strong inference-time strategy is Best-of-N sampling that selects the best generation among N candidates. In this paper, we propose Best-of-N Distillation (BOND), a novel RLHF algorithm that seeks to emulate Best-of-N but without its significant computational overhead at inference time. Specifically, BOND is a distribution matching algorithm that forces the distribution of generations from the policy to get closer to the Best-of-N distribution. We use the Jeffreys divergence (a linear combination of forward and backward KL) to balance between mode-covering and mode-seeking behavior, and derive an iterative formulation that utilizes a moving anchor for efficiency. We demonstrate the effectiveness of our approach and several design choices through experiments on abstractive summarization and Gemma models. Aligning Gemma policies with BOND outperforms other RLHF algorithms by improving results on several benchmarks.

Zero-shot learning relies on semantic class representations such as hand-engineered attributes or learned embeddings to predict classes without any labeled examples. We propose to learn class representations by embedding nodes from common sense knowledge graphs in a vector space. Common sense knowledge graphs are an untapped source of explicit high-level knowledge that requires little human effort to apply to a range of tasks. To capture the knowledge in the graph, we introduce ZSL-KG, a general-purpose framework with a novel transformer graph convolutional network (TrGCN) for generating class representations. Our proposed TrGCN architecture computes non-linear combinations of node neighbourhoods. Our results show that ZSL-KG improves over existing WordNet-based methods on five out of six zero-shot benchmark datasets in language and vision.

In this paper, we present TailorNet, a neural model which predicts clothing deformation in 3D as a function of three factors: pose, shape and style (garment geometry), while retaining wrinkle detail. This goes beyond prior models, which are either specific to one style and shape, or generalize to different shapes producing smooth results, despite being style specific. Our hypothesis is that (even non-linear) combinations of examples smooth out high frequency components such as fine-wrinkles, which makes learning the three factors jointly hard. At the heart of our technique is a decomposition of deformation into a high frequency and a low frequency component. While the low-frequency component is predicted from pose, shape and style parameters with an MLP, the high-frequency component is predicted with a mixture of shape-style specific pose models. The weights of the mixture are computed with a narrow bandwidth kernel to guarantee that only predictions with similar high-frequency patterns are combined. The style variation is obtained by computing, in a canonical pose, a subspace of deformation, which satisfies physical constraints such as inter-penetration, and draping on the body. TailorNet delivers 3D garments which retain the wrinkles from the physics based simulations (PBS) it is learned from, while running more than 1000 times faster. In contrast to PBS, TailorNet is easy to use and fully differentiable, which is crucial for computer vision algorithms. Several experiments demonstrate TailorNet produces more realistic results than prior work, and even generates temporally coherent deformations on sequences of the AMASS dataset, despite being trained on static poses from a different dataset. To stimulate further research in this direction, we will make a dataset consisting of 55800 frames, as well as our model publicly available at https://virtualhumans.mpi-inf.mpg.de/tailornet.

Monocular dynamic reconstruction is a challenging and long-standing vision problem due to the highly ill-posed nature of the task. Existing approaches are limited in that they either depend on templates, are effective only in quasi-static scenes, or fail to model 3D motion explicitly. In this work, we introduce a method capable of reconstructing generic dynamic scenes, featuring explicit, full-sequence-long 3D motion, from casually captured monocular videos. We tackle the under-constrained nature of the problem with two key insights: First, we exploit the low-dimensional structure of 3D motion by representing scene motion with a compact set of SE3 motion bases. Each point's motion is expressed as a linear combination of these bases, facilitating soft decomposition of the scene into multiple rigidly-moving groups. Second, we utilize a comprehensive set of data-driven priors, including monocular depth maps and long-range 2D tracks, and devise a method to effectively consolidate these noisy supervisory signals, resulting in a globally consistent representation of the dynamic scene. Experiments show that our method achieves state-of-the-art performance for both long-range 3D/2D motion estimation and novel view synthesis on dynamic scenes. Project Page: https://shape-of-motion.github.io/

Model merging has shown great promise at combining expert models, but the benefit of merging is unclear when merging ``generalist'' models trained on many tasks. We explore merging in the context of large (sim100B) models, by recycling checkpoints that exhibit tradeoffs among different tasks. Such checkpoints are often created in the process of developing a frontier model, and many suboptimal ones are usually discarded. Given a pool of model checkpoints obtained from different training runs (e.g., different stages, objectives, hyperparameters, and data mixtures), which naturally show tradeoffs across different language capabilities (e.g., instruction following vs. code generation), we investigate whether merging can recycle such suboptimal models into a Pareto-optimal one. Our optimization algorithm tunes the weight of each checkpoint in a linear combination, resulting in a Pareto-optimal models that outperforms both individual models and merge-based baselines. Further analysis shows that good merges tend to include almost all checkpoints with with non-zero weights, indicating that even seemingly bad initial checkpoints can contribute to good final merges.

Most deep neural networks are trained under fixed network architectures and require retraining when the architecture changes. If expanding the network's size is needed, it is necessary to retrain from scratch, which is expensive. To avoid this, one can grow from a small network by adding random weights over time to gradually achieve the target network size. However, this naive approach falls short in practice as it brings too much noise to the growing process. Prior work tackled this issue by leveraging the already learned weights and training data for generating new weights through conducting a computationally expensive analysis step. In this paper, we introduce MixtureGrowth, a new approach to growing networks that circumvents the initialization overhead in prior work. Before growing, each layer in our model is generated with a linear combination of parameter templates. Newly grown layer weights are generated by using a new linear combination of existing templates for a layer. On one hand, these templates are already trained for the task, providing a strong initialization. On the other, the new coefficients provide flexibility for the added layer weights to learn something new. We show that our approach boosts top-1 accuracy over the state-of-the-art by 2-2.5% on CIFAR-100 and ImageNet datasets, while achieving comparable performance with fewer FLOPs to a larger network trained from scratch. Code is available at https://github.com/chaudatascience/mixturegrowth.

Sparse AutoEnocders (SAEs) have recently been employed as an unsupervised approach for understanding the inner workings of Large Language Models (LLMs). They reconstruct the model's activations with a sparse linear combination of interpretable features. However, training SAEs is computationally intensive, especially as models grow in size and complexity. To address this challenge, we propose a novel training strategy that reduces the number of trained SAEs from one per layer to one for a given group of contiguous layers. Our experimental results on Pythia 160M highlight a speedup of up to 6x without compromising the reconstruction quality and performance on downstream tasks. Therefore, layer clustering presents an efficient approach to train SAEs in modern LLMs.

In-context Learning (ICL) empowers large language models (LLMs) to adapt to unseen tasks during inference by prefixing a few demonstration examples prior to test queries. Despite its versatility, ICL incurs substantial computational and memory overheads compared to zero-shot learning and is susceptible to the selection and order of demonstration examples. In this work, we introduce Implicit In-context Learning (I2CL), an innovative paradigm that addresses the challenges associated with traditional ICL by absorbing demonstration examples within the activation space. I2CL first generates a condensed vector representation, namely a context vector, from the demonstration examples. It then integrates the context vector during inference by injecting a linear combination of the context vector and query activations into the model's residual streams. Empirical evaluation on nine real-world tasks across three model architectures demonstrates that I2CL achieves few-shot performance with zero-shot cost and exhibits robustness against the variation of demonstration examples. Furthermore, I2CL facilitates a novel representation of "task-ids", enhancing task similarity detection and enabling effective transfer learning. We provide a comprehensive analysis of I2CL, offering deeper insights into its mechanisms and broader implications for ICL. The source code is available at: https://github.com/LzVv123456/I2CL.

We demonstrate that a deep model can be reparametrized as a linear combination of several randomly initialized and frozen deep models in the weight space. During training, we seek local minima that reside within the subspace spanned by these random models (i.e., `basis' networks). Our framework, PRANC, enables significant compaction of a deep model. The model can be reconstructed using a single scalar `seed,' employed to generate the pseudo-random `basis' networks, together with the learned linear mixture coefficients. In practical applications, PRANC addresses the challenge of efficiently storing and communicating deep models, a common bottleneck in several scenarios, including multi-agent learning, continual learners, federated systems, and edge devices, among others. In this study, we employ PRANC to condense image classification models and compress images by compacting their associated implicit neural networks. PRANC outperforms baselines with a large margin on image classification when compressing a deep model almost 100 times. Moreover, we show that PRANC enables memory-efficient inference by generating layer-wise weights on the fly. The source code of PRANC is here: https://github.com/UCDvision/PRANC

Low-bit quantization of network weights and activations can drastically reduce the memory footprint, complexity, energy consumption and latency of Deep Neural Networks (DNNs). However, low-bit quantization can also cause a considerable drop in accuracy, in particular when we apply it to complex learning tasks or lightweight DNN architectures. In this paper, we propose a training procedure that relaxes the low-bit quantization. We call this procedure DNN Quantization with Attention (DQA). The relaxation is achieved by using a learnable linear combination of high, medium and low-bit quantizations. Our learning procedure converges step by step to a low-bit quantization using an attention mechanism with temperature scheduling. In experiments, our approach outperforms other low-bit quantization techniques on various object recognition benchmarks such as CIFAR10, CIFAR100 and ImageNet ILSVRC 2012, achieves almost the same accuracy as a full precision DNN, and considerably reduces the accuracy drop when quantizing lightweight DNN architectures.

Predicting face attributes in the wild is challenging due to complex face variations. We propose a novel deep learning framework for attribute prediction in the wild. It cascades two CNNs, LNet and ANet, which are fine-tuned jointly with attribute tags, but pre-trained differently. LNet is pre-trained by massive general object categories for face localization, while ANet is pre-trained by massive face identities for attribute prediction. This framework not only outperforms the state-of-the-art with a large margin, but also reveals valuable facts on learning face representation. (1) It shows how the performances of face localization (LNet) and attribute prediction (ANet) can be improved by different pre-training strategies. (2) It reveals that although the filters of LNet are fine-tuned only with image-level attribute tags, their response maps over entire images have strong indication of face locations. This fact enables training LNet for face localization with only image-level annotations, but without face bounding boxes or landmarks, which are required by all attribute recognition works. (3) It also demonstrates that the high-level hidden neurons of ANet automatically discover semantic concepts after pre-training with massive face identities, and such concepts are significantly enriched after fine-tuning with attribute tags. Each attribute can be well explained with a sparse linear combination of these concepts.

Achieving disentangled control over multiple facial motions and accommodating diverse input modalities greatly enhances the application and entertainment of the talking head generation. This necessitates a deep exploration of the decoupling space for facial features, ensuring that they a) operate independently without mutual interference and b) can be preserved to share with different modal input, both aspects often neglected in existing methods. To address this gap, this paper proposes a novel Efficient Disentanglement framework for Talking head generation (EDTalk). Our framework enables individual manipulation of mouth shape, head pose, and emotional expression, conditioned on video or audio inputs. Specifically, we employ three lightweight modules to decompose the facial dynamics into three distinct latent spaces representing mouth, pose, and expression, respectively. Each space is characterized by a set of learnable bases whose linear combinations define specific motions. To ensure independence and accelerate training, we enforce orthogonality among bases and devise an efficient training strategy to allocate motion responsibilities to each space without relying on external knowledge. The learned bases are then stored in corresponding banks, enabling shared visual priors with audio input. Furthermore, considering the properties of each space, we propose an Audio-to-Motion module for audio-driven talking head synthesis. Experiments are conducted to demonstrate the effectiveness of EDTalk. We recommend watching the project website: https://tanshuai0219.github.io/EDTalk/

In this paper, we propose LEURN: a neural network architecture that learns univariate decision rules. LEURN is a white-box algorithm that results into univariate trees and makes explainable decisions in every stage. In each layer, LEURN finds a set of univariate rules based on an embedding of the previously checked rules and their corresponding responses. Both rule finding and final decision mechanisms are weighted linear combinations of these embeddings, hence contribution of all rules are clearly formulated and explainable. LEURN can select features, extract feature importance, provide semantic similarity between a pair of samples, be used in a generative manner and can give a confidence score. Thanks to a smoothness parameter, LEURN can also controllably behave like decision trees or vanilla neural networks. Besides these advantages, LEURN achieves comparable performance to state-of-the-art methods across 30 tabular datasets for classification and regression problems.

Understanding how Transformer-based Language Models (LMs) learn and recall information is a key goal of the deep learning community. Recent interpretability methods project weights and hidden states obtained from the forward pass to the models' vocabularies, helping to uncover how information flows within LMs. In this work, we extend this methodology to LMs' backward pass and gradients. We first prove that a gradient matrix can be cast as a low-rank linear combination of its forward and backward passes' inputs. We then develop methods to project these gradients into vocabulary items and explore the mechanics of how new information is stored in the LMs' neurons.

Recent representation learning approaches enhance neural topic models by optimizing the weighted linear combination of the evidence lower bound (ELBO) of the log-likelihood and the contrastive learning objective that contrasts pairs of input documents. However, document-level contrastive learning might capture low-level mutual information, such as word ratio, which disturbs topic modeling. Moreover, there is a potential conflict between the ELBO loss that memorizes input details for better reconstruction quality, and the contrastive loss which attempts to learn topic representations that generalize among input documents. To address these issues, we first introduce a novel contrastive learning method oriented towards sets of topic vectors to capture useful semantics that are shared among a set of input documents. Secondly, we explicitly cast contrastive topic modeling as a gradient-based multi-objective optimization problem, with the goal of achieving a Pareto stationary solution that balances the trade-off between the ELBO and the contrastive objective. Extensive experiments demonstrate that our framework consistently produces higher-performing neural topic models in terms of topic coherence, topic diversity, and downstream performance.

3D Morphable Models (3DMMs) demonstrate great potential for reconstructing faithful and animatable 3D facial surfaces from a single image. The facial surface is influenced by the coarse shape, as well as the static detail (e,g., person-specific appearance) and dynamic detail (e.g., expression-driven wrinkles). Previous work struggles to decouple the static and dynamic details through image-level supervision, leading to reconstructions that are not realistic. In this paper, we aim at high-fidelity 3D face reconstruction and propose HiFace to explicitly model the static and dynamic details. Specifically, the static detail is modeled as the linear combination of a displacement basis, while the dynamic detail is modeled as the linear interpolation of two displacement maps with polarized expressions. We exploit several loss functions to jointly learn the coarse shape and fine details with both synthetic and real-world datasets, which enable HiFace to reconstruct high-fidelity 3D shapes with animatable details. Extensive quantitative and qualitative experiments demonstrate that HiFace presents state-of-the-art reconstruction quality and faithfully recovers both the static and dynamic details. Our project page can be found at https://project-hiface.github.io.

Federated learning (FL) aims to perform privacy-preserving machine learning on distributed data held by multiple data owners. To this end, FL requires the data owners to perform training locally and share the gradient updates (instead of the private inputs) with the central server, which are then securely aggregated over multiple data owners. Although aggregation by itself does not provably offer privacy protection, prior work showed that it may suffice if the batch size is sufficiently large. In this paper, we propose the Cocktail Party Attack (CPA) that, contrary to prior belief, is able to recover the private inputs from gradients aggregated over a very large batch size. CPA leverages the crucial insight that aggregate gradients from a fully connected layer is a linear combination of its inputs, which leads us to frame gradient inversion as a blind source separation (BSS) problem (informally called the cocktail party problem). We adapt independent component analysis (ICA)--a classic solution to the BSS problem--to recover private inputs for fully-connected and convolutional networks, and show that CPA significantly outperforms prior gradient inversion attacks, scales to ImageNet-sized inputs, and works on large batch sizes of up to 1024.

The recent surge in large-scale foundation models has spurred the development of efficient methods for adapting these models to various downstream tasks. Low-rank adaptation methods, such as LoRA, have gained significant attention due to their outstanding parameter efficiency and no additional inference latency. This paper investigates a more general form of adapter module based on the analysis that parallel and sequential adaptation branches learn novel and general features during fine-tuning, respectively. The proposed method, named Hydra, due to its multi-head computational branches, combines parallel and sequential branch to integrate capabilities, which is more expressive than existing single branch methods and enables the exploration of a broader range of optimal points in the fine-tuning process. In addition, the proposed adaptation method explicitly leverages the pre-trained weights by performing a linear combination of the pre-trained features. It allows the learned features to have better generalization performance across diverse downstream tasks. Furthermore, we perform a comprehensive analysis of the characteristics of each adaptation branch with empirical evidence. Through an extensive range of experiments, encompassing comparisons and ablation studies, we substantiate the efficiency and demonstrate the superior performance of Hydra. This comprehensive evaluation underscores the potential impact and effectiveness of Hydra in a variety of applications. Our code is available on https://github.com/extremebird/Hydra

Incremental Task learning (ITL) is a category of continual learning that seeks to train a single network for multiple tasks (one after another), where training data for each task is only available during the training of that task. Neural networks tend to forget older tasks when they are trained for the newer tasks; this property is often known as catastrophic forgetting. To address this issue, ITL methods use episodic memory, parameter regularization, masking and pruning, or extensible network structures. In this paper, we propose a new incremental task learning framework based on low-rank factorization. In particular, we represent the network weights for each layer as a linear combination of several rank-1 matrices. To update the network for a new task, we learn a rank-1 (or low-rank) matrix and add that to the weights of every layer. We also introduce an additional selector vector that assigns different weights to the low-rank matrices learned for the previous tasks. We show that our approach performs better than the current state-of-the-art methods in terms of accuracy and forgetting. Our method also offers better memory efficiency compared to episodic memory- and mask-based approaches. Our code will be available at https://github.com/CSIPlab/task-increment-rank-update.git

Most methods for Personalized PageRank (PPR) precompute and store all accurate PPR vectors, and at query time, return the ones of interest directly. However, the storage and computation of all accurate PPR vectors can be prohibitive for large graphs, especially in caching them in memory for real-time online querying. In this paper, we propose a distributed framework that strikes a better balance between offline indexing and online querying. The offline indexing attains a fingerprint of the PPR vector of each vertex by performing billions of "short" random walks in parallel across a cluster of machines. We prove that our indexing method has an exponential convergence, achieving the same precision with previous methods using a much smaller number of random walks. At query time, the new PPR vector is composed by a linear combination of related fingerprints, in a highly efficient vertex-centric decomposition manner. Interestingly, the resulting PPR vector is much more accurate than its offline counterpart because it actually uses more random walks in its estimation. More importantly, we show that such decomposition for a batch of queries can be very efficiently processed using a shared decomposition. Our implementation, PowerWalk, takes advantage of advanced distributed graph engines and it outperforms the state-of-the-art algorithms by orders of magnitude. Particularly, it responses to tens of thousands of queries on graphs with billions of edges in just a few seconds.

We propose a diffusion model-based approach, FloAtControlNet to generate cinemagraphs composed of animations of human clothing. We focus on human clothing like dresses, skirts and pants. The input to our model is a text prompt depicting the type of clothing and the texture of clothing like leopard, striped, or plain, and a sequence of normal maps that capture the underlying animation that we desire in the output. The backbone of our method is a normal-map conditioned ControlNet which is operated in a training-free regime. The key observation is that the underlying animation is embedded in the flow of the normal maps. We utilize the flow thus obtained to manipulate the self-attention maps of appropriate layers. Specifically, the self-attention maps of a particular layer and frame are recomputed as a linear combination of itself and the self-attention maps of the same layer and the previous frame, warped by the flow on the normal maps of the two frames. We show that manipulating the self-attention maps greatly enhances the quality of the clothing animation, making it look more natural as well as suppressing the background artifacts. Through extensive experiments, we show that the method proposed beats all baselines both qualitatively in terms of visual results and user study. Specifically, our method is able to alleviate the background flickering that exists in other diffusion model-based baselines that we consider. In addition, we show that our method beats all baselines in terms of RMSE and PSNR computed using the input normal map sequences and the normal map sequences obtained from the output RGB frames. Further, we show that well-established evaluation metrics like LPIPS, SSIM, and CLIP scores that are generally for visual quality are not necessarily suitable for capturing the subtle motions in human clothing animations.

Monocular depth estimation (MDE) is a fundamental topic of geometric computer vision and a core technique for many downstream applications. Recently, several methods reframe the MDE as a classification-regression problem where a linear combination of probabilistic distribution and bin centers is used to predict depth. In this paper, we propose a novel concept of iterative elastic bins (IEBins) for the classification-regression-based MDE. The proposed IEBins aims to search for high-quality depth by progressively optimizing the search range, which involves multiple stages and each stage performs a finer-grained depth search in the target bin on top of its previous stage. To alleviate the possible error accumulation during the iterative process, we utilize a novel elastic target bin to replace the original target bin, the width of which is adjusted elastically based on the depth uncertainty. Furthermore, we develop a dedicated framework composed of a feature extractor and an iterative optimizer that has powerful temporal context modeling capabilities benefiting from the GRU-based architecture. Extensive experiments on the KITTI, NYU-Depth-v2 and SUN RGB-D datasets demonstrate that the proposed method surpasses prior state-of-the-art competitors. The source code is publicly available at https://github.com/ShuweiShao/IEBins.

Recently, various methods have been proposed to address the inconsistency issue of DDIM inversion to enable image editing, such as EDICT [36] and Null-text inversion [22]. However, the above methods introduce considerable computational overhead. In this paper, we propose a new technique, named bi-directional integration approximation (BDIA), to perform exact diffusion inversion with neglible computational overhead. Suppose we would like to estimate the next diffusion state z_{i-1} at timestep t_i with the historical information (i,z_i) and (i+1,z_{i+1}). We first obtain the estimated Gaussian noise boldsymbol{epsilon}(z_i,i), and then apply the DDIM update procedure twice for approximating the ODE integration over the next time-slot [t_i, t_{i-1}] in the forward manner and the previous time-slot [t_i, t_{t+1}] in the backward manner. The DDIM step for the previous time-slot is used to refine the integration approximation made earlier when computing z_i. A nice property of BDIA-DDIM is that the update expression for z_{i-1} is a linear combination of (z_{i+1}, z_i, boldsymbol{epsilon}(z_i,i)). This allows for exact backward computation of z_{i+1} given (z_i, z_{i-1}), thus leading to exact diffusion inversion. It is demonstrated with experiments that (round-trip) BDIA-DDIM is particularly effective for image editing. Our experiments further show that BDIA-DDIM produces markedly better image sampling qualities than DDIM for text-to-image generation. BDIA can also be applied to improve the performance of other ODE solvers in addition to DDIM. In our work, it is found that applying BDIA to the EDM sampling procedure produces consistently better performance over four pre-trained models.

Dictionary learning is a key tool for representation learning, that explains the data as linear combination of few basic elements. Yet, this analysis is not amenable in the context of graph learning, as graphs usually belong to different metric spaces. We fill this gap by proposing a new online Graph Dictionary Learning approach, which uses the Gromov Wasserstein divergence for the data fitting term. In our work, graphs are encoded through their nodes' pairwise relations and modeled as convex combination of graph atoms, i.e. dictionary elements, estimated thanks to an online stochastic algorithm, which operates on a dataset of unregistered graphs with potentially different number of nodes. Our approach naturally extends to labeled graphs, and is completed by a novel upper bound that can be used as a fast approximation of Gromov Wasserstein in the embedding space. We provide numerical evidences showing the interest of our approach for unsupervised embedding of graph datasets and for online graph subspace estimation and tracking.

A key goal in mechanistic interpretability is circuit analysis: finding sparse subgraphs of models corresponding to specific behaviors or capabilities. However, MLP sublayers make fine-grained circuit analysis on transformer-based language models difficult. In particular, interpretable features -- such as those found by sparse autoencoders (SAEs) -- are typically linear combinations of extremely many neurons, each with its own nonlinearity to account for. Circuit analysis in this setting thus either yields intractably large circuits or fails to disentangle local and global behavior. To address this we explore transcoders, which seek to faithfully approximate a densely activating MLP layer with a wider, sparsely-activating MLP layer. We successfully train transcoders on language models with 120M, 410M, and 1.4B parameters, and find them to perform at least on par with SAEs in terms of sparsity, faithfulness, and human-interpretability. We then introduce a novel method for using transcoders to perform weights-based circuit analysis through MLP sublayers. The resulting circuits neatly factorize into input-dependent and input-invariant terms. Finally, we apply transcoders to reverse-engineer unknown circuits in the model, and we obtain novel insights regarding the greater-than circuit in GPT2-small. Our results suggest that transcoders can prove effective in decomposing model computations involving MLPs into interpretable circuits. Code is available at https://github.com/jacobdunefsky/transcoder_circuits.

Sparse coding, which refers to modeling a signal as sparse linear combinations of the elements of a learned dictionary, has proven to be a successful (and interpretable) approach in applications such as signal processing, computer vision, and medical imaging. While this success has spurred much work on provable guarantees for dictionary recovery when the learned dictionary is the same size as the ground-truth dictionary, work on the setting where the learned dictionary is larger (or over-realized) with respect to the ground truth is comparatively nascent. Existing theoretical results in this setting have been constrained to the case of noise-less data. We show in this work that, in the presence of noise, minimizing the standard dictionary learning objective can fail to recover the elements of the ground-truth dictionary in the over-realized regime, regardless of the magnitude of the signal in the data-generating process. Furthermore, drawing from the growing body of work on self-supervised learning, we propose a novel masking objective for which recovering the ground-truth dictionary is in fact optimal as the signal increases for a large class of data-generating processes. We corroborate our theoretical results with experiments across several parameter regimes showing that our proposed objective also enjoys better empirical performance than the standard reconstruction objective.

We propose a general framework called Network Dissection for quantifying the interpretability of latent representations of CNNs by evaluating the alignment between individual hidden units and a set of semantic concepts. Given any CNN model, the proposed method draws on a broad data set of visual concepts to score the semantics of hidden units at each intermediate convolutional layer. The units with semantics are given labels across a range of objects, parts, scenes, textures, materials, and colors. We use the proposed method to test the hypothesis that interpretability of units is equivalent to random linear combinations of units, then we apply our method to compare the latent representations of various networks when trained to solve different supervised and self-supervised training tasks. We further analyze the effect of training iterations, compare networks trained with different initializations, examine the impact of network depth and width, and measure the effect of dropout and batch normalization on the interpretability of deep visual representations. We demonstrate that the proposed method can shed light on characteristics of CNN models and training methods that go beyond measurements of their discriminative power.

Reward design is a fundamental, yet challenging aspect of practical reinforcement learning (RL). For simple tasks, researchers typically handcraft the reward function, e.g., using a linear combination of several reward factors. However, such reward engineering is subject to approximation bias, incurs large tuning cost, and often cannot provide the granularity required for complex tasks. To avoid these difficulties, researchers have turned to reinforcement learning from human feedback (RLHF), which learns a reward function from human preferences between pairs of trajectory sequences. By leveraging preference-based reward modeling, RLHF learns complex rewards that are well aligned with human preferences, allowing RL to tackle increasingly difficult problems. Unfortunately, the applicability of RLHF is limited due to the high cost and difficulty of obtaining human preference data. In light of this cost, we investigate learning reward functions for complex tasks with less human effort; simply by ranking the importance of the reward factors. More specifically, we propose a new RL framework -- HERON, which compares trajectories using a hierarchical decision tree induced by the given ranking. These comparisons are used to train a preference-based reward model, which is then used for policy learning. We find that our framework can not only train high performing agents on a variety of difficult tasks, but also provide additional benefits such as improved sample efficiency and robustness. Our code is available at https://github.com/abukharin3/HERON.

We present Backpacks: a new neural architecture that marries strong modeling performance with an interface for interpretability and control. Backpacks learn multiple non-contextual sense vectors for each word in a vocabulary, and represent a word in a sequence as a context-dependent, non-negative linear combination of sense vectors in this sequence. We find that, after training, sense vectors specialize, each encoding a different aspect of a word. We can interpret a sense vector by inspecting its (non-contextual, linear) projection onto the output space, and intervene on these interpretable hooks to change the model's behavior in predictable ways. We train a 170M-parameter Backpack language model on OpenWebText, matching the loss of a GPT-2 small (124Mparameter) Transformer. On lexical similarity evaluations, we find that Backpack sense vectors outperform even a 6B-parameter Transformer LM's word embeddings. Finally, we present simple algorithms that intervene on sense vectors to perform controllable text generation and debiasing. For example, we can edit the sense vocabulary to tend more towards a topic, or localize a source of gender bias to a sense vector and globally suppress that sense.

We consider the problem of segmenting objects in videos based on their motion and no other forms of supervision. Prior work has often approached this problem by using the principle of common fate, namely the fact that the motion of points that belong to the same object is strongly correlated. However, most authors have only considered instantaneous motion from optical flow. In this work, we present a way to train a segmentation network using long-term point trajectories as a supervisory signal to complement optical flow. The key difficulty is that long-term motion, unlike instantaneous motion, is difficult to model -- any parametric approximation is unlikely to capture complex motion patterns over long periods of time. We instead draw inspiration from subspace clustering approaches, proposing a loss function that seeks to group the trajectories into low-rank matrices where the motion of object points can be approximately explained as a linear combination of other point tracks. Our method outperforms the prior art on motion-based segmentation, which shows the utility of long-term motion and the effectiveness of our formulation.

Concept Bottleneck Models (CBMs) offer inherent interpretability by initially translating images into human-comprehensible concepts, followed by a linear combination of these concepts for classification. However, the annotation of concepts for visual recognition tasks requires extensive expert knowledge and labor, constraining the broad adoption of CBMs. Recent approaches have leveraged the knowledge of large language models to construct concept bottlenecks, with multimodal models like CLIP subsequently mapping image features into the concept feature space for classification. Despite this, the concepts produced by language models can be verbose and may introduce non-visual attributes, which hurts accuracy and interpretability. In this study, we investigate to avoid these issues by constructing CBMs directly from multimodal models. To this end, we adopt common words as base concept vocabulary and leverage auxiliary unlabeled images to construct a Vision-to-Concept (V2C) tokenizer that can explicitly quantize images into their most relevant visual concepts, thus creating a vision-oriented concept bottleneck tightly coupled with the multimodal model. This leads to our V2C-CBM which is training efficient and interpretable with high accuracy. Our V2C-CBM has matched or outperformed LLM-supervised CBMs on various visual classification benchmarks, validating the efficacy of our approach.

Vocabulary adaptation, which integrates new vocabulary into pre-trained language models (LMs), enables expansion to new languages and mitigates token over-fragmentation. However, existing approaches are limited by their reliance on heuristic or external embeddings. We propose VocADT, a novel method for vocabulary adaptation using adapter modules that are trained to learn the optimal linear combination of existing embeddings while keeping the model's weights fixed. VocADT offers a flexible and scalable solution without requiring external resources or language constraints. Across 11 languages-with various scripts, resource availability, and fragmentation-we demonstrate that VocADT outperforms the original Mistral model and other baselines across various multilingual tasks. We find that Latin-script languages and highly fragmented languages benefit the most from vocabulary adaptation. We further fine-tune the adapted model on the generative task of machine translation and find that vocabulary adaptation is still beneficial after fine-tuning and that VocADT is the most effective method.

Online updating of time series forecasting models aims to address the concept drifting problem by efficiently updating forecasting models based on streaming data. Many algorithms are designed for online time series forecasting, with some exploiting cross-variable dependency while others assume independence among variables. Given every data assumption has its own pros and cons in online time series modeling, we propose Online ensembling Network (OneNet). It dynamically updates and combines two models, with one focusing on modeling the dependency across the time dimension and the other on cross-variate dependency. Our method incorporates a reinforcement learning-based approach into the traditional online convex programming framework, allowing for the linear combination of the two models with dynamically adjusted weights. OneNet addresses the main shortcoming of classical online learning methods that tend to be slow in adapting to the concept drift. Empirical results show that OneNet reduces online forecasting error by more than 50% compared to the State-Of-The-Art (SOTA) method. The code is available at https://github.com/yfzhang114/OneNet.

We propose a novel unsupervised object localization method that allows us to explain the predictions of the model by utilizing self-supervised pre-trained models without additional finetuning. Existing unsupervised and self-supervised object localization methods often utilize class-agnostic activation maps or self-similarity maps of a pre-trained model. Although these maps can offer valuable information for localization, their limited ability to explain how the model makes predictions remains challenging. In this paper, we propose a simple yet effective unsupervised object localization method based on representer point selection, where the predictions of the model can be represented as a linear combination of representer values of training points. By selecting representer points, which are the most important examples for the model predictions, our model can provide insights into how the model predicts the foreground object by providing relevant examples as well as their importance. Our method outperforms the state-of-the-art unsupervised and self-supervised object localization methods on various datasets with significant margins and even outperforms recent weakly supervised and few-shot methods.

Structured pruning and quantization are promising approaches for reducing the inference time and memory footprint of neural networks. However, most existing methods require the original training dataset to fine-tune the model. This not only brings heavy resource consumption but also is not possible for applications with sensitive or proprietary data due to privacy and security concerns. Therefore, a few data-free methods are proposed to address this problem, but they perform data-free pruning and quantization separately, which does not explore the complementarity of pruning and quantization. In this paper, we propose a novel framework named Unified Data-Free Compression(UDFC), which performs pruning and quantization simultaneously without any data and fine-tuning process. Specifically, UDFC starts with the assumption that the partial information of a damaged(e.g., pruned or quantized) channel can be preserved by a linear combination of other channels, and then derives the reconstruction form from the assumption to restore the information loss due to compression. Finally, we formulate the reconstruction error between the original network and its compressed network, and theoretically deduce the closed-form solution. We evaluate the UDFC on the large-scale image classification task and obtain significant improvements over various network architectures and compression methods. For example, we achieve a 20.54% accuracy improvement on ImageNet dataset compared to SOTA method with 30% pruning ratio and 6-bit quantization on ResNet-34.

Automated model selection is often proposed to users to choose which machine learning model (or method) to apply to a given regression task. In this paper, we show that combining different regression models can yield better results than selecting a single ('best') regression model, and outline an efficient method that obtains optimally weighted convex linear combination from a heterogeneous set of regression models. More specifically, in this paper, a heuristic weight optimization, used in a preceding conference paper, is replaced by an exact optimization algorithm using convex quadratic programming. We prove convexity of the quadratic programming formulation for the straightforward formulation and for a formulation with weighted data points. The novel weight optimization is not only (more) exact but also more efficient. The methods we develop in this paper are implemented and made available via github-open source. They can be executed on commonly available hardware and offer a transparent and easy to interpret interface. The results indicate that the approach outperforms model selection methods on a range of data sets, including data sets with mixed variable type from drug discovery applications.

Deep learning models have achieved remarkable success in different areas of machine learning over the past decade; however, the size and complexity of these models make them difficult to understand. In an effort to make them more interpretable, several recent works focus on explaining parts of a deep neural network through human-interpretable, semantic attributes. However, it may be impossible to completely explain complex models using only semantic attributes. In this work, we propose to augment these attributes with a small set of uninterpretable features. Specifically, we develop a novel explanation framework ELUDE (Explanation via Labelled and Unlabelled DEcomposition) that decomposes a model's prediction into two parts: one that is explainable through a linear combination of the semantic attributes, and another that is dependent on the set of uninterpretable features. By identifying the latter, we are able to analyze the "unexplained" portion of the model, obtaining insights into the information used by the model. We show that the set of unlabelled features can generalize to multiple models trained with the same feature space and compare our work to two popular attribute-oriented methods, Interpretable Basis Decomposition and Concept Bottleneck, and discuss the additional insights ELUDE provides.

Cross-entropy loss and focal loss are the most common choices when training deep neural networks for classification problems. Generally speaking, however, a good loss function can take on much more flexible forms, and should be tailored for different tasks and datasets. Motivated by how functions can be approximated via Taylor expansion, we propose a simple framework, named PolyLoss, to view and design loss functions as a linear combination of polynomial functions. Our PolyLoss allows the importance of different polynomial bases to be easily adjusted depending on the targeting tasks and datasets, while naturally subsuming the aforementioned cross-entropy loss and focal loss as special cases. Extensive experimental results show that the optimal choice within the PolyLoss is indeed dependent on the task and dataset. Simply by introducing one extra hyperparameter and adding one line of code, our Poly-1 formulation outperforms the cross-entropy loss and focal loss on 2D image classification, instance segmentation, object detection, and 3D object detection tasks, sometimes by a large margin.

Understanding the glassy nature of neural networks is pivotal both for theoretical and computational advances in Machine Learning and Theoretical Artificial Intelligence. Keeping the focus on dense associative Hebbian neural networks, the purpose of this paper is two-fold: at first we develop rigorous mathematical approaches to address properly a statistical mechanical picture of the phenomenon of {\em replica symmetry breaking} (RSB) in these networks, then -- deepening results stemmed via these routes -- we aim to inspect the {\em glassiness} that they hide. In particular, regarding the methodology, we provide two techniques: the former is an adaptation of the transport PDE to the case, while the latter is an extension of Guerra's interpolation breakthrough. Beyond coherence among the results, either in replica symmetric and in the one-step replica symmetry breaking level of description, we prove the Gardner's picture and we identify the maximal storage capacity by a ground-state analysis in the Baldi-Venkatesh high-storage regime. In the second part of the paper we investigate the glassy structure of these networks: in contrast with the replica symmetric scenario (RS), RSB actually stabilizes the spin-glass phase. We report huge differences w.r.t. the standard pairwise Hopfield limit: in particular, it is known that it is possible to express the free energy of the Hopfield neural network as a linear combination of the free energies of an hard spin glass (i.e. the Sherrington-Kirkpatrick model) and a soft spin glass (the Gaussian or "spherical" model). This is no longer true when interactions are more than pairwise (whatever the level of description, RS or RSB): for dense networks solely the free energy of the hard spin glass survives, proving a huge diversity in the underlying glassiness of associative neural networks.

We present NeX, a new approach to novel view synthesis based on enhancements of multiplane image (MPI) that can reproduce next-level view-dependent effects -- in real time. Unlike traditional MPI that uses a set of simple RGBalpha planes, our technique models view-dependent effects by instead parameterizing each pixel as a linear combination of basis functions learned from a neural network. Moreover, we propose a hybrid implicit-explicit modeling strategy that improves upon fine detail and produces state-of-the-art results. Our method is evaluated on benchmark forward-facing datasets as well as our newly-introduced dataset designed to test the limit of view-dependent modeling with significantly more challenging effects such as rainbow reflections on a CD. Our method achieves the best overall scores across all major metrics on these datasets with more than 1000times faster rendering time than the state of the art. For real-time demos, visit https://nex-mpi.github.io/

Recently, increasing attention has been drawn to the internal mechanisms of convolutional neural networks, and the reason why the network makes specific decisions. In this paper, we develop a novel post-hoc visual explanation method called Score-CAM based on class activation mapping. Unlike previous class activation mapping based approaches, Score-CAM gets rid of the dependence on gradients by obtaining the weight of each activation map through its forward passing score on target class, the final result is obtained by a linear combination of weights and activation maps. We demonstrate that Score-CAM achieves better visual performance and fairness for interpreting the decision making process. Our approach outperforms previous methods on both recognition and localization tasks, it also passes the sanity check. We also indicate its application as debugging tools. Official code has been released.

Low-Rank Adaptation (LoRA) and its variants have shown impressive results in reducing the number of trainable parameters and memory requirements of large transformer networks while maintaining fine-tuning performance. However, the low-rank nature of the weight update inherently limits the representation power of fine-tuned models, potentially compromising performance on complex tasks. This raises a critical question: when a performance gap between LoRA and standard fine-tuning is observed, is it due to the reduced number of trainable parameters or the rank deficiency? This paper aims to answer this question by introducing RandLoRA, a parameter-efficient method that performs full-rank updates using a learned linear combinations of low-rank, non-trainable random matrices. Our method limits the number of trainable parameters by restricting optimization to diagonal scaling matrices applied to the fixed random matrices. This allows us to effectively overcome the low-rank limitations while maintaining parameter and memory efficiency during training. Through extensive experimentation across vision, language, and vision-language benchmarks, we systematically evaluate the limitations of LoRA and existing random basis methods. Our findings reveal that full-rank updates are beneficial across vision and language tasks individually, and even more so for vision-language tasks, where RandLoRA significantly reduces -- and sometimes eliminates -- the performance gap between standard fine-tuning and LoRA, demonstrating its efficacy.

To adapt a well-trained large model to downstream tasks, we propose constraining learning within its original latent space by leveraging linear combinations of its basis vectors. This approach ensures stable training without compromising the model's capabilities. Traditionally, constructing orthonormal bases from a matrix requires a transfer matrix, which significantly increases storage and computational overhead for parameters and feature maps. In this paper, we introduce Absorb and Decompose for Q, K, V, and O matrices, enabling their orthogonalization without the need for transfer matrices. Furthermore, the Absorb-Decompose operation eliminates redundant vectors, reducing the encoder attention parameters of Whisper-large-v3 by 46.42% without requiring additional training. For parameter-efficient and stable fine-tuning, we orthonormalized Q, K, V, and O and fine-tuned only the singular values, allowing efficient adaptation while constraining changes to the original latent space. When fine-tuning LLaMA-2-7B on eight commonsense reasoning datasets, our method outperforms LoRA by 5.4% and DoRA by 4.4%.

In this work, the human parsing task, namely decomposing a human image into semantic fashion/body regions, is formulated as an Active Template Regression (ATR) problem, where the normalized mask of each fashion/body item is expressed as the linear combination of the learned mask templates, and then morphed to a more precise mask with the active shape parameters, including position, scale and visibility of each semantic region. The mask template coefficients and the active shape parameters together can generate the human parsing results, and are thus called the structure outputs for human parsing. The deep Convolutional Neural Network (CNN) is utilized to build the end-to-end relation between the input human image and the structure outputs for human parsing. More specifically, the structure outputs are predicted by two separate networks. The first CNN network is with max-pooling, and designed to predict the template coefficients for each label mask, while the second CNN network is without max-pooling to preserve sensitivity to label mask position and accurately predict the active shape parameters. For a new image, the structure outputs of the two networks are fused to generate the probability of each label for each pixel, and super-pixel smoothing is finally used to refine the human parsing result. Comprehensive evaluations on a large dataset well demonstrate the significant superiority of the ATR framework over other state-of-the-arts for human parsing. In particular, the F1-score reaches 64.38% by our ATR framework, significantly higher than 44.76% based on the state-of-the-art algorithm.

Diagrams matter. Unfortunately, the deep learning community has no standard method for diagramming architectures. The current combination of linear algebra notation and ad-hoc diagrams fails to offer the necessary precision to understand architectures in all their detail. However, this detail is critical for faithful implementation, mathematical analysis, further innovation, and ethical assurances. I present neural circuit diagrams, a graphical language tailored to the needs of communicating deep learning architectures. Neural circuit diagrams naturally keep track of the changing arrangement of data, precisely show how operations are broadcast over axes, and display the critical parallel behavior of linear operations. A lingering issue with existing diagramming methods is the inability to simultaneously express the detail of axes and the free arrangement of data, which neural circuit diagrams solve. Their compositional structure is analogous to code, creating a close correspondence between diagrams and implementation. In this work, I introduce neural circuit diagrams for an audience of machine learning researchers. After introducing neural circuit diagrams, I cover a host of architectures to show their utility and breed familiarity. This includes the transformer architecture, convolution (and its difficult-to-explain extensions), residual networks, the U-Net, and the vision transformer. I include a Jupyter notebook that provides evidence for the close correspondence between diagrams and code. Finally, I examine backpropagation using neural circuit diagrams. I show their utility in providing mathematical insight and analyzing algorithms' time and space complexities.

Cosine-similarity is the cosine of the angle between two vectors, or equivalently the dot product between their normalizations. A popular application is to quantify semantic similarity between high-dimensional objects by applying cosine-similarity to a learned low-dimensional feature embedding. This can work better but sometimes also worse than the unnormalized dot-product between embedded vectors in practice. To gain insight into this empirical observation, we study embeddings derived from regularized linear models, where closed-form solutions facilitate analytical insights. We derive analytically how cosine-similarity can yield arbitrary and therefore meaningless `similarities.' For some linear models the similarities are not even unique, while for others they are implicitly controlled by the regularization. We discuss implications beyond linear models: a combination of different regularizations are employed when learning deep models; these have implicit and unintended effects when taking cosine-similarities of the resulting embeddings, rendering results opaque and possibly arbitrary. Based on these insights, we caution against blindly using cosine-similarity and outline alternatives.

Neural networks have shown tremendous growth in recent years to solve numerous problems. Various types of neural networks have been introduced to deal with different types of problems. However, the main goal of any neural network is to transform the non-linearly separable input data into more linearly separable abstract features using a hierarchy of layers. These layers are combinations of linear and nonlinear functions. The most popular and common non-linearity layers are activation functions (AFs), such as Logistic Sigmoid, Tanh, ReLU, ELU, Swish and Mish. In this paper, a comprehensive overview and survey is presented for AFs in neural networks for deep learning. Different classes of AFs such as Logistic Sigmoid and Tanh based, ReLU based, ELU based, and Learning based are covered. Several characteristics of AFs such as output range, monotonicity, and smoothness are also pointed out. A performance comparison is also performed among 18 state-of-the-art AFs with different networks on different types of data. The insights of AFs are presented to benefit the researchers for doing further research and practitioners to select among different choices. The code used for experimental comparison is released at: https://github.com/shivram1987/ActivationFunctions.

We investigate compositional structures in data embeddings from pre-trained vision-language models (VLMs). Traditionally, compositionality has been associated with algebraic operations on embeddings of words from a pre-existing vocabulary. In contrast, we seek to approximate representations from an encoder as combinations of a smaller set of vectors in the embedding space. These vectors can be seen as "ideal words" for generating concepts directly within the embedding space of the model. We first present a framework for understanding compositional structures from a geometric perspective. We then explain what these compositional structures entail probabilistically in the case of VLM embeddings, providing intuitions for why they arise in practice. Finally, we empirically explore these structures in CLIP's embeddings and we evaluate their usefulness for solving different vision-language tasks such as classification, debiasing, and retrieval. Our results show that simple linear algebraic operations on embedding vectors can be used as compositional and interpretable methods for regulating the behavior of VLMs.

Large linear systems play an important role in high-energy theory, appearing in amplitude bootstraps and during integral reduction. This paper introduces FiniteFieldSolve, a general-purpose toolkit for exactly solving large linear systems over the rationals. The solver interfaces directly with Mathematica, is straightforward to install, and seamlessly replaces Mathematica's native solvers. In testing, FiniteFieldSolve is approximately two orders of magnitude faster than Mathematica and uses an order of magnitude less memory. The package also compares favorably against other public solvers in FiniteFieldSolve's intended use cases. As the name of the package suggests, solutions are obtained via well-known finite field methods. These methods suffer from introducing an inordinate number of modulo (or integer division) operations with respect to different primes. By automatically recompiling itself for each prime, FiniteFieldSolve converts the division operations into much faster combinations of instructions, dramatically improving performance. The technique of compiling the prime can be applied to any finite field solver, where the time savings will be solver dependent. The operation of the package is illustrated through a detailed example of an amplitude bootstrap.

Averaging neural network parameters is an intuitive method for fusing the knowledge of two independent models. It is most prominently used in federated learning. If models are averaged at the end of training, this can only lead to a good performing model if the loss surface of interest is very particular, i.e., the loss in the midpoint between the two models needs to be sufficiently low. This is impossible to guarantee for the non-convex losses of state-of-the-art networks. For averaging models trained on vastly different datasets, it was proposed to average only the parameters of particular layers or combinations of layers, resulting in better performing models. To get a better understanding of the effect of layer-wise averaging, we analyse the performance of the models that result from averaging single layers, or groups of layers. Based on our empirical and theoretical investigation, we introduce a novel notion of the layer-wise linear connectivity, and show that deep networks do not have layer-wise barriers between them.

We study reinforcement learning with linear function approximation and adversarially changing cost functions, a setup that has mostly been considered under simplifying assumptions such as full information feedback or exploratory conditions.We present a computationally efficient policy optimization algorithm for the challenging general setting of unknown dynamics and bandit feedback, featuring a combination of mirror-descent and least squares policy evaluation in an auxiliary MDP used to compute exploration bonuses.Our algorithm obtains an widetilde O(K^{6/7}) regret bound, improving significantly over previous state-of-the-art of widetilde O (K^{14/15}) in this setting. In addition, we present a version of the same algorithm under the assumption a simulator of the environment is available to the learner (but otherwise no exploratory assumptions are made), and prove it obtains state-of-the-art regret of widetilde O (K^{2/3}).

Nearest neighbour based methods have proved to be one of the most successful self-supervised learning (SSL) approaches due to their high generalization capabilities. However, their computational efficiency decreases when more than one neighbour is used. In this paper, we propose a novel contrastive SSL approach, which we call All4One, that reduces the distance between neighbour representations using ''centroids'' created through a self-attention mechanism. We use a Centroid Contrasting objective along with single Neighbour Contrasting and Feature Contrasting objectives. Centroids help in learning contextual information from multiple neighbours whereas the neighbour contrast enables learning representations directly from the neighbours and the feature contrast allows learning representations unique to the features. This combination enables All4One to outperform popular instance discrimination approaches by more than 1% on linear classification evaluation for popular benchmark datasets and obtains state-of-the-art (SoTA) results. Finally, we show that All4One is robust towards embedding dimensionalities and augmentations, surpassing NNCLR and Barlow Twins by more than 5% on low dimensionality and weak augmentation settings. The source code would be made available soon.

Many complex tasks can be decomposed into simpler, independent parts. Discovering such underlying compositional structure has the potential to enable compositional generalization. Despite progress, our most powerful systems struggle to compose flexibly. It therefore seems natural to make models more modular to help capture the compositional nature of many tasks. However, it is unclear under which circumstances modular systems can discover hidden compositional structure. To shed light on this question, we study a teacher-student setting with a modular teacher where we have full control over the composition of ground truth modules. This allows us to relate the problem of compositional generalization to that of identification of the underlying modules. In particular we study modularity in hypernetworks representing a general class of multiplicative interactions. We show theoretically that identification up to linear transformation purely from demonstrations is possible without having to learn an exponential number of module combinations. We further demonstrate empirically that under the theoretically identified conditions, meta-learning from finite data can discover modular policies that generalize compositionally in a number of complex environments.

In this paper, we give an in-depth analysis on the mathematical problem formulations and the probabilistic optimization explorations for some of the key components in Transformer model [33] in the field of generative AI. We explore and discuss some potential further enhancement for current state of the art methods for some key underlying technologies of generative AI models from algorithmic and probabilistic optimization perspective. In particular, we present an optimal solution for sub-word encoding (SWE) based on similar initial settings as that of byte-pair encoding (BPE) algorithm in [9] with similar objectives as that of WordPiece approach in [28, 31] to maximize the likelihood of the training data. We also present cross entropy optimization method to optimize hyperparameters for word2vec model [17]. In addition, we propose a factored combination of rotary positional encoding (RoPE) [32] and attention with linear biases (ALiBi) [23] with a harmonic series. We also present a probabilistic FlashAttention [6, 7] (PrFlashAttention) method with a probability distribution over block distances in the matrix to decide which block is likely to participate in a given round of attention computation while maintaining the lower triangle shape of the tensor for autoregressive language models by re-shaping the tensors. Finally, we present staircase adaptive quantization (SAQ) of key-value (KV) cache for multi-query attention (MQA) based on the framework presented in [16] to have gradual quantization degradation while achieving reasonable model quality and cost savings.

Selective state-space models (SSMs) are an emerging alternative to the Transformer, offering the unique advantage of parallel training and sequential inference. Although these models have shown promising performance on a variety of tasks, their formal expressiveness and length generalization properties remain underexplored. In this work, we provide insight into the workings of selective SSMs by analyzing their expressiveness and length generalization performance on regular language tasks, i.e., finite-state automaton (FSA) emulation. We address certain limitations of modern SSM-based architectures by introducing the Selective Dense State-Space Model (SD-SSM), the first selective SSM that exhibits perfect length generalization on a set of various regular language tasks using a single layer. It utilizes a dictionary of dense transition matrices, a softmax selection mechanism that creates a convex combination of dictionary matrices at each time step, and a readout consisting of layer normalization followed by a linear map. We then proceed to evaluate variants of diagonal selective SSMs by considering their empirical performance on commutative and non-commutative automata. We explain the experimental results with theoretical considerations. Our code is available at https://github.com/IBM/selective-dense-state-space-model.

The prevalent use of commercial and open-source diffusion models (DMs) for text-to-image generation prompts risk mitigation to prevent undesired behaviors. Existing concept erasing methods in academia are all based on full parameter or specification-based fine-tuning, from which we observe the following issues: 1) Generation alternation towards erosion: Parameter drift during target elimination causes alternations and potential deformations across all generations, even eroding other concepts at varying degrees, which is more evident with multi-concept erased; 2) Transfer inability & deployment inefficiency: Previous model-specific erasure impedes the flexible combination of concepts and the training-free transfer towards other models, resulting in linear cost growth as the deployment scenarios increase. To achieve non-invasive, precise, customizable, and transferable elimination, we ground our erasing framework on one-dimensional adapters to erase multiple concepts from most DMs at once across versatile erasing applications. The concept-SemiPermeable structure is injected as a Membrane (SPM) into any DM to learn targeted erasing, and meantime the alteration and erosion phenomenon is effectively mitigated via a novel Latent Anchoring fine-tuning strategy. Once obtained, SPMs can be flexibly combined and plug-and-play for other DMs without specific re-tuning, enabling timely and efficient adaptation to diverse scenarios. During generation, our Facilitated Transport mechanism dynamically regulates the permeability of each SPM to respond to different input prompts, further minimizing the impact on other concepts. Quantitative and qualitative results across ~40 concepts, 7 DMs and 4 erasing applications have demonstrated the superior erasing of SPM. Our code and pre-tuned SPMs will be available on the project page https://lyumengyao.github.io/projects/spm.

It has recently been conjectured that neural network solution sets reachable via stochastic gradient descent (SGD) are convex, considering permutation invariances (Entezari et al., 2022). This means that a linear path can connect two independent solutions with low loss, given the weights of one of the models are appropriately permuted. However, current methods to test this theory often require very wide networks to succeed. In this work, we conjecture that more generally, the SGD solution set is a "star domain" that contains a "star model" that is linearly connected to all the other solutions via paths with low loss values, modulo permutations. We propose the Starlight algorithm that finds a star model of a given learning task. We validate our claim by showing that this star model is linearly connected with other independently found solutions. As an additional benefit of our study, we demonstrate better uncertainty estimates on the Bayesian Model Averaging over the obtained star domain. Further, we demonstrate star models as potential substitutes for model ensembles. Our code is available at https://github.com/aktsonthalia/starlight.

Combining simple elements from the literature, we define a linear model that is geared toward sparse data, in particular implicit feedback data for recommender systems. We show that its training objective has a closed-form solution, and discuss the resulting conceptual insights. Surprisingly, this simple model achieves better ranking accuracy than various state-of-the-art collaborative-filtering approaches, including deep non-linear models, on most of the publicly available data-sets used in our experiments.

Gated Linear Units (arXiv:1612.08083) consist of the component-wise product of two linear projections, one of which is first passed through a sigmoid function. Variations on GLU are possible, using different nonlinear (or even linear) functions in place of sigmoid. We test these variants in the feed-forward sublayers of the Transformer (arXiv:1706.03762) sequence-to-sequence model, and find that some of them yield quality improvements over the typically-used ReLU or GELU activations.

Linear Sequence Modeling (LSM) like linear attention, state space models and linear RNNs, and Mixture-of-Experts (MoE) have recently emerged as significant architectural improvements. In this paper, we introduce Linear-MoE, a production-level system for modeling and training large-scale models that integrate LSM with MoE. Linear-MoE leverages the advantages of both LSM modules for linear-complexity sequence modeling and MoE layers for sparsely activation, aiming to offer high performance with efficient training. The Linear-MoE system comprises: 1) Modeling subsystem, which provides a unified framework supporting all instances of LSM. and 2) Training subsystem, which facilitates efficient training by incorporating various advanced parallelism technologies, particularly Sequence Parallelism designed for Linear-MoE models. Additionally, we explore hybrid models that combine Linear-MoE layers with standard Transformer-MoE layers with its Sequence Parallelism to further enhance model flexibility and performance. Evaluations on two model series, A0.3B-2B and A1B-7B, demonstrate Linear-MoE achieves efficiency gains while maintaining competitive performance on various benchmarks, showcasing its potential as a next-generation foundational model architecture. Code: https://github.com/OpenSparseLLMs/Linear-MoE.

With LLMs shifting their role from statistical modeling of language to serving as general-purpose AI agents, how should LLM evaluations change? Arguably, a key ability of an AI agent is to flexibly combine, as needed, the basic skills it has learned. The capability to combine skills plays an important role in (human) pedagogy and also in a paper on emergence phenomena (Arora & Goyal, 2023). This work introduces Skill-Mix, a new evaluation to measure ability to combine skills. Using a list of N skills the evaluator repeatedly picks random subsets of k skills and asks the LLM to produce text combining that subset of skills. Since the number of subsets grows like N^k, for even modest k this evaluation will, with high probability, require the LLM to produce text significantly different from any text in the training set. The paper develops a methodology for (a) designing and administering such an evaluation, and (b) automatic grading (plus spot-checking by humans) of the results using GPT-4 as well as the open LLaMA-2 70B model. Administering a version of to popular chatbots gave results that, while generally in line with prior expectations, contained surprises. Sizeable differences exist among model capabilities that are not captured by their ranking on popular LLM leaderboards ("cramming for the leaderboard"). Furthermore, simple probability calculations indicate that GPT-4's reasonable performance on k=5 is suggestive of going beyond "stochastic parrot" behavior (Bender et al., 2021), i.e., it combines skills in ways that it had not seen during training. We sketch how the methodology can lead to a Skill-Mix based eco-system of open evaluations for AI capabilities of future models.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

The hull of a linear code C is the intersection of C with its dual code. We present and analyze the number of linear q-ary codes of the same length and dimension but with different dimensions for their hulls. We prove that for given dimension k and length nge 2k the number of all [n,k]_q linear codes with hull dimension l decreases as l increases. We also present classification results for binary and ternary linear codes with trivial hulls (LCD and self-orthogonal) for some values of the length n and dimension k, comparing the obtained numbers with the number of all linear codes for the given n and k.

In a compound AI system, components such as an LLM call, a retriever, a code interpreter, or tools are interconnected. The system's behavior is primarily driven by parameters such as instructions or tool definitions. Recent advancements enable end-to-end optimization of these parameters using an LLM. Notably, leveraging an LLM as an optimizer is particularly efficient because it avoids gradient computation and can generate complex code and instructions. This paper presents a survey of the principles and emerging trends in LLM-based optimization of compound AI systems. It covers archetypes of compound AI systems, approaches to LLM-based end-to-end optimization, and insights into future directions and broader impacts. Importantly, this survey uses concepts from program analysis to provide a unified view of how an LLM optimizer is prompted to optimize a compound AI system. The exhaustive list of paper is provided at https://github.com/linyuhongg/LLM-based-Optimization-of-Compound-AI-Systems.

Imagine two high-dimensional clusters and a hyperplane separating them. Consider in particular the angle between: the direction joining the two clusters' centroids and the normal to the hyperplane. In linear classification, this angle depends on the level of L2 regularization used. Can you explain why?

Combining different models is a widely used paradigm in machine learning applications. While the most common approach is to form an ensemble of models and average their individual predictions, this approach is often rendered infeasible by given resource constraints in terms of memory and computation, which grow linearly with the number of models. We present a layer-wise model fusion algorithm for neural networks that utilizes optimal transport to (soft-) align neurons across the models before averaging their associated parameters. We show that this can successfully yield "one-shot" knowledge transfer (i.e, without requiring any retraining) between neural networks trained on heterogeneous non-i.i.d. data. In both i.i.d. and non-i.i.d. settings , we illustrate that our approach significantly outperforms vanilla averaging, as well as how it can serve as an efficient replacement for the ensemble with moderate fine-tuning, for standard convolutional networks (like VGG11), residual networks (like ResNet18), and multi-layer perceptrons on CIFAR10, CIFAR100, and MNIST. Finally, our approach also provides a principled way to combine the parameters of neural networks with different widths, and we explore its application for model compression. The code is available at the following link, https://github.com/sidak/otfusion.

In the field of quantitative trading, it is common practice to transform raw historical stock data into indicative signals for the market trend. Such signals are called alpha factors. Alphas in formula forms are more interpretable and thus favored by practitioners concerned with risk. In practice, a set of formulaic alphas is often used together for better modeling precision, so we need to find synergistic formulaic alpha sets that work well together. However, most traditional alpha generators mine alphas one by one separately, overlooking the fact that the alphas would be combined later. In this paper, we propose a new alpha-mining framework that prioritizes mining a synergistic set of alphas, i.e., it directly uses the performance of the downstream combination model to optimize the alpha generator. Our framework also leverages the strong exploratory capabilities of reinforcement learning~(RL) to better explore the vast search space of formulaic alphas. The contribution to the combination models' performance is assigned to be the return used in the RL process, driving the alpha generator to find better alphas that improve upon the current set. Experimental evaluations on real-world stock market data demonstrate both the effectiveness and the efficiency of our framework for stock trend forecasting. The investment simulation results show that our framework is able to achieve higher returns compared to previous approaches.

Optimization problems with nonlinear cost functions and combinatorial constraints appear in many real-world applications but remain challenging to solve efficiently compared to their linear counterparts. To bridge this gap, we propose SurCo that learns linear text{Sur}rogate costs which can be used in existing text{Co}mbinatorial solvers to output good solutions to the original nonlinear combinatorial optimization problem. The surrogate costs are learned end-to-end with nonlinear loss by differentiating through the linear surrogate solver, combining the flexibility of gradient-based methods with the structure of linear combinatorial optimization. We propose three SurCo variants: SurCo-zero for individual nonlinear problems, SurCo-prior for problem distributions, and SurCo-hybrid to combine both distribution and problem-specific information. We give theoretical intuition motivating SurCo, and evaluate it empirically. Experiments show that SurCo finds better solutions faster than state-of-the-art and domain expert approaches in real-world optimization problems such as embedding table sharding, inverse photonic design, and nonlinear route planning.

Recently, Ainsworth et al. showed that using weight matching (WM) to minimize the L_2 distance in a permutation search of model parameters effectively identifies permutations that satisfy linear mode connectivity (LMC), in which the loss along a linear path between two independently trained models with different seeds remains nearly constant. This paper provides a theoretical analysis of LMC using WM, which is crucial for understanding stochastic gradient descent's effectiveness and its application in areas like model merging. We first experimentally and theoretically show that permutations found by WM do not significantly reduce the L_2 distance between two models and the occurrence of LMC is not merely due to distance reduction by WM in itself. We then provide theoretical insights showing that permutations can change the directions of the singular vectors, but not the singular values, of the weight matrices in each layer. This finding shows that permutations found by WM mainly align the directions of singular vectors associated with large singular values across models. This alignment brings the singular vectors with large singular values, which determine the model functionality, closer between pre-merged and post-merged models, so that the post-merged model retains functionality similar to the pre-merged models, making it easy to satisfy LMC. Finally, we analyze the difference between WM and straight-through estimator (STE), a dataset-dependent permutation search method, and show that WM outperforms STE, especially when merging three or more models.

As the probability (and thus perplexity) of a text is calculated based on the product of the probabilities of individual tokens, it may happen that one unlikely token significantly reduces the probability (i.e., increase the perplexity) of some otherwise highly probable input, while potentially representing a simple typographical error. Also, given that perplexity is a scalar value that refers to the entire input, information about the probability distribution within it is lost in the calculation (a relatively good text that has one unlikely token and another text in which each token is equally likely they can have the same perplexity value), especially for longer texts. As an alternative to scalar perplexity this research proposes a simple algorithm used to calculate vector values based on n-gram perplexities within the input. Such representations consider the previously mentioned aspects, and instead of a unique value, the relative perplexity of each text token is calculated, and these values are combined into a single vector representing the input.

Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b, find a vector x such that Ax=b. We consider the case where one doesn't need to know the solution x itself, but rather an approximation of the expectation value of some operator associated with x, e.g., x'Mx for some matrix M. In this case, when A is sparse, N by N and has condition number kappa, classical algorithms can find x and estimate x'Mx in O(N sqrt(kappa)) time. Here, we exhibit a quantum algorithm for this task that runs in poly(log N, kappa) time, an exponential improvement over the best classical algorithm.

This paper investigates the problem of ensembling multiple strategies for sequential portfolios to outperform individual strategies in terms of long-term wealth. Due to the uncertainty of strategies' performances in the future market, which are often based on specific models and statistical assumptions, investors often mitigate risk and enhance robustness by combining multiple strategies, akin to common approaches in collective learning prediction. However, the absence of a distribution-free and consistent preference framework complicates decisions of combination due to the ambiguous objective. To address this gap, we introduce a novel framework for decision-making in combining strategies, irrespective of market conditions, by establishing the investor's preference between decisions and then forming a clear objective. Through this framework, we propose a combinatorial strategy construction, free from statistical assumptions, for any scale of component strategies, even infinite, such that it meets the determined criterion. Finally, we test the proposed strategy along with its accelerated variant and some other multi-strategies. The numerical experiments show results in favor of the proposed strategies, albeit with small tradeoffs in their Sharpe ratios, in which their cumulative wealths eventually exceed those of the best component strategies while the accelerated strategy significantly improves performance.

We present a new way to merge any two point distribution approaches using distance fields. Our new process allows us to produce digital stippling that fills areas with stipple dots without visual artifacts as well as includes clear linear features without fussiness. Our merging thus benefits from past work that can optimize for either goal individually, yet typically by sacrificing the other. The new possibility of combining any two distributions using different distance field functions and their parameters also allows us to produce a vast range of stippling styles, which we demonstrate as well.

Recent studies have shown that, relative position encoding performs well in selective state space model scanning algorithms, and the architecture that balances SSM and Attention enhances the efficiency and effectiveness of the algorithm, while the sparse activation of the mixture of experts reduces the training cost. I studied the effectiveness of using different position encodings in structured state space dual algorithms, and the more effective SSD-Attn internal and external function mixing method, and designed a more efficient cross domain mixture of experts. I found that the same matrix is very wonderful in different algorithms, which allows us to establish a new hybrid sparse architecture: Cheems. Compared with other hybrid architectures, it is more efficient and more effective in language modeling tasks.

A new class of affine scaling matrices for the interior point Newton-type methods is considered to solve the nonlinear systems with simple bounds. We review the essential properties of a scaling matrix and consider several well-known scaling matrices proposed in the literature. We define a new scaling matrix that is the convex combination of these matrices. The proposed scaling matrix inherits those interesting properties of the individual matrices and satisfies additional desired requirements. The numerical experiments demonstrate the superiority of the new scaling matrix in solving several important test problems.

Linear transformers have emerged as a subquadratic-time alternative to softmax attention and have garnered significant interest due to their fixed-size recurrent state that lowers inference cost. However, their original formulation suffers from poor scaling and underperforms compute-matched transformers. Recent linear models such as RWKV and Mamba have attempted to address these shortcomings by proposing novel time-mixing and gating architectures, but pre-training large language models requires significant data and compute investments. Thus, the search for subquadratic architectures is limited by the availability of compute and quality pre-training datasets. As a cost-effective alternative to pre-training linear transformers, we propose Scalable UPtraining for Recurrent Attention (SUPRA). We present a method to uptrain existing large pre-trained transformers into Recurrent Neural Networks (RNNs) with a modest compute budget. This allows us to leverage the strong pre-training data and performance of existing transformer LLMs, while requiring 5% of the training cost. We find that our linearization technique leads to competitive performance on standard benchmarks, but we identify persistent in-context learning and long-context modeling shortfalls for even the largest linear models. Our code and models can be found at https://github.com/TRI-ML/linear_open_lm.

The democratization of machine learning systems has made the process of fine-tuning accessible to practitioners, leading to a wide range of open-source models fine-tuned on specialized tasks and datasets. Recent work has proposed to merge such models to combine their functionalities. However, prior approaches are usually restricted to models that are fine-tuned from the same base model. Furthermore, the final merged model is typically required to be of the same size as the original models. In this work, we propose a new two-step algorithm to merge models -- termed PLeaS -- which relaxes these constraints. First, leveraging the Permutation symmetries inherent in the two models, PLeaS partially matches nodes in each layer by maximizing alignment. Next, PLeaS computes the weights of the merged model as a layer-wise Least Squares solution to minimize the approximation error between the features of the merged model and the permuted features of the original models. PLeaS allows a practitioner to merge two models sharing the same architecture into a single performant model of a desired size, even when the two original models are fine-tuned from different base models. We also demonstrate how our method can be extended to address a challenging scenario where no data is available from the fine-tuning domains. We demonstrate our method to merge ResNet and ViT models trained with shared and different label spaces, and show improvement over the state-of-the-art merging methods of up to 15 percentage points for the same target compute while merging models trained on DomainNet and fine-grained classification tasks. Our code is open-sourced at https://github.com/SewoongLab/PLeaS-Merging .

Multi-layer perceptron (MLP) is a fundamental component of deep learning that has been extensively employed for various problems. However, recent empirical successes in MLP-based architectures, particularly the progress of the MLP-Mixer, have revealed that there is still hidden potential in improving MLPs to achieve better performance. In this study, we reveal that the MLP-Mixer works effectively as a wide MLP with certain sparse weights. Initially, we clarify that the mixing layer of the Mixer has an effective expression as a wider MLP whose weights are sparse and represented by the Kronecker product. This expression naturally defines a permuted-Kronecker (PK) family, which can be regarded as a general class of mixing layers and is also regarded as an approximation of Monarch matrices. Subsequently, because the PK family effectively constitutes a wide MLP with sparse weights, one can apply the hypothesis proposed by Golubeva, Neyshabur and Gur-Ari (2021) that the prediction performance improves as the width (sparsity) increases when the number of weights is fixed. We empirically verify this hypothesis by maximizing the effective width of the MLP-Mixer, which enables us to determine the appropriate size of the mixing layers quantitatively.

We characterize the cut patterns that can be produced by "orthogonal fold & cut": folding an axis-aligned rectangular sheet of paper along horizontal and vertical creases, and then making a single straight cut (at any angle). Along the way, we solve a handful of related problems: orthogonal fold & punch, 1D fold & cut, signed 1D fold & cut, and 1D interval fold & cut.

We extend the capabilities of neural networks by coupling them to external memory resources, which they can interact with by attentional processes. The combined system is analogous to a Turing Machine or Von Neumann architecture but is differentiable end-to-end, allowing it to be efficiently trained with gradient descent. Preliminary results demonstrate that Neural Turing Machines can infer simple algorithms such as copying, sorting, and associative recall from input and output examples.

This paper explores the relationship between matrix factorizations and linear matrix equations. It shows that every matrix factorization defines two hidden projectors, one for the column space and one for the row space of a matrix, and how to calculate them. The projectors can be applied to solve linear matrix equations, generate low-rank approximations, or design randomized matrix algorithms. But also, as demonstrated, they can be applied in cryptography to encrypt and decrypt messages. The paper discusses some of the security implications of this application and leaves some questions open for further investigation. The basic concepts are illustrated with source code listings. Finally, this work shares some personal reflections on the meaning and importance of understanding in the time of the artificial intelligence revolution.

Linear sequence modeling methods, such as linear attention, state space modeling, and linear RNNs, offer significant efficiency improvements by reducing the complexity of training and inference. However, these methods typically compress the entire input sequence into a single fixed-size memory state, which leads to suboptimal performance on recall-intensive downstream tasks. Drawing inspiration from neuroscience, particularly the brain's ability to maintain robust long-term memory while mitigating "memory interference", we introduce a novel architecture called Mixture-of-Memories (MoM). MoM utilizes multiple independent memory states, with a router network directing input tokens to specific memory states. This approach greatly enhances the overall memory capacity while minimizing memory interference. As a result, MoM performs exceptionally well on recall-intensive tasks, surpassing existing linear sequence modeling techniques. Despite incorporating multiple memory states, the computation of each memory state remains linear in complexity, allowing MoM to retain the linear-complexity advantage during training, while constant-complexity during inference. Our experimental results show that MoM significantly outperforms current linear sequence models on downstream language tasks, particularly recall-intensive tasks, and even achieves performance comparable to Transformer models. The code is released at https://github.com/OpenSparseLLMs/MoM and is also released as a part of https://github.com/OpenSparseLLMs/Linear-MoE.

Transformers with linear attention (i.e., linear transformers) and state-space models have recently been suggested as a viable linear-time alternative to transformers with softmax attention. However, these models still underperform transformers especially on tasks that require in-context retrieval. While more expressive variants of linear transformers which replace the additive outer-product update in linear transformers with the delta rule have been found to be more effective at associative recall, existing algorithms for training such models do not parallelize over sequence length and are thus inefficient to train on modern hardware. This work describes a hardware-efficient algorithm for training linear transformers with the delta rule, which exploits a memory-efficient representation for computing products of Householder matrices. This algorithm allows us to scale up DeltaNet to standard language modeling settings. We train a 1.3B model for 100B tokens and find that it outperforms recent linear-time baselines such as Mamba and GLA in terms of perplexity and zero-shot performance on downstream tasks (including on tasks that focus on recall). We also experiment with two hybrid models which combine DeltaNet layers with (1) sliding-window attention layers every other layer or (2) two global attention layers, and find that these hybrid models outperform strong transformer baselines.

The ability of neural networks to represent more features than neurons makes interpreting them challenging. This phenomenon, known as superposition, has spurred efforts to find architectures that are more interpretable than standard multilayer perceptrons (MLPs) with elementwise activation functions. In this note, I examine bilinear layers, which are a type of MLP layer that are mathematically much easier to analyze while simultaneously performing better than standard MLPs. Although they are nonlinear functions of their input, I demonstrate that bilinear layers can be expressed using only linear operations and third order tensors. We can integrate this expression for bilinear layers into a mathematical framework for transformer circuits, which was previously limited to attention-only transformers. These results suggest that bilinear layers are easier to analyze mathematically than current architectures and thus may lend themselves to deeper safety insights by allowing us to talk more formally about circuits in neural networks. Additionally, bilinear layers may offer an alternative path for mechanistic interpretability through understanding the mechanisms of feature construction instead of enumerating a (potentially exponentially) large number of features in large models.

We present PeFLL, a new personalized federated learning algorithm that improves over the state-of-the-art in three aspects: 1) it produces more accurate models, especially in the low-data regime, and not only for clients present during its training phase, but also for any that may emerge in the future; 2) it reduces the amount of on-client computation and client-server communication by providing future clients with ready-to-use personalized models that require no additional finetuning or optimization; 3) it comes with theoretical guarantees that establish generalization from the observed clients to future ones. At the core of PeFLL lies a learning-to-learn approach that jointly trains an embedding network and a hypernetwork. The embedding network is used to represent clients in a latent descriptor space in a way that reflects their similarity to each other. The hypernetwork takes as input such descriptors and outputs the parameters of fully personalized client models. In combination, both networks constitute a learning algorithm that achieves state-of-the-art performance in several personalized federated learning benchmarks.

A sequence of operators T_n from a Hilbert space {mathfrak H} to Hilbert spaces {mathfrak K}_n which is nondecreasing in the sense of contractive domination is shown to have a limit which is still a linear operator T from {mathfrak H} to a Hilbert space {mathfrak K}. Moreover, the closability or closedness of T_n is preserved in the limit. The closures converge likewise and the connection between the limits is investigated. There is no similar way of dealing directly with linear relations. However, the sequence of closures is still nondecreasing and then the convergence is governed by the monotonicity principle. There are some related results for nonincreasing sequences.

Convolutional networks are large linear systems divided into layers and connected by non-linear units. These units are the "articulations" that allow the network to adapt to the input. To understand how a network manages to solve a problem we must look at the articulated decisions in entirety. If we could capture the actions of non-linear units for a particular input, we would be able to replay the whole system back and forth as if it was always linear. It would also reveal the actions of non-linearities because the resulting linear system, a Linear Interpreter, depends on the input image. We introduce a hooking layer, called a LinearScope, which allows us to run the network and the linear interpreter in parallel. Its implementation is simple, flexible and efficient. From here we can make many curious inquiries: how do these linear systems look like? When the rows and columns of the transformation matrix are images, how do they look like? What type of basis do these linear transformations rely on? The answers depend on the problems presented, through which we take a tour to some popular architectures used for classification, super-resolution (SR) and image-to-image translation (I2I). For classification we observe that popular networks use a pixel-wise vote per class strategy and heavily rely on bias parameters. For SR and I2I we find that CNNs use wavelet-type basis similar to the human visual system. For I2I we reveal copy-move and template-creation strategies to generate outputs.

Current LLM training positions mathematical reasoning as a core capability. With publicly available sources fully tapped, there is unmet demand for diverse and challenging math questions. Relying solely on human experts is both time-consuming and costly, while LLM-generated questions often lack the requisite diversity and difficulty. We present a design framework that combines the strengths of LLMs with a human-in-the-loop approach to generate a diverse array of challenging math questions. We leverage LLM metacognition skills [Didolkar et al., 2024] of a strong LLM to extract core "skills" from existing math datasets. These skills serve as the basis for generating novel and difficult questions by prompting the LLM with random pairs of core skills. The use of two different skills within each question makes finding such questions an "out of distribution" task for both LLMs and humans. Our pipeline employs LLMs to iteratively generate and refine questions and solutions through multiturn prompting. Human annotators then verify and further refine the questions, with their efficiency enhanced via further LLM interactions. Applying this pipeline on skills extracted from the MATH dataset [Hendrycks et al., 2021] resulted in MATH^2 - a dataset of higher-quality math questions, as evidenced by: (a) Lower performance of all models on MATH^2 than on MATH (b) Higher performance on MATH when using MATH^2 questions as in-context examples. Although focused on mathematics, our methodology seems applicable to other domains requiring structured reasoning, and potentially as a component of scalable oversight. Also of interest is a striking relationship observed between models' performance on the new dataset: the success rate on MATH^2 is the square on MATH, suggesting that successfully solving the question in MATH^2 requires a nontrivial combination of two distinct math skills.

We study the approximability of an existing framework for clustering edge-colored hypergraphs, which is closely related to chromatic correlation clustering and is motivated by machine learning and data mining applications where the goal is to cluster a set of objects based on multiway interactions of different categories or types. We present improved approximation guarantees based on linear programming, and show they are tight by proving a matching integrality gap. Our results also include new approximation hardness results, a combinatorial 2-approximation whose runtime is linear in the hypergraph size, and several new connections to well-studied objectives such as vertex cover and hypergraph multiway cut.

The presence of linear paths in parameter space between two different network solutions in certain cases, i.e., linear mode connectivity (LMC), has garnered interest from both theoretical and practical fronts. There has been significant research that either practically designs algorithms catered for connecting networks by adjusting for the permutation symmetries as well as some others that more theoretically construct paths through which networks can be connected. Yet, the core reasons for the occurrence of LMC, when in fact it does occur, in the highly non-convex loss landscapes of neural networks are far from clear. In this work, we take a step towards understanding it by providing a model of how the loss landscape needs to behave topographically for LMC (or the lack thereof) to manifest. Concretely, we present a `mountainside and ridge' perspective that helps to neatly tie together different geometric features that can be spotted in the loss landscape along the training runs. We also complement this perspective by providing a theoretical analysis of the barrier height, for which we provide empirical support, and which additionally extends as a faithful predictor of layer-wise LMC. We close with a toy example that provides further intuition on how barriers arise in the first place, all in all, showcasing the larger aim of the work -- to provide a working model of the landscape and its topography for the occurrence of LMC.

This research enhances linear regression models by integrating a Kalman filter and analysing curve areas to minimize loss. The goal is to develop an optimal linear regression equation using stochastic gradient descent (SGD) for weight updating. Our approach involves a stepwise process, starting with user-defined parameters. The linear regression model is trained using SGD, tracking weights and loss separately and zipping them finally. A Kalman filter is then trained based on weight and loss arrays to predict the next consolidated weights. Predictions result from multiplying input averages with weights, evaluated for loss to form a weight-versus-loss curve. The curve's equation is derived using the two-point formula, and area under the curve is calculated via integration. The linear regression equation with minimum area becomes the optimal curve for prediction. Benefits include avoiding constant weight updates via gradient descent and working with partial datasets, unlike methods needing the entire set. However, computational complexity should be considered. The Kalman filter's accuracy might diminish beyond a certain prediction range.

Conceptual combination is a cognitive process that merges basic concepts, enabling the creation of complex expressions. During this process, the properties of combination (e.g., the whiteness of a peeled apple) can be inherited from basic concepts, newly emerge, or be canceled. However, previous studies have evaluated a limited set of properties and have not examined the generative process. To address this gap, we introduce the Conceptual Combination with Property Type dataset (CCPT), which consists of 12.3K annotated triplets of noun phrases, properties, and property types. Using CCPT, we establish three types of tasks to evaluate LLMs for conceptual combination thoroughly. Our key findings are threefold: (1) Our automatic metric grading property emergence and cancellation closely corresponds with human judgments. (2) LLMs, including OpenAI's o1, struggle to generate noun phrases which possess given emergent properties. (3) Our proposed method, inspired by cognitive psychology model that explains how relationships between concepts are formed, improves performances in all generative tasks. The dataset and experimental code are available at https://github.com/seokwon99/CCPT.git.