论文检索

Deep Learning · Algorithms

Jiaxi Hu, Yongqi Pan, Jusen Du, Disen Lan, Tang, Qingsong Wen, Yuxuan Liang, Weigao Sun

Recent efficient sequence modeling methods, such as Gated DeltaNet, TTT, and RWKV-7, have achieved performance improvements by supervising the recurrent memory management through the Delta learning rule. Unlike previous state-space models (e.g., Mamba) and gated linear attentions (e.g., GLA), these models introduce interactions between the recurrent state and the key vector, resulting in a bilinear recursive structure. In this paper, we first introduce the concept of Bilinear RNNs with a comprehensive analysis on the advantages and limitations of these models. Then based on the closed-loop control theory, we propose a novel Bilinear RNN variant named Comba, which adopts a scalar-plus-low-rank state transition, with both state feedback and output feedback corrections. We also implement a hardware-efficient chunk-wise parallel kernel in Triton and train models with 340M/1.3B parameters on a large-scale corpus. Comba demonstrates its superior performance and computation efficiency on both language modeling and vision tasks.

General Machine Learning · Transfer, Multitask and Meta-learning

Xiaohan Qin, Xiaoxing Wang, Ning Liao, Junchi Yan

Multi-Task Learning (MTL) enables a single model to learn multiple tasks simultaneously, leveraging knowledge transfer among tasks for enhanced generalization, and has been widely applied across various domains. However, task imbalance remains a major challenge in MTL. Although balancing the convergence speeds of different tasks is an effective approach to address this issue, it is highly challenging to accurately characterize the training dynamics and convergence speeds of multiple tasks within the complex MTL system. To this end, we attempt to analyze the training dynamics in MTL by leveraging Neural Tangent Kernel (NTK) theory and propose a new MTL method, NTKMTL. Specifically, we introduce an extended NTK matrix for MTL and adopt spectral analysis to balance the convergence speeds of multiple tasks, thereby mitigating task imbalance. Based on the approximation via shared representation, we further propose NTKMTL-SR, achieving training efficiency while maintaining competitive performance. Extensive experiments demonstrate that our methods achieve state-of-the-art performance across a wide range of benchmarks, including both multi-task supervised learning and multi-task reinforcement learning. Source code is available at https://github.com/jianke0604/NTKMTL.

Probabilistic Methods · Monte Carlo and Sampling Methods

Zuheng (David) Xu, Trevor Campbell

Most expressive variational families---such as normalizing flows---lack practical convergence guarantees, as their theoretical assurances typically hold only at the intractable global optimum. In this work, we present a general recipe for constructing tuning-free, asymptotically exact variational flows on *arbitrary* state spaces from involutive MCMC kernels. The core methodological component is a novel representation of general involutive MCMC kernels as invertible, measure- preserving iterated random function systems, which act as the flow maps of our variational flows. This leads to three new variational families with provable total variation convergence. Our framework resolves key practical limitations of existing variational families with similar guarantees (e.g., MixFlows), while requiring substantially weaker theoretical assumptions. Finally, we demonstrate the competitive performance of our flows across tasks including posterior approximation, Monte Carlo estimates, and normalization constant estimation, outperforming or matching No-U-Turn sampler (NUTS) and black-box normalizing flows.

Theory · Learning Theory

Nathael Da Costa, Cyrus Mostajeran, Juan-Pablo Ortega, Salem Said

Kernel methods are powerful tools in machine learning. Classical kernel methods are based on positive definite kernels, which enable learning in reproducing kernel Hilbert spaces (RKHS). For non-Euclidean data spaces, positive definite kernels are difficult to come by. In this case, we propose the use of reproducing kernel Krein space (RKKS) based methods, which require only kernels that admit a positive decomposition. We show that one does not need to access this decomposition to learn in RKKS. We then investigate the conditions under which a kernel is positively decomposable. We show that invariant kernels admit a positive decomposition on homogeneous spaces under tractable regularity assumptions. This makes them much easier to construct than positive definite kernels, providing a route for learning with kernels for non-Euclidean data. By the same token, this provides theoretical foundations for RKKS-based methods in general.

Deep Learning · Attention Mechanisms

Shuo Yang, Haocheng Xi, Yilong Zhao, Muyang Li, Jintao Zhang, Han Cai, Yujun Lin, Xiuyu Li, Chenfeng Xu, Kelly Peng 等

Diffusion Transformers (DiTs) are essential for video generation but suffer from significant latency due to the quadratic complexity of attention. By computing only critical tokens, sparse attention reduces computational costs and offers a promising acceleration approach. However, we identify that existing methods fail to approach optimal generation quality under the same computation budget for two reasons: (1) Inaccurate critical token identification: current methods cluster tokens based on position rather than semantics, leading to imprecise aggregated representations. (2) Excessive computation waste: critical tokens are scattered among non-critical ones, leading to wasted computation on GPUs, which are optimized for processing contiguous tokens. In this paper, we propose SVG2, a training-free framework that maximizes identification accuracy and minimizes computation waste, achieving a Pareto frontier trade-off between generation quality and efficiency. The core of SVG2 is semantic-aware permutation, which clusters and reorders tokens based on semantic similarity using k-means. This approach ensures both a precise cluster representation, improving identification accuracy, and a densified layout of critical tokens, enabling efficient computation without padding. Additionally, SVG2 integrates Top-p dynamic budget control and customized kernel implementations, achieving up to $2.30\times$ and $1.89\times$ speedup while maintaining a PSNR of up to $30$ and $26$ on HunyuanVideo and Wan 2.1, respectively. Our code is open-sourced at https://github.com/svg-project/Sparse-VideoGen.

Computer Vision · 3D Rendering & Reconstruction

Xuankai Zhang, Junjin Xiao, Qing Zhang

This paper presents a unified framework that allows high-quality dynamic Gaussian Splatting from both defocused and motion-blurred monocular videos. Due to the significant difference between the formation processes of defocus blur and motion blur, existing methods are tailored for either one of them, lacking the ability to simultaneously deal with both of them. Although the two can be jointly modeled as blur kernel-based convolution, the inherent difficulty in estimating accurate blur kernels greatly limits the progress in this direction. In this work, we go a step further towards this direction. Particularly, we propose to estimate per-pixel reliable blur kernels using a blur prediction network that exploits blur-related scene and camera information and is subject to a blur-aware sparsity constraint. Besides, we introduce a dynamic Gaussian densification strategy to mitigate the lack of Gaussians for incomplete regions, and boost the performance of novel view synthesis by incorporating unseen view information to constrain scene optimization. Extensive experiments show that our method outperforms the state-of-the-art methods in generating photorealistic novel view synthesis from defocused and motion-blurred monocular videos. Our code is available at https://github.com/hhhddddddd/dydeblur.

General Machine Learning · Representation Learning

Adrien Aumon, Shuang Ni, Myriam Lizotte, Guy Wolf, Kevin Moon, Jake Rhodes

Extensive research has produced robust methods for unsupervised data visualization. Yet supervised visualization—where expert labels guide representations—remains underexplored, as most supervised approaches prioritize classification over visualization. Recently, RF-PHATE, a diffusion-based manifold learning method leveraging random forests and information geometry, marked significant progress in supervised visualization. However, its lack of an explicit mapping function limits scalability and its application to unseen data, posing challenges for large datasets and label-scarce scenarios. To overcome these limitations, we introduce Random Forest Autoencoders (RF-AE), a neural network-based framework for out-of-sample kernel extension that combines the flexibility of autoencoders with the supervised learning strengths of random forests and the geometry captured by RF-PHATE. RF-AE enables efficient out-of-sample supervised visualization and outperforms existing methods, including RF-PHATE's standard kernel extension, in both accuracy and interpretability. Additionally, RF-AE is robust to the choice of hyperparameters and generalizes to any kernel-based dimensionality reduction method.

Theory · Learning Theory

Yunrui Guan, Krishnakumar Balasubramanian, Shiqian Ma

We introduce the \textit{Riemannian Proximal Sampler}, a method for sampling from densities defined on Riemannian manifolds. The performance of this sampler critically depends on two key oracles: the \textit{Manifold Brownian Increments (MBI)} oracle and the \textit{Riemannian Heat-kernel (RHK)} oracle. We establish high-accuracy sampling guarantees for the Riemannian Proximal Sampler, showing that generating samples with \(\varepsilon\)-accuracy requires \(\mathcal{O}(\log(1/\varepsilon))\) iterations in Kullback-Leibler divergence assuming access to exact oracles and \(\mathcal{O}(\log^2(1/\varepsilon))\) iterations in the total variation metric assuming access to sufficiently accurate inexact oracles. Furthermore, we present practical implementations of these oracles by leveraging heat-kernel truncation and Varadhan’s asymptotics. In the latter case, we interpret the Riemannian Proximal Sampler as a discretization of the entropy-regularized Riemannian Proximal Point Method on the associated Wasserstein space. We provide preliminary numerical results that illustrate the effectiveness of the proposed methodology.

Deep Learning · Theory

Alistair Shilton, Sunil Gupta, Santu Rana, Svetha Venkatesh

This paper explores the use of Hermite transform based reproducing kernel Banach space methods to construct exact or un-approximated models of feedforward neural networks of arbitrary width, depth and topology, including ResNet and Transformers networks, assuming only a feedforward topology, finite energy activations and finite (spectral-) norm weights and biases. Using this model, two straightforward but surprisingly tight bounds on Rademacher complexity are derived, precisely (1) a general bound that is width-independent and scales exponentially with depth; and (2) a width- and depth-independent bound for networks with appropriately constrained (below threshold) weights and biases.

Deep Learning · Attention Mechanisms

Coleman Hooper, Sebastian Zhao, Luca Manolache, Sehoon Kim, Michael Mahoney, Sophia Shao, Kurt Keutzer, Amir Gholami

Large Reasoning Models (LRMs) have shown promising accuracy improvements on complex problem-solving tasks. While these models have attained high accuracy by leveraging additional computation at test time, they need to generate long chain-of-thought reasoning in order to think before answering, which requires generating thousands of tokens. While sparse attention methods can help reduce the KV cache pressure induced by this long autoregressive reasoning, these methods can introduce errors which disrupt the reasoning process. Our work addresses these challenges by introducing Multipole Attention, which accelerates autoregressive reasoning by only computing exact attention for the most important tokens, while maintaining approximate representations for the remaining tokens. Our method first performs clustering to group together semantically similar key vectors, and then uses the cluster centroids both to identify important key vectors and to approximate the remaining key vectors in order to retain high accuracy. Additionally, in order to accelerate long generation tasks, we design a fast cluster update process to quickly re-cluster the input and previously generated tokens, thereby allowing for accelerating attention to the previous output tokens. We evaluate our method using emerging LRMs such as Qwen-8B and Deepseek-R1-Distil-Qwen2.5-14B, demonstrating that our approach can maintain accuracy on complex reasoning tasks even with aggressive attention sparsity settings. We also provide kernel implementations to demonstrate the practical efficiency gains from our method, achieving up to 4.5$\times$ speedup for attention in long-context reasoning applications.

Probabilistic Methods · Gaussian Processes

Daniel Augusto de Souza, Yuchen Zhu, Jake Cunningham, Yuri Saporito, Diego Mesquita, Marc Deisenroth

A variety of infinitely wide neural architectures (e.g., dense NNs, CNNs, and transformers) induce Gaussian process (GP) priors over their outputs. These relationships provide both an accurate characterization of the prior predictive distribution and enable the use of GP machinery to improve the uncertainty quantification of deep neural networks. In this work, we extend this connection to neural operators (NOs), a class of models designed to learn mappings between function spaces. Specifically, we show conditions for when arbitrary-depth NOs with Gaussian-distributed convolution kernels converge to function-valued GPs. Based on this result, we show how to compute the covariance functions of these NO-GPs for two NO parametrizations, including the popular Fourier neural operator (FNO). With this, we compute the posteriors of these GPs in regression scenarios, including PDE solution operators. This work is an important step towards uncovering the inductive biases of current FNO architectures and opens a path to incorporate novel inductive biases for use in kernel-based operator learning methods.

Deep Learning · Theory

Chaoyue Liu, Han Bi, Like Hui, Xiao Liu

Nonlinear activation functions are widely recognized for enhancing the expressivity of neural networks, which is the primary reason for their widespread implementation. In this work, we focus on ReLU activation and reveal a novel and intriguing property of nonlinear activations. By comparing enabling and disabling the nonlinear activations in the neural network, we demonstrate their specific effects on wide neural networks: (a) *better feature separation*, i.e., a larger angle separation for similar data in the feature space of model gradient, and (b) *better NTK conditioning*, i.e., a smaller condition number of neural tangent kernel (NTK). Furthermore, we show that the network depth (i.e., with more nonlinear activation operations) further amplifies these effects; in addition, in the infinite-width-then-depth limit, all data are equally separated with a fixed angle in the model gradient feature space, regardless of how similar they are originally in the input space. Note that, without the nonlinear activation, i.e., in a linear neural network, the data separation remains the same as for the original inputs and NTK condition number is equivalent to the Gram matrix, regardless of the network depth. Due to the close connection between NTK condition number and convergence theories, our results imply that nonlinear activation helps to improve the worst-case convergence rates of gradient based methods.

Deep Learning · Generative Models and Autoencoders

Neta Shaul, Uriel Singer, Itai Gat, Yaron Lipman

Diffusion and flow matching models have significantly advanced media generation, yet their design space is well-explored, somewhat limiting further improvements. Concurrently, autoregressive (AR) models, particularly those generating continuous tokens, have emerged as a promising direction for unifying text and media generation, showing improved performance at scale. This paper introduces Transition Matching (TM), a novel discrete-time, continuous-state generative paradigm that unifies and advances both diffusion/flow models and continuous AR generation. TM decomposes complex generation tasks into simpler Markov transitions, allowing for expressive non-deterministic probability transition kernels and arbitrary non-continuous supervision processes, thereby unlocking new flexible design avenues. We explore these choices through three TM variants: (i) Difference Transition Matching (DTM), which generalizes flow matching to discrete-time by directly learning transition probabilities, yielding state-of-the-art image quality and text adherence. (ii) Autoregressive Transition Matching (ARTM) and (iii) Full History Transition Matching (FHTM) are partially and fully causal models, respectively, that generalize continuous AR methods. They achieve continuous causal AR generation quality comparable to non-causal approaches and potentially enable seamless integration with existing AR text generation techniques. Notably, FHTM is the first fully causal model to match or surpass the performance of flow-based methods on text-to-image task in continuous domains. We demonstrate these contributions through a rigorous large-scale comparison of TM variants and relevant baselines, maintaining a fixed architecture, training data, and hyperparameters.

General Machine Learning · Everything Else

Louis Allain, Sébastien Da Veiga, Brian Staber

Conformal Prediction (CP) is a popular framework for constructing prediction bands with valid coverage in finite samples, while being free of any distributional assumption. A well-known limitation of conformal prediction is the lack of adaptivity, although several works introduced practically efficient alternate procedures. In this work, we build upon recent ideas that rely on recasting the CP problem as a statistical learning problem, directly targeting coverage and adaptivity. This statistical learning problem is based on reproducible kernel Hilbert spaces (RKHS) and kernel sum-of-squares (SoS) methods. First, we extend previous results with a general representer theorem and exhibit the dual formulation of the learning problem. Crucially, such dual formulation can be solved efficiently by accelerated gradient methods with several hundreds or thousands of samples, unlike previous strategies based on off-the-shelf semidefinite programming algorithms. Second, we introduce a new hyperparameter tuning strategy tailored specifically to target adaptivity through bounds on test-conditional coverage. This strategy, based on the Hilbert-Schmidt Independence Criterion (HSIC), is introduced here to tune kernel lengthscales in our framework, but has broader applicability since it could be used in any CP algorithm where the score function is learned. Finally, extensive experiments are conducted to show how our method compares to related work. All figures can be reproduced with the accompanying code at https://www.gitlab.com/drti/ksos-bands.

Social Aspects · Accountability, Transparency and Interpretability

Alessio Ragno, Marc Plantevit, Céline Robardet

Graphs are complex, non-Euclidean structures that require specialized models, such as Graph Neural Networks (GNNs), Graph Transformers, or kernel-based approaches, to effectively capture their relational patterns. This inherent complexity makes explaining GNNs decisions particularly challenging. Most existing explainable AI (XAI) methods for GNNs focus on identifying influential nodes or extracting subgraphs that highlight relevant motifs. However, these approaches often fall short of clarifying how such elements contribute to the final prediction. To overcome this limitation, logic-based explanations aim to derive explicit logical rules that reflect the model's decision-making process. Current logic-based methods are limited to post-hoc analyzes and are predominantly applied to graph classification, leaving a significant gap in intrinsically explainable GNN architectures. In this paper, we explore the potential of integrating logic reasoning directly into graph learning. We introduce LogiX-GIN, a novel, self-explainable GNN architecture that incorporates logic layers to produce interpretable logical rules as part of the learning process. Unlike post-hoc methods, LogiX-GIN provides faithful, transparent, and inherently interpretable explanations aligned with the model's internal computations. We evaluate LogiX-GIN across several graph-based tasks and show that it achieves competitive predictive performance while delivering clear, logic-based insights into its decision-making process.

Social Aspects · Accountability, Transparency and Interpretability

R. Teal Witter, Yurong Liu, Christopher Musco

With origins in game-theory, probabilistic values like Shapley values, Banzhaf values, and semi-values have emerged as a central tool in explainable AI. They are used for feature attribution, data attribution, data valuation, and more. Since all of these values require exponential time to compute exactly, research has focused on efficient approximation methods using two techniques: Monte Carlo sampling and linear regression formulations. In this work, we present a new way of combining both of these techniques. Our approach is more flexible than prior algorithms, allowing for linear regression to be replaced with any function family whose probabilistic values can be computed efficiently. This allows us to harness the accuracy of tree-based models like XGBoost, while still producing unbiased estimates. From experiments across eight datasets, we find that our methods give state-of-the-art performance for estimating probabilistic values. For Shapley values, the error of our methods is up to $6\times$ lower than Permutation SHAP (the most popular Monte Carlo method), $2.75\times$ lower than Kernel SHAP (the most popular linear regression method), and $1.75\times$ lower than Leverage SHAP (the prior state-of-the-art Shapley value estimator). For more general probabilistic values, we can obtain error up to $60\times$ lower than prior work.

Theory · Learning Theory

Luc Brogat-Motte, Alessandro Rudi, Riccardo Bonalli

We address the problem of safely learning controlled stochastic dynamics from discrete-time trajectory observations, ensuring system trajectories remain within predefined safe regions during both training and deployment. Safety-critical constraints of this kind are crucial in applications such as autonomous robotics, finance, and biomedicine. We introduce a method that ensures safe exploration and efficient estimation of system dynamics by iteratively expanding an initial known safe control set using kernel-based confidence bounds. After training, the learned model enables predictions of the system's dynamics and permits safety verification of any given control. Our approach requires only mild smoothness assumptions and access to an initial safe control set, enabling broad applicability to complex real-world systems. We provide theoretical guarantees for safety and derive adaptive learning rates that improve with increasing Sobolev regularity of the true dynamics. Experimental evaluations demonstrate the practical effectiveness of our method in terms of safety, estimation accuracy, and computational efficiency.

Deep Learning · Graph Neural Networks

Jiaxin Wang, Wenxuan Tu, Jieren Cheng

Graph kernels have emerged as a fundamental and widely adopted technique in graph machine learning. However, most existing graph kernel methods rely on fixed graph similarity estimation that cannot be directly optimized for task-specific objectives, leading to sub-optimal performance. To address this limitation, we propose a kernel-based learning framework called Hierarchical Shortest-Path Graph Kernel Network HSP-GKN, which seamlessly integrates graph similarity estimation with downstream tasks within a unified optimization framework. Specifically, we design a hierarchical shortest-path graph kernel that efficiently preserves both the semantic and structural information of a given graph by transforming it into hierarchical features used for subsequent neural network learning. Building upon this kernel, we develop a novel end-to-end learning framework that matches hierarchical graph features with learnable $hidden$ graph features to produce a similarity vector. This similarity vector subsequently serves as the graph embedding for end-to-end training, enabling the neural network to learn task-specific representations. Extensive experimental results demonstrate the effectiveness and superiority of the designed kernel and its corresponding learning framework compared to current competitors.

Deep Learning · Attention Mechanisms

Boris Bonev, Max Rietmann, Andrea Paris, Alberto Carpentieri, Thorsten Kurth

We introduce a generalized attention mechanism for spherical domains, enabling Transformer architectures to natively process data defined on the two-dimensional sphere - a critical need in fields such as atmospheric physics, cosmology, and robotics, where preserving spherical symmetries and topology is essential for physical accuracy. By integrating numerical quadrature weights into the attention mechanism, we obtain a geometrically faithful spherical attention that is approximately rotationally equivariant, providing strong inductive biases and leading to better performance than Cartesian approaches. To further enhance both scalability and model performance, we propose neighborhood attention on the sphere, which confines interactions to geodesic neighborhoods. This approach reduces computational complexity and introduces the additional inductive bias for locality, while retaining the symmetry properties of our method. We provide optimized CUDA kernels and memory-efficient implementations to ensure practical applicability. The method is validated on three diverse tasks: simulating shallow water equations on the rotating sphere, spherical image segmentation, and spherical depth estimation. Across all tasks, our spherical Transformers consistently outperform their planar counterparts, highlighting the advantage of geometric priors for learning on spherical domains.

Computer Vision · Classification and Understanding

Wenhao Li, Qiangchang Wang, Xianjing Meng, Zhibin Wu, Yilong Yin

Few-shot learning (FSL) aims to recognize novel concepts from only a few labeled support samples. Recent studies enhance support features by incorporating additional semantic information (e.g., class descriptions) or designing complex semantic fusion modules. However, these methods still suffer from hallucinating semantics that contradict the visual evidence due to the lack of grounding in actual instances, resulting in noisy guidance and costly corrections. To address these issues, we propose a novel framework, bridging Vision and Text with LLMs for Few-Shot Learning (VT-FSL), which constructs precise cross-modal prompts conditioned on Large Language Models (LLMs) and support images, seamlessly integrating them through a geometry-aware alignment mechanism. It mainly consists of Cross-modal Iterative Prompting (CIP) and Cross-modal Geometric Alignment (CGA). Specifically, the CIP conditions an LLM on both class names and support images to generate precise class descriptions iteratively in a single structured reasoning pass. These descriptions not only enrich the semantic understanding of novel classes but also enable the zero-shot synthesis of semantically consistent images. The descriptions and synthetic images act respectively as complementary textual and visual prompts, providing high-level class semantics and low-level intra-class diversity to compensate for limited support data. Furthermore, the CGA jointly aligns the fused textual, support, and synthetic visual representations by minimizing the kernelized volume of the 3-dimensional parallelotope they span. It captures global and nonlinear relationships among all representations, enabling structured and consistent multimodal integration. The proposed VT-FSL method establishes new state-of-the-art performance across ten diverse benchmarks, including standard, cross-domain, and fine-grained few-shot learning scenarios. Code is available at https://github.com/peacelwh/VT-FSL.