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Probabilistic Methods · Monte Carlo and Sampling Methods

Samuel Howard, Nikolas Nüsken, Jakiw Pidstrigach

Simulating the conditioned dynamics of diffusion processes, given their initial and terminal states, is an important but challenging problem in the sciences. The difficulty is particularly pronounced for rare events, for which the unconditioned dynamics rarely reach the terminal state. In this work, we propose a novel approach for learning diffusion bridges based on a self-consistency property of the optimal control. The resulting algorithm learns the conditioned dynamics in an iterative online manner, and exhibits strong performance in a range of empirical settings without requiring differentiation through simulated trajectories. Beyond the diffusion bridge setting, we draw connections between our self-consistency framework and recent advances in the wider stochastic optimal control literature.

Reinforcement Learning · Batch/Offline

Imad AOUALI, Otmane Sakhi

Off-policy evaluation (OPE) and off-policy learning (OPL) are foundational for decision-making in offline contextual bandits. Recent advances in OPL primarily optimize OPE estimators with improved statistical properties, assuming that better estimators inherently yield superior policies. Although theoretically justified, this estimator-centric approach neglects a critical practical obstacle: challenging optimization landscapes. In this paper, we provide theoretical insights and empirical evidence showing that current OPL methods encounter severe optimization issues, particularly as the action space grows. We show that estimator-aware policy parametrization can mitigate, but not fully resolve, optimization challenges. Building on this, we explore simpler weighted log-likelihood objectives and demonstrate that they enjoy substantially better optimization properties and still recover competitive, often superior, learned policies. Our findings emphasize the necessity of explicitly addressing optimization considerations in the development of OPL algorithms for large action spaces.

Applications · Computer Vision

Junwei Wu, Yihang Liu, Ruixuan Yu, Jian Sun

Predicting 3D geometric trajectory requires capturing complex spatiotemporal dependencies while preserving physical symmetries. While flow matching offers a powerful generative paradigm, extending it to SE(3)-equivariant dynamics is challenging due to the inherent gap between deterministic history and stochastic evolving flows. To address this, we introduce GSE-Flow, an SE(3)-equivariant flow matching framework. We first propose a Coherent Sequence Encoding and Time-Modulated Embedding strategy that unifies historical and evolving streams, incorporating velocity and flow time via equivariant affine transformations to guide continuous evolution. We further design a Geometry-Feature Tensorization mechanism that projects node states into a tensor product space, enabling Context-Flow Fusion to guide trajectory evolution with historical context. GSE-Flow guarantees theoretical SE(3)-equivariance and achieves SOTA accuracy on MD17, MD22, and CMU MoCap benchmarks for geometric trajectory prediction, while demonstrating generality by enhancing deterministic baselines.

Social Aspects · Accountability, Transparency, and Interpretability

Hans Farrell Soegeng, Sarthak Modi, Thomas Peyrin

Interpretable machine learning is essential in high-stakes domains where decision-making requires accountability, transparency, and trust. While rule-based models offer global and exact interpretability, learning rule sets that achieve high performance while maintaining low complexity to be human understandable and generalizability across tasks remains a difficult challenge. To address this, we introduce TT-Sparse, a flexible neural building block that leverages differentiable truth tables as nodes to learn sparse, effective connections. A key contribution of our approach is a novel soft TopK operator that allows straight-through estimation, ensuring differentiability to backpropagate gradients through the sparse connections and identify meaningful connections. This design allows each node to be exactly transformed into DNF/CNF equations via the Quine-McCluskey algorithm, effectively reducing the entire model to interpretable Boolean formulas. Extensive empirical results across 28 datasets spanning binary, multiclass, and regression tasks show the sparse rules exhibit superior predictive performance with lower complexity compared to existing state-of-the-art methods.

Applications · Social Sciences

Zherui Huang, Guanjie Zheng, Hao Xue, Linghe Kong

Origin–destination (OD) flow modeling underpins urban planning and mobility analysis, but prevailing graph-based methods often neglect salient geographic attributes, limiting their ability to model long-range and multi-area dependencies. In this paper, we introduce GeoFlow, a novel framework that (i) augments area representations with geospatial attributes, including relative positions, -hop and geodesic distances, (ii) employs a specialized geometric-intrinsic fusion encoder design that combines graph attention for intrinsic area signals with coordinate-aware encoders for global structure, and (iii) adopts an axial-global attention decoder to capture OD-specific competitive dependencies. For OD flow generation, GeoFlow is paired with flow matching models to produce more authentic and diverse mobility samples. Empirically, GeoFlow achieves superior performance in predictive accuracy, while substantially improving generative fidelity and diversity. Ablation and analytical studies confirm the contribution of each component.

Social Aspects · Security

Shuangshuang Pu, Wen Yang, Min Li, guodong liu, Chris Ding, Di Ming

Adversarial examples pose serious threats to deep neural networks (DNNs), revealing fundamental vulnerabilities in model robustness. However, most existing adversarial attacks directly manipulate densely activated and highly redundant feature representations, which often leads to overfitting on surrogate models and poor black-box transferability. Recent SVD-based attack attempts to exploit low-rank feature subspaces, yet its reliance on single-layer optimization and single-gradient pathway neglects both structural redundancy in feature representations and hierarchical heterogeneity across network layers. To address these limitations, we propose LRS-Attack, a Low-Rank and Sparse decomposition based adversarial attack that explicitly models robust hierarchical subspaces in latent feature spaces.Specifically, the low-rank component captures dominant semantic directions, while the sparse component models localized and highly sensitive discriminative patterns. To efficiently extract low-rank structure while preserving subspace quality, we develop a Warm-started Alternating Low-rank Approximation (WALA) algorithm. Furthermore, we design a hierarchical mixture of robust experts that models depth-dependent feature characteristics and guides gradient optimization toward more transferable adversarial directions. Extensive experiments on ImageNet demonstrate that the proposed LRS-Attack consistently improves black-box adversarial transferability over state-of-the-art methods across diverse CNN/ViT architectures and defense settings.

Deep Learning · Large Language Models

Md Kowsher, Ali Polat, Ehsan Ardehaly, Mehrdad Salehi, Zia Ghiasi, Prasanth Murali, Chen Chen

This paper presents a theoretical framework that explains why fine-tuning small, randomly selected subnetworks (slices) within pre-trained models is sufficient for downstream adaptation. We prove that pretrained networks exhibit a universal winning slice property, arising from two phenomena: (1) spectral balance— the eigenspectra of different weight matrix slices are remarkably similar—and (2) high task energy—their backbone representations (pretrained weights) retain rich, task-relevant features. This leads to the Universal Winning Slice Hypothesis, which provides a theoretical foundation for parameter-efficient fine-tuning (PEFT) in large-scale models. Inspired by this, we propose SliceFine, a PEFT method that uses this inherent redundancy by updating only selected slices of the origi- nal weights—introducing zero new parameters, unlike adapter-based approaches. Empirically, SliceFine matches the performance of SOTA PEFT methods across various language and vision tasks, while significantly improving training speed, memory efficiency, and model compactness. Our work bridges theory and prac- tice, offering a theoretically grounded alternative to existing PEFT techniques.

Deep Learning · Graph Neural Networks

Zhiqiang Li, Jianqing Liang, Zhiqiang Wang, Xizhao Luo, Jiye Liang

Molecular representation learning has achieved remarkable progress in molecular property prediction, yet out-of-distribution (OOD) generalization remains challenging. In practice, training data typically cover only a limited portion of the chemical space, causing models to rely on environment-dependent factors that fail to transfer when scaffold structures or functional compositions shift. To address this issue, we propose MoSIR, a framework for learning molecular semantic invariant representation with prototype constraint, which projects entangled molecular embeddings into a learnable semantic prototype space to extract semantic invariant representation while isolating environment-sensitive variations. Building upon this decomposition, we optimize a bi-level min-max objective that introduces representation perturbations to simulate plausible environment shifts and enforce semantic stability. We further provide theoretical guarantees for MoSIR by deriving an OOD generalization bound under distribution shifts. Extensive experiments on multiple molecular OOD benchmarks demonstrate that MoSIR consistently outperforms strong baselines across diverse shift settings, and qualitative analyses confirm that the learned prototypes capture meaningful chemical semantics.

Liang CHEN, Xueting Han, Li Shen, Jing Bai, Kam-Fai Wong

Supervised fine-tuning (SFT) and reinforcement learning with verifiable rewards (RLVR) are two widely used post-training paradigms for improving the reasoning ability of large language models (LLMs). Recent methods attempt to integrate SFT and RLVR in a single stage by reweighting or scheduling their objectives. However, such coupling can be counterproductive because supervised updates are not uniformly beneficial for reward optimization, which can diminish reward gains. To address this, we propose \textsc{BRIDGE}, a scalable framework in which SFT learns to supervise RL by selectively transferring knowledge that improves reward optimization. Specifically, \textsc{BRIDGE} employs two nested optimization loops during meta-training: the inner loop updates base model parameters using a fused SFT--RL gradient. Concurrently, the outer loop updates a lightweight low-rank adapter (LoRA) to coordinate the two objectives by maximizing a reward-gap signal, defined as the reward of joint SFT--RL training over an RL-only baseline. Across three model scales and five reasoning benchmarks, \textsc{BRIDGE} consistently outperforms two-stage cold start, naive mixing, and representative single-stage integration baselines, yielding over three points average absolute improvement and more stable training dynamics.

Social Aspects · Accountability, Transparency, and Interpretability

Gabriel Franco, Carson Loughridge, Mark Crovella

Identifying feature representations in language models is a central task in mechanistic interpretability. Several recent studies have made an implicit assumption that feature representations can be inferred in some cases from singular vectors of attention matrices. However, sound justification for this assumption is lacking. In this paper we address that question, asking: why and when do singular vectors align with features? First, we demonstrate that singular vectors robustly align with features in a model where features can be directly observed. We then show theoretically that such alignment is expected under a variety of general conditions. We close by asking how, operationally, alignment may be recognized in real models where feature representations are not directly observable. We identify *sparse attention decomposition* as a testable prediction of alignment, and show evidence that it emerges consistent with predictions in real models. Together these results suggest that alignment of singular vectors with features can be a sound and theoretically justified basis for feature identification in language models.

Theory · Learning Theory

Diego Martinez Taboada, Aaditya Ramdas

We develop novel "empirical Bernstein" inequalities for the variance of bounded random variables. Our inequalities hold under constant conditional variance and mean, without further assumptions like independence or identical distribution of the random variables, making them suitable for sequential decision making contexts. The results are instantiated for both the batch setting (where the sample size is fixed) and the sequential setting (where the sample size is a stopping time). Our bounds are asymptotically "sharp": when the data are iid, our CI adapts optimally to both unknown mean $\mu$ and unknown $\mathbb{V}[(X-\mu)^2]$, meaning that the first order term of our CI exactly matches that of the oracle Bernstein inequality which knows those quantities. We compare our results to a widely used (non-sharp) concentration inequality for the variance based on self-bounding random variables, showing both the theoretical gains and improved empirical performance of our approach. We finally extend our methods to work in any separable Hilbert space.

Theory · Learning Theory

WENHAI CUI, Xiaoting Ji, Wen Su, Xingqiu Zhao

Fair regression methods typically rely on squared error loss, making them fragile under heavy tailed noise. We propose a general framework for robust regression under demographic parity (DP) that applies to a wide class of M-estimators, including Cauchy, Huber, least absolute deviation, quantile, and Tukey losses. We propose an optimal fair transformation that guarantees DP while achieving the minimum population risk among all rank preserving fair predictors. We also establish convergence rates for the resulting estimators. To balance fairness and predictive accuracy, we develop an interpolation scheme whose risk decreases while unfairness grows linearly with the interpolation parameter. The proposed framework can be further extended to conditional DP to account for legitimate covariates. Extensive simulation studies and real data applications show clear improvements over existing fair regression approaches in both robustness and predictive performance.

Deep Learning · Large Language Models

Jaemin Kim, Hangeol Chang, Hyunmin Hwang, Choonghan Kim, Jong Chul YE

Large Language Models (LLMs) have demonstrated remarkable general capabilities, but enhancing skills such as reasoning often demands substantial computational resources and may compromise generalization. While Parameter-Efficient Fine-Tuning (PEFT) methods offer a more resource-conscious alternative, they typically require retraining for each LLM backbone due to architectural dependencies. To address these challenges, we propose Universal Reasoner (UniR)—a lightweight, composable, and plug-and-play reasoning module that can be used with larger frozen LLMs to provide specialized reasoning capabilities. Specifically, UniR decomposes the reward into a standalone reasoning module trained in a decoupled manner using verifiable rewards, effectively translating trajectory-level signals into token-level guidance. Once trained, UniR is combined with frozen LLMs at inference time by simply adding its output logits to those of the backbone. This additive structure enables modular composition: multiple UniR modules trained for different tasks can be jointly applied by summing their logits, enabling complex reasoning via composition. Furthermore, UniR demonstrates weak-to-strong generalization, where reasoning modules trained on smaller models effectively guide much larger LLMs in the same model family, and generalize across domains such as in vision language models and medical reasoning. Experiments on mathematical reasoning and machine translation show that UniR surpasses existing fine-tuning methods.

General Machine Learning · Data

Tzu-Heng Huang, Manjot Bilkhu, John Cooper, Frederic Sala, Javier Movellan

Large-scale web-crawled datasets contain noise, bias, and irrelevant information, necessitating data selection techniques. Existing methods depend on hand-crafted heuristics, downstream datasets, or require expensive influence-based computations---all of which limit scalability and introduce unwanted data dependencies. To address this, we introduce the Mimic Score, a simple and geometry-based data-quality metric that evaluates utility by measuring alignment between a sample’s gradients and a target direction induced by a pre-trained reference model. This leverages readily available model weights, avoids needing validation datasets, and incurs minimal computational overheads. Building on this metric, we propose Grad-Mimic, a two-stage framework that re-weights samples online to accelerate training and aggregates sample utilities offline to construct effective data filters. Empirically, we show that using mimic scores to guide training improves data efficiency, accelerates convergence, yields consistent performance gains across six image datasets, and enhances CLIP models with 20.7% fewer training steps. Additionally, mimic score-based filters augment existing filtering techniques, enabling improved CLIP models trained with 4.7 million fewer samples.

Hengchao Chen, Yuanyao Tan, Chao Huang, Hongtu Zhu, Qiang Sun

This paper introduces Mixtures of Geodesic Factor Analyzers (MGFA) on Riemannian homogeneous spaces. MGFA uses a geodesic factor model within each mixture component, providing greater expressiveness than mixtures of Riemannian radial distributions and enabling clustering of manifold-valued data with anisotropic subpopulations. We establish root-$n$ consistency for the MGFA maximum likelihood estimator (MLE), thereby filling a theoretical gap for mixtures of Riemannian radial distributions as a special case. We also propose an iterative estimation algorithm and implement it on spheres, shape spaces, and hyperbolic spaces. Numerical experiments show that MGFA substantially outperforms competing methods in well-specified regimes while remaining robust under model misspecification. Finally, case studies on corpus callosum and left hippocampus shape datasets demonstrate MGFA’s effectiveness for both 2D contour and 3D shape analysis.

Theory · Learning Theory

Qin-Cheng Zheng, Shao-Qun Zhang, Shen-Huan Lyu, Yuan Jiang, Zhi-Hua Zhou

Isolation Forest (iForest) stands out as a widely-used unsupervised anomaly detector, primarily owing to its remarkable runtime efficiency and superior performance in large-scale tasks. Despite its widespread adoption, a theoretical foundation explaining iForest's success remains unclear. This paper focuses on the inductive bias of iForest, which theoretically elucidates under what circumstances and to what extent iForest works well. The key is to formulate the growth process of iForest, where the split dimensions and split values are randomly selected. We model the growth process of iForest as a random walk, enabling us to derive the expected depth function, which is the outcome of iForest, using transition probabilities. The case studies reveal key inductive biases: iForest exhibits lower sensitivity to central anomalies while demonstrating greater parameter adaptability compared to $k$-Nearest Neighbor. The infinite sample size analysis shows that, unlike $k$-NN, iForest scores any point by considering both the density and the distances to the endpoints. Our study provides a theoretical understanding of the effectiveness of iForest and establishes a foundation for further theoretical exploration.

General Machine Learning · Online Learning, Active Learning and Bandits

Hang Yu, Yu-Hu Yan, Peng Zhao

Gradient-variation online learning has drawn increasing attention due to its deep connections to game theory, optimization, etc. It has been studied extensively in the full-information setting, but is underexplored with bandit feedback. In this work, we focus on gradient variation in Bandit Convex Optimization (BCO) with two-point feedback. By proposing a refined analysis on the *non-consecutive* gradient variation, a fundamental quantity in gradient variation with bandits, we improve the dimension dependence for both convex and strongly convex functions compared with the best known results (Chiang et al., 2013). Our improved analysis for the non-consecutive gradient variation also implies other favorable problem-dependent guarantees, such as gradient-variance and small-loss regrets. Beyond the two-point setup, we demonstrate the versatility of our technique by achieving the *first* gradient-variation bound for one-point bandit linear optimization over hyper-rectangular domains. Finally, we validate the effectiveness of our results in more challenging tasks such as dynamic/universal regret minimization and bandit games, establishing the *first* gradient-variation dynamic and universal regret bounds for two-point BCO and fast convergence rates in bandit games.

Muzhi Zhu, Hao Zhong, Canyu Zhao, Zongze Du, Mingyu Liu, Zheng Huang, Anzhou Li, Hao Chen, Cheng Zou, Jingdong Chen 等

Active vision, also known as active perception, refers to actively selecting where and how to look in order to gather task-relevant information. It is a critical component of efficient perception and decision-making in humans and advanced embodied agents. With the rise of Multimodal Large Language Models (MLLMs) as central planners in robotic systems, the lack of methods for equipping MLLMs with active perception has become a key gap. We first provide a systematic definition of MLLM-based active perception tasks and show that GPT-o3's zoom-in strategy can be viewed as a special case, though it suffers from low efficiency and inaccurate region selection. To address these issues, we propose Active-o3, a reinforcement learning framework built on GRPO that equips MLLMs with active perception capabilities. Leveraging a modular sensing-action design and a dual-form reward, Active-o3 autonomously learns efficient and stable region selection strategies without explicit supervision. We further establish a comprehensive benchmark covering both open-world tasks (small/dense-object grounding) and domain-specific scenarios (remote sensing, autonomous driving, interactive segmentation). Experimental results demonstrate that Active-o3 significantly enhances active perception capabilities compared to Qwen2.5-VL-CoT. Moreover, we show that our RL framework not only preserves the model’s general understanding ability but can also serve as a proxy task for leveraging perception data, further improving performance on benchmarks such as RealWorldQA. We hope that our work can provide a simple codebase and unified evaluation protocol to facilitate future research on active perception with MLLMs.

Mingqi Wu, Archer Yang, Qiang Sun

Iterative self-training (self-distillation) repeatedly refits a model on pseudo-labels generated by its own predictions. We study this procedure in overparameterized linear regression: an initial estimator is trained on noisy labels, and each subsequent iterate is trained on fresh covariates with noiseless pseudo-labels from the previous model. In the high-dimensional regime, we derive deterministic-equivalent recursions for the prediction risk and effective noise across iterations, and prove that the empirical quantities concentrate sharply around these limits. The recursion separates two competing forces: a systematic component that grows with iteration due to progressive \emph{signal forgetting}, and a stochastic component that decays due to \emph{denoising} via repeated data-dependent projections. Their interaction yields a $U$-shaped test-risk curve and an optimal early-stopping time. In spiked covariance models, iteration further acts as an iteration-dependent spectral filter that preserves strong eigendirections while suppressing weaker ones, inducing an implicit form of soft feature selection distinct from ridge regression. Finally, we propose an \emph{iterated} generalized cross-validation criterion and prove its uniform consistency for estimating the risk along the self-training trajectory, enabling fully data-driven selection of the stopping time and regularization. Experiments on synthetic covariances validate the theory and illustrate the predicted denoising–forgetting trade-off.

Theory · Learning Theory

Yuheng Ma, Qiang Sun

We study the stability properties of feature bagging, an ensemble technique that improves robustness by training each learner on a randomly selected subset of features. We introduce feature stability (FS), a notion that quantifies the sensitivity of an algorithm’s output to the removal of a single feature. This notion complements classical instance stability (IS) and together provides a more comprehensive framework for evaluating algorithmic stability. Within this framework, we analyze feature bagging in both a parametric linear model and an assumption-free setting inspired by recursive feature subsampling in random forests. In both cases, we establish formal stability guarantees showing that feature bagging strictly outperforms its non-bagged counterpart, with larger gains achieved at smaller subsampling ratios, and that only a modest number of bagging rounds is sufficient to attain near-optimal stability.