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Theory · Learning Theory

Jingyuan Liu, Hao Qiu, Lin Yang, Mengfan Xu

We study the distributed multi-agent multi-armed bandit problem with heterogeneous rewards over random communication graphs. Uniquely, at each time step $t$ agents communicate over a time-varying random graph $\mathcal{G}\_t$ generated by applying the Erdős–Rényi model to a fixed connected base graph $\mathcal{G}$ (for classical Erdos-Rényi graphs, $\mathcal{G}$ is a complete graph), where each potential edge in $\mathcal{G}$ is randomly and independently present with the link probability $p$. Notably, the resulting random graph is not necessarily connected at each time step. Each agent's arm rewards follow time-invariant distributions, and the reward distribution for the same arm may differ across agents. The goal is to minimize the cumulative expected regret relative to the global mean reward of each arm, defined as the average of that arm’s mean rewards across all agents. To this end, we propose a fully distributed algorithm that integrates the arm elimination strategy with the random gossip algorithm. We theoretically show that the regret upper bound is of order $\log T$ and is highly interpretable, where $T$ is the time horizon. It includes the optimal centralized regret $\mathcal O\left(\sum_{k: \Delta_k>0} \frac{\log T}{\Delta_k}\right)$ and an additional term $\mathcal O\left(\frac{N^2 \log T}{p \lambda_{N-1}(\operatorname{Lap}(\mathcal{G}))} + \frac{KN^2 \log T}{p}\right)$ where $N$ and $K$ denote the total number of agents and arms, respectively. This term reflects the impact of $\mathcal G$'s algebraic connectivity $\lambda_{N-1}(\operatorname{Lap}(\mathcal{G}))$ and the link probability $p$, and thus highlights a fundamental trade-off between communication efficiency and regret. As a by-product, we show a nearly optimal regret lower bound. Finally, our numerical experiments not only show the superiority of our algorithm over existing benchmarks, but also validate the theoretical regret scaling with problem complexity.

Deep Learning · Attention Mechanisms

Anthony Fuller, Yousef Yassin, Junfeng Wen, Tarek Ibrahim, Daniel Kyrollos, James Green, Evan Shelhamer

Vision transformers are ever larger, more accurate, and more expensive to compute. At high resolution, the expense is even more extreme as the number of tokens grows quadratically in the image size. We turn to adaptive computation to cope with this cost by learning to predict where to compute. Our LookWhere method divides the computation between a low-resolution selector and a high-resolution extractor without ever processing the full high-resolution input. We jointly pretrain the selector and extractor without task supervision by distillation from a self-supervised teacher, in effect learning where and what to compute at the same time. Unlike prior token reduction methods, which pay to save by pruning already-computed tokens, and prior token selection methods, which require complex and expensive per-task optimization, LookWhere economically and accurately selects and extracts transferrable representations of images. We show that LookWhere excels at sparse recognition on high-resolution inputs (Traffic Signs), maintaining accuracy while reducing FLOPs by 17x and time by 4x, and standard recognition tasks that are global (ImageNet classification) and local (ADE20K segmentation), improving accuracy while reducing time by 1.36x.

Computer Vision · Everything Else

Huaijin Pi, Zhi Cen, Zhiyang Dou, Taku Komura

Synthesizing whole-body manipulation of articulated objects, including body motion, hand motion, and object motion, is a critical yet challenging task with broad applications in virtual humans and robotics. The core challenges are twofold. First, achieving realistic whole-body motion requires tight coordination between the hands and the rest of the body, as their movements are interdependent during manipulation. Second, articulated object manipulation typically involves high degrees of freedom and demands higher precision, often requiring the fingers to be placed at specific regions to actuate movable parts. To address these challenges, we propose a novel coordinated diffusion noise optimization framework. Specifically, we perform noise-space optimization over three specialized diffusion models for the body, left hand, and right hand, each trained on its own motion dataset to improve generalization. Coordination naturally emerges through gradient flow along the human kinematic chain, allowing the global body posture to adapt in response to hand motion objectives with high fidelity. To further enhance precision in hand-object interaction, we adopt a unified representation based on basis point sets (BPS), where end-effector positions are encoded as distances to the same BPS used for object geometry. This unified representation captures fine-grained spatial relationships between the hand and articulated object parts, and the resulting trajectories serve as targets to guide the optimization of diffusion noise, producing highly accurate interaction motion. We conduct extensive experiments demonstrating that our method outperforms existing approaches in motion quality and physical plausibility, and enables various capabilities such as object pose control, simultaneous walking and manipulation, and whole-body generation from hand-only data. The code will be released for reproducibility.

Theory · Reinforcement Learning and Planning

Samuel Robertson, Thang Chu, Bo Dai, Dale Schuurmans, Csaba Szepesvari, Jincheng Mei

We prove that the classic REINFORCE stochastic policy gradient (SPG) method converges to globally optimal policies in finite-horizon Markov Decision Processes (MDPs) with $\textit{any}$ constant learning rate. To avoid the need for small or decaying learning rates, we introduce two key innovations in the stochastic bandit setting, which we then extend to MDPs. $\textbf{First}$, we identify a new exploration property of SPG: the online SPG method samples every action infinitely often (i.o.), improving on previous results that only guaranteed at least two actions would be sampled i.o. This means SPG inherently achieves asymptotic exploration without modification. $\textbf{Second}$, we eliminate the assumption of unique mean reward values, a condition that previous convergence analyses in the bandit setting relied on, but that does not translate to MDPs. Our results deepen the theoretical understanding of SPG in both bandit problems and MDPs, with a focus on how it handles the exploration-exploitation trade-off when standard optimization and stochastic approximation methods cannot be applied, as is the case with large constant learning rates.

Deep Learning · Robustness

Jinyong Jeong, Hyungu Kahng, Seoung Bum Kim

Distribution shifts between training and test data undermine the reliability of deep neural networks, challenging real-world applications across domains and subpopulations. While distributionally robust optimization (DRO) methods like GroupDRO aim to improve robustness by optimizing worst-case performance over predefined groups, their use of a single global classifier can be restrictive when facing substantial inter-environment variability. We propose Multi-Expert Distributionally Robust Optimization (MEDRO), a novel extension of GroupDRO designed to address such complex shifts. MEDRO employs a shared feature extractor with $m$ environment-specific expert classifier heads, and introduces a min-max objective over all $m^{2}$ expert-environment pairings, explicitly modeling cross-environment risks. This expanded uncertainty set captures fine-grained distributional variations that a single classifier might overlook. Empirical evaluations on a range of standard distribution shift benchmarks demonstrate that MEDRO often achieves robust predictive performance compared to existing methods. Furthermore, MEDRO offers practical inference strategies, such as ensembling or gating mechanisms, for typical scenarios where environment labels are unavailable at test time. Our findings suggest MEDRO as a promising step toward resilient and generalizable machine learning under real-world distribution shifts.

Reinforcement Learning · Everything Else

Sara Klein, Xiangyuan Zhang, Tamer Basar, Simon Weissmann, Leif Döring

In this work, we study $\gamma$-discounted infinite-horizon tabular Markov decision processes (MDPs) and introduce a framework called dynamic policy gradient (DynPG). The framework directly integrates dynamic programming with (any) policy gradient method, explicitly leveraging the Markovian property of the environment. DynPG dynamically adjusts the problem horizon during training, decomposing the original infinite-horizon MDP into a sequence of contextual bandit problems. By iteratively solving these contextual bandits, DynPG converges to the stationary optimal policy of the infinite-horizon MDP. To demonstrate the power of DynPG, we establish its non-asymptotic global convergence rate under the tabular softmax parametrization, focusing on the dependencies on salient but essential parameters of the MDP. By combining classical arguments from dynamic programming with more recent convergence arguments of policy gradient schemes, we prove that softmax DynPG scales polynomially in the effective horizon $(1-\gamma)^{-1}$. Our findings contrast recent exponential lower bound examples for vanilla policy gradient.

Applications · Robotics

Rui Zhao, Yuze Fan, Ziguo Chen, Fei Gao, Zhenhai Gao

End-to-end learning has emerged as a transformative paradigm for autonomous driving. However, the inherently multimodal nature of driving behaviors remains a fundamental challenge to robust deployment. We propose DiffE2E, a diffusion-based end-to-end autonomous driving framework. The architecture first performs multi-scale alignment of perception features from multiple sensors via a hierarchical bidirectional cross-attention mechanism. Subsequently, we design a hybrid diffusion-regression-classification decoder based on the Transformer architecture, adopting a collaborative training paradigm to seamlessly fuse the strengths of diffusion and explicit strategies. DiffE2E conducts structured modeling in the latent space: diffusion captures the multimodal distribution of future trajectories, while regression and classification act as explicit strategies to precisely model key control variables such as velocity, enhancing both the precision and controllability of the model. A global condition integration module further enables deep fusion of perception features with high-level goals, significantly improving the quality of trajectory generation. The subsequent cross-attention mechanism facilitates efficient interaction between integrated features and hybrid latent variables, promoting joint optimization of diffusion and explicit strategies for structured output generation and thereby yielding more robust control. Experimental results demonstrate that DiffE2E achieves state-of-the-art performance on both CARLA closed-loop benchmarks and NAVSIM evaluations. The proposed unified framework that integrates diffusion and explicit strategies provides a generalizable paradigm for hybrid action representation and shows substantial potential for extension to broader domains, including embodied intelligence.

Probabilistic Methods · Monte Carlo and Sampling Methods

Guan-Horng Liu, Jaemoo Choi, Yongxin Chen, Benjamin K Miller, Ricky T. Q. Chen

Computational methods for learning to sample from the Boltzmann distribution—where the target distribution is known only up to an unnormalized energy function—have advanced significantly recently. Due to the lack of explicit target samples, however, prior diffusion-based methods, known as _diffusion samplers_, often require importance-weighted estimation or complicated learning processes. Both trade off scalability with extensive evaluations of the energy and model, thereby limiting their practical usage. In this work, we propose **Adjoint Schrödinger Bridge Sampler (ASBS)**, a new diffusion sampler that employs simple and scalable matching-based objectives yet without the need to estimate target samples during training. ASBS is grounded on a mathematical model—the Schrödinger Bridge—which enhances sampling efficiency via kinetic-optimal transportation. Through a new lens of stochastic optimal control theory, we demonstrate how SB-based diffusion samplers can be learned at scale via Adjoint Matching and prove convergence to the global solution. Notably, ASBS generalizes the recent Adjoint Sampling (Havens et al., 2025) to arbitrary source distributions by relaxing the so-called memoryless condition that largely restricts the design space. Through extensive experiments, we demonstrate the effectiveness of ASBS on sampling from classical energy functions, amortized conformer generation, and molecular Boltzmann distributions. Codes are available at https://github.com/facebookresearch/adjoint_samplers

Optimization · Large Scale, Parallel and Distributed

Geeho Kim, Jinu Lee, Bohyung Han

Federated Generalized Category Discovery (Fed-GCD) requires a global model to classify seen classes and discover novel classes when data are siloed across heterogeneous clients. Existing GCD work often makes unrealistic assumptions, such as the need for prior knowledge of the number of novel classes or the assumption of uniform class distribution. We present Federated Local Prior Alignment (FedLPA), which eliminates these unrealistic assumptions by grounding learning in client-local structure and aligning predictions to client-local priors. Each client builds a similarity graph refined with reliable seen-class signals and discovers client-specific concepts and prototypes via Infomap. Leveraging the discovered concept structures, we introduce Local Prior Alignment (LPA): a self-distillation loss that matches the batch-mean prediction to an empirical prior computed from current concept assignments. The iterative process of local structure discovery and dynamic prior adaptation enables robust generalized category discovery under severe data heterogeneity. Our framework significantly outperforms existing federated generalized category discovery approaches on fine-grained and standard benchmarks, as demonstrated by extensive experimental results.

General Machine Learning · Representation Learning

Miaomiao Huang, Yuhai Zhao, Daniel Zhengkui Wang, Fenglong Ma, Yejiang Wang, Meixia Wang, Xingwei Wang

Graph self-supervised learning aims to learn the intrinsic graph representations from unlabeled data, with broad applicability in areas such as computing networks. Although graph contrastive learning (GCL) has achieved remarkable progress by generating perturbed views via data augmentation and optimizing sample similarity, it performs poorly in heterophilic graph scenarios (where connected nodes are likely to belong to different classes or exhibit dissimilar features). In heterophilic graphs, existing methods typically rely on random or carefully designed augmentation strategies (e.g., edge dropping) for contrastive views. However, such graph structures exhibit intricate edge relationships, where topological perturbations may completely alter the semantics of neighborhoods. Moreover, most methods focus solely on local contrastive signals while neglecting global structural constraints. To address these limitations, inspired by graph coloring, we propose a novel Coloring learning for heterophilic graph Representation framework, CoRep, which: 1) Pioneers a coloring classifier to generate coloring labels, explicitly minimizing the discrepancy between homophilic nodes while maximizing that of heterophilic nodes. A global positive sample set is constructed using multi-hop same-color nodes to capture global semantic consistency. 2) Introduces a learnable edge evaluator to guide the coloring learning dynamically and utilizes the edges' triplet relations to enhance its robustness. 3) Leverages Gumbel-Softmax to differentially discretize color distributions, suppressing noise via a redundancy constraint and enhancing intra-class compactness. Experimental results on 14 benchmark datasets demonstrate that CoRep significantly outperforms current state-of-the-art methods.

Optimization

He Chen, Jiajin Li, Anthony Man-Cho So

Solving bilevel optimization (BLO) problems to global optimality is generally intractable. A common surrogate is to compute a hyper-stationary point—a stationary point of the hyper-objective function obtained by minimizing or maximizing the upper-level objective over the lower-level solution set. Existing methods, however, either provide weak notions of stationarity or require restrictive assumptions to guarantee the smoothness of hyper-objective functions. In this paper, we eliminate these impractical assumptions and show that strong (Clarke) hyper-stationarity remains computable even when the hyper-objective is nonsmooth. Our key ingredient is a new structural property, called set smoothness, which captures the variational dependence of the lower-level solution set on the upper-level variable. We prove that this property holds for a broad class of BLO problems and ensures weak convexity (resp. concavity) of pessimistic (resp. optimistic) hyper-objective functions. Building on this foundation, we show that a zeroth-order algorithm that computes approximate Clarke hyper-stationary points with non-asymptotic convergence guarantees. To the best of our knowledge, this is the first computational guarantee for Clarke-type stationarity in nonsmooth BLO. Beyond this specific application, the set smoothness property emerges as a structural concept of independent interest, with potential to inform the analysis of broader classes of optimization and variational problems.

Deep Learning · Theory

Sofiane Ennadir, Levente Zólyomi, Oleg Smirnov, Tianze Wang, John Pertoft, Filip Cornell, Lele Cao

Transformer models have become the dominant backbone for sequence modeling, leveraging self-attention to produce contextualized token representations. These are typically aggregated into fixed-size vectors via pooling operations for downstream tasks. While much of the literature has focused on attention mechanisms, the role of pooling remains underexplored despite its critical impact on model behavior. In this paper, we introduce a theoretical framework that rigorously characterizes the expressivity of Transformer-based models equipped with widely used pooling methods by deriving closed-form bounds on their representational capacity and the ability to distinguish similar inputs. Our analysis extends to different variations of attention formulations, demonstrating that these bounds hold across diverse architectural variants. We empirically evaluate pooling strategies across tasks requiring both global and local contextual understanding, spanning three major modalities: computer vision, natural language processing, and time-series analysis. Results reveal consistent trends in how pooling choices affect accuracy, sensitivity, and optimization behavior. Our findings unify theoretical and empirical perspectives, providing practical guidance for selecting or designing pooling mechanisms suited to specific tasks. This work positions pooling as a key architectural component in Transformer models and lays the foundation for more principled model design beyond attention alone.

Computer Vision · Image and Video Generation

Huanlin Gao, Ping Chen, Fuyuan Shi, Chao Tan, Zhaoxiang Liu, Fang Zhao, Kai Wang, Shiguo Lian

We present LeMiCa, a training-free and efficient acceleration framework for diffusion-based video generation. While existing caching strategies primarily focus on reducing local heuristic errors, they often overlook the accumulation of global errors, leading to noticeable content degradation between accelerated and original videos. To address this issue, we formulate cache scheduling as a directed graph with error-weighted edges and introduce a Lexicographic Minimax Path Optimization strategy that explicitly bounds the worst-case path error. This approach substantially improves the consistency of global content and style across generated frames. Extensive experiments on multiple text-to-video benchmarks demonstrate that LeMiCa delivers dual improvements in both inference speed and generation quality. Notably, our method achieves a 2.9× speedup on the Latte model and reaches an LPIPS score of 0.05 on Open-Sora, outperforming prior caching techniques. Importantly, these gains come with minimal perceptual quality degradation, making LeMiCa a robust and generalizable paradigm for accelerating diffusion-based video generation. We believe this approach can serve as a strong foundation for future research on efficient and reliable video synthesis.

Theory · Reinforcement Learning and Planning

Navdeep Kumar, Priyank Agrawal, Giorgia Ramponi, Kfir Y. Levy, Shie Mannor

We analyze the global convergence of the single-timescale actor-critic (AC) algorithm for the infinite-horizon discounted Markov Decision Processes (MDPs) with finite state spaces. To this end, we introduce an elegant analytical framework for handling complex, coupled recursions inherent in the algorithm. Leveraging this framework, we establish that the algorithm converges to an $\epsilon$-close \textbf{globally optimal} policy with a sample complexity of $ O(\epsilon^{-3}) $. This significantly improves upon the existing complexity of $O(\epsilon^{-2})$ to achieve $\epsilon$-close \textbf{stationary policy}, which is equivalent to the complexity of $O(\epsilon^{-4})$ to achieve $\epsilon$-close \textbf{globally optimal} policy using gradient domination lemma. Furthermore, we demonstrate that to achieve this improvement, the step sizes for both the actor and critic must decay as $ O(k^{-\frac{2}{3}}) $ with iteration $k$, diverging from the conventional $O(k^{-\frac{1}{2}}) $ rates commonly used in (non)convex optimization.

Optimization · Large Scale, Parallel and Distributed

DongWon Kim, Sungdong Lee, Joong-Ho (Johann) Won

We develop a scalable second-order algorithm for a recently proposed $\ell_1$-regularized pseudolikelihood-based partial correlation network estimation framework. While the latter method admits statistical guarantees and is inherently scalable compared to likelihood-based methods such as graphical lasso, the currently available implementations rely only on first-order information and require thousands of iterations to obtain reliable estimates even on high-performance supercomputers. In this paper, we further investigate the inherent scalability of the framework and propose locally and globally convergent semismooth Newton methods. Despite the nonsmoothness of the problem, these second-order algorithms converge at a locally quadratic rate, and require only a few tens of iterations in practice. Each iteration reduces to solving linear systems of small dimensions or linear complementary problems of smaller dimensions, making the computation also suitable for less powerful computing environments. Experiments on both simulated and real-world genomic datasets demonstrate the superior convergence behavior and computational efficiency of the proposed algorithm, which position our method as a promising tool for massive-scale network analysis sought for in, e.g., modern multi-omics research.

Deep Learning · Algorithms

Senkang Hu, Xudong Han, Jinqi Jiang, Yihang Tao, Zihan Fang, Yong Dai, Sam Kwong, Yuguang Fang

Adapting billion-parameter language models to a downstream task is still costly, even with parameter-efficient fine-tuning (PEFT). We re-cast task adaptation as output-distribution alignment: the objective is to steer the output distribution toward the task distribution directly during decoding rather than indirectly through weight updates. Building on this view, we introduce Steering Vector Decoding (SVDecode), a lightweight, PEFT-compatible, and theoretically grounded method. We start with a short warm-start fine-tune and extract a task-aware steering vector from the Kullback-Leibler (KL) divergence gradient between the output distribution of the warm-started and pre-trained models. This steering vector is then used to guide the decoding process to steer the model's output distribution towards the task distribution. We theoretically prove that SVDecode is first-order equivalent to the gradient step of full fine-tuning and derive a globally optimal solution for the strength of the steering vector. Across three tasks and nine benchmarks, SVDecode paired with four standard PEFT methods improves multiple-choice accuracy by up to 5 percentage points and open-ended truthfulness by 2 percentage points, with similar gains (1-2 percentage points) on commonsense datasets without adding trainable parameters beyond the PEFT adapter. SVDecode thus offers a lightweight, theoretically grounded path to stronger task adaptation for large language models.

Optimization · Discrete Optimization

Ni Zhang, Zhiguang Cao

Existing GFlowNet-based methods for vehicle routing problems (VRPs) typically employ Trajectory Balance (TB) to achieve global optimization but often neglect important aspects of local optimization. While Detailed Balance (DB) addresses local optimization more effectively, it alone falls short in solving VRPs, which inherently require holistic trajectory optimization. To address these limitations, we introduce the Hybrid-Balance GFlowNet (HBG) framework, which uniquely integrates TB and DB in a principled and adaptive manner by aligning their intrinsically complementary strengths. Additionally, we propose a specialized inference strategy for depot-centric scenarios like the Capacitated Vehicle Routing Problem (CVRP), leveraging the depot node's greater flexibility in selecting successors. Despite this specialization, HBG maintains broad applicability, extending effectively to problems without explicit depots, such as the Traveling Salesman Problem (TSP). We evaluate HBG by integrating it into two established GFlowNet-based solvers, i.e., AGFN and GFACS, and demonstrate consistent and significant improvements across both CVRP and TSP, underscoring the enhanced solution quality and generalization afforded by our approach.

Computer Vision · Vision Models & Multimodal

Jingjun Yang, Liangwei Fan, Jinpu Zhang, Xiangkai Lian, Hui Shen, Dewen Hu

The integration of image and event streams offers a promising approach for achieving robust visual object tracking in complex environments. However, current fusion methods achieve high performance at the cost of significant computational overhead and struggle to efficiently extract the sparse, asynchronous information from event streams, failing to leverage the energy-efficient advantages of event-driven spiking paradigms. To address this challenge, we propose the first fully Spiking Frame-Event Tracking framework called SpikeFET. This network achieves synergistic integration of convolutional local feature extraction and Transformer-based global modeling within the spiking paradigm, effectively fusing frame and event data. To overcome the degradation of translation invariance caused by convolutional padding, we introduce a Random Patchwork Module (RPM) that eliminates positional bias through randomized spatial reorganization and learnable type encoding while preserving residual structures. Furthermore, we propose a Spatial-Temporal Regularization (STR) strategy that overcomes similarity metric degradation from asymmetric features by enforcing spatio-temporal consistency among temporal template features in latent space. Extensive experiments across multiple benchmarks demonstrate that the proposed framework achieves superior tracking accuracy over existing methods while significantly reducing power consumption, attaining an optimal balance between performance and efficiency.

Applications · Genetics, Cell Biology, etc

Kristiyan Sakalyan, Alessandro Palma, Filippo Guerranti, Fabian Theis, Stephan Günnemann

Understanding the evolution of cellular microenvironments in spatiotemporal data is essential for deciphering tissue development and disease progression. While experimental techniques like spatial transcriptomics now enable high-resolution mapping of tissue organization across space and time, current methods that model cellular evolution operate at the single-cell level, overlooking the coordinated development of cellular states in a tissue. We introduce NicheFlow, a flow-based generative model that infers the temporal trajectory of cellular microenvironments across sequential spatial slides. By representing local cell neighborhoods as point clouds, NicheFlow jointly models the evolution of cell states and spatial coordinates using optimal transport and Variational Flow Matching. Our approach successfully recovers both global spatial architecture and local microenvironment composition across diverse spatiotemporal datasets, from embryonic to brain development.

Deep Learning · Theory

Alexandru Crăciun, Debarghya Ghoshdastidar

The theory of training deep networks has become a central question of modern machine learning and has inspired many practical advancements. In particular, the gradient descent (GD) optimization algorithm has been extensively studied in recent years. A key assumption about GD has appeared in several recent works: the \emph{GD map is non-singular} --- it preserves sets of measure zero under preimages. Crucially, this assumption has been used to prove that GD avoids saddle points and maxima, and to establish the existence of a computable quantity that determines the convergence to global minima (both for GD and stochastic GD). However, the current literature either assumes the non-singularity of the GD map or imposes restrictive assumptions, such as Lipschitz smoothness of the loss (for example, Lipschitzness does not hold for deep ReLU networks with the cross-entropy loss) and restricts the analysis to GD with small step-sizes. In this paper, we investigate the neural network map as a function on the space of weights and biases. We also prove, for the first time, the non-singularity of the gradient descent (GD) map on the loss landscape of realistic neural network architectures (with fully connected, convolutional, or softmax attention layers) and piecewise analytic activations (which includes sigmoid, ReLU, leaky ReLU, etc.) for almost all step-sizes. Our work significantly extends the existing results on the convergence of GD and SGD by guaranteeing that they apply to practical neural network settings and has the potential to unlock further exploration of learning dynamics.