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Theory · Optimization

Loucas Pillaud-Vivien, Adrien Schertzer

We consider the problem of jointly learning a one-dimensional projection and a univariate function in high-dimensional Gaussian models. Specifically, we study predictors of the form $f(x)=\varphi^\star(\langle w^\star, x \rangle)$, where both the direction $w^\star \in \mathcal{S}_{d-1}$, the sphere of $\mathbb{R}^d$, and the function $\varphi^\star: \mathbb{R} \to \mathbb{R}$ are learned from Gaussian data. This setting captures a fundamental non-convex problem at the intersection of representation learning and nonlinear regression. We analyze the gradient flow dynamics of a natural alternating scheme and prove convergence, with a rate controlled by the information exponent reflecting the *Gaussian regularity* of the function $\varphi^\star$. Strikingly, our analysis shows that convergence still occurs even when the initial direction is negatively correlated with the target. On the practical side, we demonstrate that such joint learning can be effectively implemented using a Reproducing Kernel Hilbert Space (RKHS) adapted to the structure of the problem, enabling efficient and flexible estimation of the univariate function. Our results offer both theoretical insight and practical methodology for learning low-dimensional structure in high-dimensional settings.

Deep Learning · Large Language Models

Seongjin Cha, Gyuwan Kim, Dongsu Han, Tao Yang, Insu Han

Self-speculative decoding (SSD) accelerates LLM inference by skipping layers to create an efficient draft model, yet existing methods often rely on static heuristics that ignore the dynamic computational overhead of attention in long-context scenarios. We propose KnapSpec, a training-free framework that reformulates draft model selection as a knapsack problem to maximize tokens-per-time throughput. By decoupling Attention and MLP layers and modeling their hardware-specific latencies as functions of context length, KnapSpec adaptively identifies optimal draft configurations on the fly via a parallel dynamic programming algorithm. Furthermore, we provide the first rigorous theoretical analysis establishing cosine similarity between hidden states as a mathematically sound proxy for the token acceptance rate. This foundation allows our method to maintain high drafting faithfulness while navigating the shifting bottlenecks of real-world hardware. Our experiments on Qwen3 and Llama3 demonstrate that KnapSpec consistently outperforms state-of-the-art SSD baselines, achieving up to 1.47$\times$ wall-clock speedup across various benchmarks. Our plug-and-play approach ensures high-speed inference for long sequences without requiring additional training or compromising the target model's output distribution.

Theory · Optimization

Jianrong Lu, Zhuoya Gu, Haobo Li, Zhiyu Zhu, Yechao Zhang, Jianhai Chen, Minghui Yang, Junwei Liu, Jian Wang, Qinming He 等

This paper approaches the fundamental challenge of accelerating the inherently autoregressive nature of gradient descent (GD) like SGD and Adam through a dynamic system perspective. Specifically, we introduce a unified framework that recasts the autoregressive GD process as solving a system of triangular nonlinear equations (TNEs), thereby enabling \textit{step-parallel} training, where gradients for different GD steps are computed concurrently without sequential dependencies. Within this generic framework, we establish that: (1) the TNE system admits a unique solution corresponding precisely to the autoregressive GD iterative trajectory; (2) solving the TNEs system guarantees convergence to the GD iterative trajectory in at most the equal iterations. Building on these insights, we present \textit{PASO}, the first step-parallel optimizer for accelerating a broad class of GD-based optimizers like SGD and Adam. Extensive experiments (\textit{e.g.}, Llama-3.2-1B and diffusion model) validate that PASO achieves up to \textbf{21}$\times$ reduction in GD steps and \textbf{4.5}$\times$ speedup in wall-clock time, with no model quality loss. Source code is available at: \url{https://anonymous.4open.science/r/PASO-0AF9}.

Theory · Optimization

Yangnan Li, Xuanyu Cao, Shenghui Song

Resilience against Byzantine attackers and faster convergence on sparse networks are critical for decentralized optimization, yet existing methods fail to achieve both simultaneously. Existing DSGD-based Byzantine-resilient methods suffer from high transient complexity of $\mathcal{O}\left((1-\lambda)^{-6}\right)$, where $1-\lambda$ denotes the spectral gap of the network. While bias-correction methods such as Exact Diffusion can improve topology dependence, directly combining them with robust aggregators can lead to error accumulation. To address this issue, we introduce the scaled dual ascent (SDA) within the augmented Lagrangian framework for decentralized optimization, which mitigates error accumulation by scaling the dual update steps. Based on this, we propose BRED, which integrates Byzantine-robust Exact Diffusion with the SDA framework. We prove that BRED attains linear speedup, and achieves transient complexity of $\mathcal{O}\left((1-\lambda)^{-2}\right)$ when the Byzantine fraction $\delta$ is small. We further propose the momentum variant BRED-M, which reduces the Byzantine-affected transient complexity from $\mathcal{O}\left(\delta^2(1-\lambda)^{-6}\right)$ to $\mathcal{O}\left(\delta^2(1-\lambda)^{-4}\right)$. Empirical results on benchmark datasets demonstrate the efficacy of the proposed methods across diverse network topologies.

Social Aspects · Privacy

Xiongtao Sun, HUI LI, Jiaming Zhang, Yujie Yang, Kaili Liu, Ruxin Feng, Wen Tan, Wei Yang Bryan Lim

Modern Vision-Language Models (VLMs) pose significant individual-level privacy risks by linking fragmented multimodal data to identifiable individuals through hierarchical chain-of-thought reasoning. However, existing privacy benchmarks remain structurally insufficient for this threat, as they primarily evaluate privacy perception while failing to address the more critical risk of privacy reasoning: a VLM’s ability to infer and link distributed information to construct individual profiles. To address this gap, we propose MultiPriv, the first benchmark designed to systematically evaluate individual-level privacy reasoning in VLMs. We introduce the Privacy Perception and Reasoning (PPR) framework and construct a bilingual multimodal dataset with synthetic individual profiles, where identifiers (e.g., faces, names) are linked to sensitive attributes. This design enables nine challenging tasks spanning attribute detection, cross-image re-identification, and chained inference. We conduct a large-scale evaluation of over 50 open-source and commercial VLMs. Our analysis shows that 60\% of widely used VLMs can perform individual-level privacy reasoning with up to 80\% accuracy, posing a significant threat to personal privacy. MultiPriv provides a foundation for developing and assessing privacy-preserving VLMs.

Deep Learning · Graph Neural Networks

Francesco Ferrini, Veronica Lachi, Antonio Longa, Bruno Lepri, Akiyoshi Matono, Andrea Passerini, Xin Liu, Manfred Jaeger

Handling missing node features is a key challenge for deploying Graph Neural Networks (GNNs) in real-world domains such as healthcare and sensor networks. Existing studies mostly address relatively benign scenarios, namely benchmark datasets with (a) high-dimensional but sparse node features and (b) incomplete data generated under Missing Completely At Random (MCAR) mechanisms. For (a), we theoretically prove that high sparsity substantially limits the information loss caused by missingness, making all models appear robust and preventing a meaningful comparison of their performance. To overcome this limitation, we introduce one synthetic and three real-world datasets with dense, semantically meaningful features. For (b), we move beyond MCAR and design evaluation protocols with more realistic missingness mechanisms. Moreover, we provide a theoretical background to state explicit assumptions on the missingness process and analyze their implications for different methods. Building on this analysis, we propose GNNmim, a simple yet effective baseline for node classification with incomplete feature data. Experiments show that GNNmim is competitive with respect to specialized architectures across diverse datasets and missingness regimes.

Reinforcement Learning · Deep RL

Yuqi Liu, Liangyu Chen, Jiazhen Liu, Mingkang Zhu, Zhisheng Zhong, Bei Yu, Jiaya Jia

Post-training Large Vision-and-Language Models (LVLMs) typically involves Supervised Fine-Tuning (SFT) for knowledge injection or Reinforcement Learning with Verifiable Rewards (RLVR) for performance enhancement. However, SFT often leads to sub-optimal performance, while RLVR remains constrained by the model's internal knowledge base. While a sequential SFT $\rightarrow$ RLVR pipeline can be used, it introduces significant computational overhead and suffers from catastrophic forgetting. To address these limitations, we propose ViSurf (\textbf{Vi}sual \textbf{Su}pervised-and-\textbf{R}einforcement \textbf{F}ine-Tuning), a unified, single-stage paradigm that integrates the strengths of both SFT and RLVR. By analyzing their training objectives, we establish a unified framework that injects ground-truth labels directly into RLVR rollouts, facilitating simultaneous external supervision and internal reinforcement. Furthermore, we introduce three novel reward control strategies to ensure training stability and optimization. Extensive experiments demonstrate that ViSurf consistently outperforms standalone SFT, RLVR, and the traditional two-stage pipeline across diverse benchmarks. In-depth analysis corroborates these findings, validating the derivation and design principles of ViSurf. Our code, data and models will be publicly available.

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.