论文检索

Generative Models · New Approaches

Andrea Bertazzi, Dario Shariatian, Umut Simsekli, Eric Moulines, Alain Durmus

We introduce a novel class of generative models based on piecewise deterministic Markov processes (PDMPs), a family of non-diffusive stochastic processes consisting of deterministic motion and random jumps at random times. Similarly to diffusions, such Markov processes admit time reversals that turn out to be PDMPs as well. We apply this observation to three PDMPs considered in the literature: the Zig-Zag process, Bouncy Particle Sampler, and Randomised Hamiltonian Monte Carlo. For these three particular instances, we show that the jump rates and kernels of the corresponding time reversals admit explicit expressions depending on some conditional densities of the PDMP under consideration before and after a jump. Based on these results, we propose efficient training procedures to learn these characteristics and consider methods to approximately simulate the reverse process. Finally, we provide bounds in the total variation distance between the data distribution and the resulting distribution of our model in the case where the base distribution is the standard $d$-dimensional Gaussian distribution. Promising numerical simulations support further investigations into this class of models.

Physical Models · Physics

Andrea Bonfanti, Giuseppe Bruno, Cristina Cipriani

The Neural Tangent Kernel (NTK) viewpoint is widely employed to analyze the training dynamics of overparameterized Physics-Informed Neural Networks (PINNs). However, unlike the case of linear Partial Differential Equations (PDEs), we show how the NTK perspective falls short in the nonlinear scenario. Specifically, we establish that the NTK yields a random matrix at initialization that is not constant during training, contrary to conventional belief. Another significant difference from the linear regime is that, even in the idealistic infinite-width limit, the Hessian does not vanish and hence it cannot be disregarded during training. This motivates the adoption of second-order optimization methods. We explore the convergence guarantees of such methods in both linear and nonlinear cases, addressing challenges such as spectral bias and slow convergence. Every theoretical result is supported by numerical examples with both linear and nonlinear PDEs, and we highlight the benefits of second-order methods in benchmark test cases.

Tong Yang, Shicong Cen, Yuting Wei, Yuxin Chen, Yuejie Chi

Federated reinforcement learning (RL) enables collaborative decision making of multiple distributed agents without sharing local data trajectories. In this work, we consider a multi-task setting, in which each agent has its own private reward function corresponding to different tasks, while sharing the same transition kernel of the environment. Focusing on infinite-horizon Markov decision processes, the goal is to learn a globally optimal policy that maximizes the sum of the discounted total rewards of all the agents in a decentralized manner, where each agent only communicates with its neighbors over some prescribed graph topology.We develop federated vanilla and entropy-regularized natural policy gradient (NPG) methods in the tabular setting under softmax parameterization, where gradient tracking is applied to estimate the global Q-function to mitigate the impact of imperfect information sharing. We establish non-asymptotic global convergence guarantees under exact policy evaluation, where the rates are nearly independent of the size of the state-action space and illuminate the impacts of network size and connectivity. To the best of our knowledge, this is the first time that global convergence is established for federated multi-task RL using policy optimization. We further go beyond the tabular setting by proposing a federated natural actor critic (NAC) method for multi-task RL with function approximation, and establish its finite-time sample complexity taking the errors of function approximation into account.

Computer Vision

Tianjing Zhang, Yuhui Quan, Hui Ji

Blind image deblurring (BID) is an important yet challenging image recovery problem. Most existing deep learning methods require supervised training with ground truth (GT) images. This paper introduces a self-supervised method for BID that does not require GT images. The key challenge is to regularize the training to prevent over-fitting due to the absence of GT images. By leveraging an exact relationship among the blurred image, latent image, and blur kernel across consecutive scales, we propose an effective cross-scale consistency loss. This is implemented by representing the image and kernel with implicit neural representations (INRs), whose resolution-free property enables consistent yet efficient computation for network training across multiple scales. Combined with a progressively coarse-to-fine training scheme, the proposed method significantly outperforms existing self-supervised methods in extensive experiments.

Computer Vision · Classification

Shufan Shen, Junshu Sun, Xiangyang Ji, Qingming Huang, Shuhui Wang

Parameter-efficient fine-tuning (PEFT) is an effective method for adapting pre-trained vision models to downstream tasks by tuning a small subset of parameters. Among PEFT methods, sparse tuning achieves superior performance by only adjusting the weights most relevant to downstream tasks, rather than densely tuning the whole weight matrix. However, this performance improvement has been accompanied by increases in memory usage, which stems from two factors, i.e., the storage of the whole weight matrix as learnable parameters in the optimizer and the additional storage of tunable weight indexes. In this paper, we propose a method named SNELL (Sparse tuning with kerNELized LoRA) for sparse tuning with low memory usage. To achieve low memory usage, SNELL decomposes the tunable matrix for sparsification into two learnable low-rank matrices, saving from the costly storage of the whole original matrix. A competition-based sparsification mechanism is further proposed to avoid the storage of tunable weight indexes. To maintain the effectiveness of sparse tuning with low-rank matrices, we extend the low-rank decomposition by applying nonlinear kernel functions to the whole-matrix merging. Consequently, we gain an increase in the rank of the merged matrix, enhancing the ability of SNELL in adapting the pre-trained models to downstream tasks. Extensive experiments on multiple downstream tasks show that SNELL achieves state-of-the-art performance with low memory usage, endowing PEFT with sparse tuning to large-scale models. Codes are available at https://github.com/ssfgunner/SNELL.

Probabilistic Methods · Variational Inference

Declan McNamara, Jackson Loper, Jeffrey Regier

In variational inference (VI), an approximation of the posterior distribution is selected from a family of distributions through numerical optimization. With the most common variational objective function, known as the evidence lower bound (ELBO), only convergence to a *local* optimum can be guaranteed. In this work, we instead establish the *global* convergence of a particular VI method. This VI method, which may be considered an instance of neural posterior estimation (NPE), minimizes an expectation of the inclusive (forward) KL divergence to fit a variational distribution that is parameterized by a neural network. Our convergence result relies on the neural tangent kernel (NTK) to characterize the gradient dynamics that arise from considering the variational objective in function space. In the asymptotic regime of a fixed, positive-definite neural tangent kernel, we establish conditions under which the variational objective admits a unique solution in a reproducing kernel Hilbert space (RKHS). Then, we show that the gradient descent dynamics in function space converge to this unique function. In ablation studies and practical problems, we demonstrate that our results explain the behavior of NPE in non-asymptotic finite-neuron settings, and show that NPE outperforms ELBO-based optimization, which often converges to shallow local optima.

Deep Learning · Attention Mechanisms

Ali Hassani, Wen-Mei Hwu, Humphrey Shi

Neighborhood attention reduces the cost of self attention by restricting each token’s attention span to its nearest neighbors. This restriction, parameterized by a window size and dilation factor, draws a spectrum of possible attention patterns between linear projection and self attention. Neighborhood attention, and more generally sliding window attention patterns, have long been bounded by infrastructure, particularly in higher-rank spaces (2-D and 3-D), calling for the development of custom kernels, which have been limited in either functionality, or performance, if not both. In this work, we aim to massively improve upon existing infrastructure by providing two new methods for implementing neighborhood attention. We first show that neighborhood attention can be represented as a batched GEMM problem, similar to standard attention, and implement it for 1-D and 2-D neighborhood attention. These kernels on average provide 895% and 272% improvement in full precision runtime compared to existing naive CUDA kernels for 1-D and 2-D neighborhood attention respectively. We find that aside from being heavily bound by memory bandwidth, certain inherent inefficiencies exist in all unfused implementations of neighborhood attention, which in most cases undo their theoretical efficiency gain. Motivated by the progress made into fused dot-product attention kernels, we developed fused neighborhood attention; an adaptation of fused dot-product attention kernels that allow fine-grained control over attention across different spatial axes. Known for reducing the quadratic time complexity of self attention to a linear complexity, neighborhood attention can now enjoy a reduced and constant memory footprint, and record-breaking half precision runtime. We observe that our fused implementation successfully circumvents some of the unavoidable inefficiencies in unfused implementations. While our unfused GEMM-based kernels only improve half precision performance compared to naive kernels by an average of 548% and 193% in 1-D and 2-D problems respectively, our fused kernels improve naive kernels by an average of 1759% and 958% in 1-D and 2-D problems respectively. These improvements translate into up to 104% improvement in inference and 39% improvement in training existing models based on neighborhood attention, and additionally extend its applicability to image and video perception, as well as other modalities. Our work is open-sourced at https://github.com/SHI-Labs/NATTEN/.

Anlan Yu, Shusen Jing, Ning Lyu, Wujie Wen, Zhiyuan Yan

Error correcting output code (ECOC) is a classic method that encodes binary classifiers to tackle the multi-class classification problem in decision trees and neural networks.Among ECOCs, the one-hot code has become the default choice in modern deep neural networks (DNNs) due to its simplicity in decision making. However, it suffers from a significant limitation in its ability to achieve high robust accuracy, particularly in the presence of weight errors. While recent studies have experimentally demonstrated that the non-one-hot ECOCs with multi-bits error correction ability, could be a better solution, there is a notable absence of theoretical foundations that can elucidate the relationship between codeword design, weight-error magnitude, and network characteristics, so as to provide robustness guarantees. This work is positioned to bridge this gap through the lens of neural tangent kernel (NTK). We have two important theoretical findings: 1) In clean models (without weight errors), utilizing one-hot code and non-one-hot ECOC is akin to altering decoding metrics from $l_2$ distance to Mahalanobis distance. 2) In non-clean models (with weight errors), if the normalized distance exceeds a threshold, then non-clean DNNs can reach the clean model's accuracy as long as the code length approaches infinity. This threshold is determined by DNN architecture (e.g. layer number, activation), weight error magnitude, and the distance between the output and the nearest codeword. Based on these findings, we further demonstrate how to practically use them to identify optimal ECOCs for simple tasks (short-code ECOCs) and complex tasks (long-code ECOCs), by balancing the code orthogonality (as per finding 1) and code distance (as per finding 2). Extensive experimental results across four datasets and four DNN models validate the superior performance of constructed codes, guided by our findings, compared to existing ECOCs. To our best knowledge, this is the first work that provides theoretical explanations for the effectiveness of ECOCS and offers associated design guidance for optimal ECOCs specifically tailored to DNNs.

Deep Learning · Representation Learning

Putri van der Linden, Alejandro García-Castellanos, Sharvaree Vadgama, Thijs Kuipers, Erik Bekkers

Group equivariance has emerged as a valuable inductive bias in deep learning, enhancing generalization, data efficiency, and robustness. Classically, group equivariant methods require the groups of interest to be known beforehand, which may not be realistic for real-world data. Additionally, baking in fixed group equivariance may impose overly restrictive constraints on model architecture. This highlights the need for methods that can dynamically discover and apply symmetries as soft constraints. For neural network architectures, equivariance is commonly achieved through group transformations of a canonical weight tensor, resulting in weight sharing over a given group $G$. In this work, we propose to *learn* such a weight-sharing scheme by defining a collection of learnable doubly stochastic matrices that act as soft permutation matrices on canonical weight tensors, which can take regular group representations as a special case. This yields learnable kernel transformations that are jointly optimized with downstream tasks. We show that when the dataset exhibits strong symmetries, the permutation matrices will converge to regular group representations and our weight-sharing networks effectively become regular group convolutions. Additionally, the flexibility of the method enables it to effectively pick up on partial symmetries.

Online Learning

Yunzhe Qi, Yikun Ban, Arindam Banerjee, Jingrui He

Contextual bandit algorithms aim to identify the optimal arm with the highest reward among a set of candidates, based on the accessible contextual information. Among these algorithms, neural contextual bandit methods have shown generally superior performances against linear and kernel ones, due to the representation power of neural networks. However, similar to other neural network applications, neural bandit algorithms can be vulnerable to adversarial attacks or corruptions on the received labels (i.e., arm rewards), which can lead to unexpected performance degradation without proper treatments. As a result, it is necessary to improve the robustness of neural bandit models against potential reward corruptions. In this work, we propose a novel neural contextual bandit algorithm named R-NeuralUCB, which utilizes a novel context-aware Gradient Descent (GD) training strategy to improve the robustness against adversarial reward corruptions. Under over-parameterized neural network settings, we provide regret analysis for R-NeuralUCB to quantify reward corruption impacts, without the commonly adopted arm separateness assumption in existing neural bandit works. We also conduct experiments against baselines on real data sets under different scenarios, in order to demonstrate the effectiveness of our proposed R-NeuralUCB.

Graph Neural Networks

Siyuan Huang, Yunchong Song, Jiayue Zhou, Zhouhan Lin

In the realm of graph learning, there is a category of methods that conceptualize graphs as hierarchical structures, utilizing node clustering to capture broader structural information. While generally effective, these methods often rely on a fixed graph coarsening routine, leading to overly homogeneous cluster representations and loss of node-level information. In this paper, we envision the graph as a network of interconnected node sets without compressing each cluster into a single embedding. To enable effective information transfer among these node sets, we propose the Node-to-Cluster Attention (N2C-Attn) mechanism. N2C-Attn incorporates techniques from Multiple Kernel Learning into the kernelized attention framework, effectively capturing information at both node and cluster levels. We then devise an efficient form for N2C-Attn using the cluster-wise message-passing framework, achieving linear time complexity. We further analyze how N2C-Attn combines bi-level feature maps of queries and keys, demonstrating its capability to merge dual-granularity information. The resulting architecture, Cluster-wise Graph Transformer (Cluster-GT), which uses node clusters as tokens and employs our proposed N2C-Attn module, shows superior performance on various graph-level tasks. Code is available at https://github.com/LUMIA-Group/Cluster-wise-Graph-Transformer.

Computer Vision

man zhou

State-of-the-art image restoration methods currently face challenges in terms of computational requirements and performance, making them impractical for deployment on edge devices such as phones and resource-limited devices. As a result, there is a need to develop alternative solutions with efficient designs that can achieve comparable performance to transformer or large-kernel methods. This motivates our research to explore techniques for improving the capability of small-size image restoration standing on the success secret of large receptive filed.Targeting at expanding receptive filed, spatial-shift operator tailored for efficient spatial communication and has achieved remarkable advances in high-level image classification tasks, like $S^2$-MLP and ShiftVit. However, its potential has rarely been explored in low-level image restoration tasks. The underlying reason behind this obstacle is that image restoration is sensitive to the spatial shift that occurs due to severe region-aware information loss, which exhibits a different behavior from high-level tasks. To address this challenge and unleash the potential of spatial shift for image restoration, we propose an information-lossless shifting operator, i.e., Deep Fourier Shifting, that is customized for image restoration. To develop our proposed operator, we first revisit the principle of shift operator and apply it to the Fourier domain, where the shift operator can be modeled in an information-lossless Fourier cycling manner. Inspired by Fourier cycling, we design two variants of Deep Fourier Shifting, namely the amplitude-phase variant and the real-imaginary variant. These variants are generic operators that can be directly plugged into existing image restoration networks as a drop-in replacement for the standard convolution unit, consuming fewer parameters. Extensive experiments across multiple low-level tasks including image denoising, low-light image enhancement, guided image super-resolution, and image de-blurring demonstrate consistent performance gains obtained by our Deep Fourier Shifting while reducing the computation burden. Additionally, ablation studies verify the robustness of the shift displacement with stable performance improvement.

Physical Models · Physics

JIAXU WANG, Jingkai SUN, ziyi Zhang, Junhao He, Qiang Zhang, Mingyuan Sun, Renjing Xu

Learning-based simulators show great potential for simulating particle dynamics when 3D groundtruth is available, but per-particle correspondences are not always accessible. The development of neural rendering presents a new solution to this field to learn 3D dynamics from 2D images by inverse rendering. However, existing approaches still suffer from ill-posed natures resulting from the 2D to 3D uncertainty, for example, specific 2D images can correspond with various 3D particle distributions. To mitigate such uncertainty, we consider a conventional, mechanically interpretable framework as the physical priors and extend it to a learning-based version. In brief, we incorporate the learnable graph kernels into the classic Discrete Element Analysis (DEA) framework to implement a novel mechanics-informed network architecture. In this case, the graph networks are only used for approximating some specific mechanical operators in the DEA framework rather than the whole dynamics mapping. By integrating the strong physics priors, our methods can effectively learn the dynamics of various materials from the partial 2D observations in a unified manner. Experiments show that our approach outperforms other learned simulators by a large margin in this context and is robust to different renderers, fewer training samples, and fewer camera views.

Graph Neural Networks

Zixiao Wang, Jicong Fan

Graph classification is a challenging problem owing to the difficulty in quantifying the similarity between graphs or representing graphs as vectors, though there have been a few methods using graph kernels or graph neural networks (GNNs). Graph kernels often suffer from computational costs and manual feature engineering, while GNNs commonly utilize global pooling operations, risking the loss of structural or semantic information. This work introduces Graph Reference Distribution Learning (GRDL), an efficient and accurate graph classification method. GRDL treats each graph's latent node embeddings given by GNN layers as a discrete distribution, enabling direct classification without global pooling, based on maximum mean discrepancy to adaptively learned reference distributions. To fully understand this new model (the existing theories do not apply) and guide its configuration (e.g., network architecture, references' sizes, number, and regularization) for practical use, we derive generalization error bounds for GRDL and verify them numerically. More importantly, our theoretical and numerical results both show that GRDL has a stronger generalization ability than GNNs with global pooling operations. Experiments on moderate-scale and large-scale graph datasets show the superiority of GRDL over the state-of-the-art, emphasizing its remarkable efficiency, being at least 10 times faster than leading competitors in both training and inference stages.

Theory · Game Theory

Zhiyuan Fan, Christian Kroer, Gabriele Farina

First-order methods (FOMs) are arguably the most scalable algorithms for equilibrium computation in large extensive-form games. To operationalize these methods, a distance-generating function, acting as a regularizer for the strategy space, must be chosen. The ratio between the strong convexity modulus and the diameter of the regularizer is a key parameter in the analysis of FOMs.A natural question is then: what is the optimal distance-generating function for extensive-form decision spaces? In this paper, we make a number of contributions, ultimately establishing that the weight-one dilated entropy (DilEnt) distance-generating function is optimal up to logarithmic factors. The DilEnt regularizer is notable due to its iterate-equivalence with Kernelized OMWU (KOMWU)---the algorithm with state-of-the-art dependence on the game tree size in extensive-form games---when used in conjunction with the online mirror descent (OMD) algorithm. However, the standard analysis for OMD is unable to establish such a result; the only current analysis is by appealing to the iterate equivalence to KOMWU. We close this gap by introducing a pair of primal-dual treeplex norms, which we contend form the natural analytic viewpoint for studying the strong convexity of DilEnt. Using these norm pairs, we recover the diameter-to-strong-convexity ratio that predicts the same performance as KOMWU. Along with a new regret lower bound for online learning in sequence-form strategy spaces, we show that this ratio is nearly optimal.Finally, we showcase our analytic techniques by refining the analysis of Clairvoyant OMD when paired with DilEnt, establishing an $\mathcal{O}(n \log |\mathcal{V}| \log T/T)$ approximation rate to coarse correlated equilibrium in $n$-player games, where $|\mathcal{V}|$ is the number of reduced normal-form strategies of the players, establishing the new state of the art.

Deep Learning · Algorithms

Haizhong Zheng, Xiaoyan Bai, Xueshen Liu, Zhuoqing Morley Mao, Beidi Chen, Fan Lai, Atul Prakash

Large Language Models (LLMs) have achieved remarkable success with their billion-level parameters, yet they incur high inference overheads. The emergence of activation sparsity in LLMs provides a natural approach to reduce this cost by involving only parts of the parameters for inference. However, existing methods only focus on utilizing this naturally formed activation sparsity in a post-training setting, overlooking the potential for further amplifying this inherent sparsity. In this paper, we hypothesize that LLMs can learn to be efficient by achieving more structured activation sparsity. To achieve this, we introduce a novel training algorithm, Learn-To-be-Efficient (LTE), designed to train efficiency-aware LLMs to learn to activate fewer neurons and achieve a better trade-off between sparsity and performance. Furthermore, unlike SOTA MoEfication methods, which mainly focus on ReLU-based models, LTE can also be applied to LLMs like LLaMA using non-ReLU activations. Extensive evaluation on language understanding, language generation, and instruction tuning tasks show that LTE consistently outperforms SOTA baselines. Along with our hardware-aware custom kernel implementation, LTE reduces LLaMA2-7B inference latency by 25% at 50% sparsity.

Optimization

Yuri Fonseca, Caio Peixoto, Yuri Saporito

Instrumental variables (IVs) provide a powerful strategy for identifying causal effects in the presence of unobservable confounders. Within the nonparametric setting (NPIV), recent methods have been based on nonlinear generalizations of Two-Stage Least Squares and on minimax formulations derived from moment conditions or duality. In a novel direction, we show how to formulate a functional stochastic gradient descent algorithm to tackle NPIV regression by directly minimizing the populational risk. We provide theoretical support in the form of bounds on the excess risk, and conduct numerical experiments showcasing our method's superior stability and competitive performance relative to current state-of-the-art alternatives. This algorithm enables flexible estimator choices, such as neural networks or kernel based methods, as well as non-quadratic loss functions, which may be suitable for structural equations beyond the setting of continuous outcomes and additive noise. Finally, we demonstrate this flexibility of our framework by presenting how it naturally addresses the important case of binary outcomes, which has received far less attention by recent developments in the NPIV literature.

Gong Zhang, Kihyuk Sohn, Meera Hahn, Humphrey Shi, Irfan Essa

Few-shot fine-tuning of text-to-image (T2I) generation models enables people to create unique images in their own style using natural languages without requiring extensive prompt engineering. However, fine-tuning with only a handful, as little as one, of image-text paired data prevents fine-grained control of style attributes at generation. In this paper, we present FineStyle, a few-shot fine-tuning method that allows enhanced controllability for style personalized text-to-image generation. To overcome the lack of training data for fine-tuning, we propose a novel concept-oriented data scaling that amplifies the number of image-text pair, each of which focuses on different concepts (e.g., objects) in the style reference image. We also identify the benefit of parameter-efficient adapter tuning of key and value kernels of cross-attention layers. Extensive experiments show the effectiveness of FineStyle at following fine-grained text prompts and delivering visual quality faithful to the specified style, measured by CLIP scores and human raters.

Trustworthy Machine Learning

Alexander Nikitin, Jannik Kossen, Yarin Gal, Pekka Marttinen

Uncertainty quantification in Large Language Models (LLMs) is crucial for applications where safety and reliability are important. In particular, uncertainty can be used to improve the trustworthiness of LLMs by detecting factually incorrect model responses, commonly called hallucinations. Critically, one should seek to capture the model's semantic uncertainty, i.e., the uncertainty over the meanings of LLM outputs, rather than uncertainty over lexical or syntactic variations that do not affect answer correctness.To address this problem, we propose Kernel Language Entropy (KLE), a novel method for uncertainty estimation in white- and black-box LLMs. KLE defines positive semidefinite unit trace kernels to encode the semantic similarities of LLM outputs and quantifies uncertainty using the von Neumann entropy. It considers pairwise semantic dependencies between answers (or semantic clusters), providing more fine-grained uncertainty estimates than previous methods based on hard clustering of answers. We theoretically prove that KLE generalizes the previous state-of-the-art method called semantic entropy and empirically demonstrate that it improves uncertainty quantification performance across multiple natural language generation datasets and LLM architectures.

Physical Models · Physics

Zipeng Xiao, Siqi Kou, Hao Zhongkai, Bokai Lin, Zhijie Deng

Fourier Neural Operators (FNOs) have shown promise for solving partial differential equations (PDEs).Typically, FNOs employ separate parameters for different frequency modes to specify tunable kernel integrals in Fourier space, which, yet, results in an undesirably large number of parameters when solving high-dimensional PDEs. A workaround is to abandon the frequency modes exceeding a predefined threshold, but this limits the FNOs' ability to represent high-frequency details and poses non-trivial challenges for hyper-parameter specification. To address these, we propose AMortized Fourier Neural Operator (AM-FNO), where an amortized neural parameterization of the kernel function is deployed to accommodate arbitrarily many frequency modes using a fixed number of parameters. We introduce two implementations of AM-FNO, based on the recently developed, appealing Kolmogorov–Arnold Network (KAN) and Multi-Layer Perceptrons (MLPs) equipped with orthogonal embedding functions respectively. We extensively evaluate our method on diverse datasets from various domains and observe up to 31\% average improvement compared to competing neural operator baselines.