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General Machine Learning · Clustering

Milind Prabhu, Chris Schwiegelshohn, Sudarshan Shyam

Clustering in a big data setting is an intensively studied problem, with coresets emerging as one of the important paradigms in this line of work. Given a cost function $\text{cost}(P,S)$ mapping input points $P$ and a solution $S$ to an objective value, a coreset is a typically weighted subset $\Omega\subseteq P$ such that $\text{cost}(\Omega,S)\approx \text{cost}(P,S)$. For example, the Euclidean $k$-means problem, arguably the most widely studied problem in this line of work, admits a coreset of size $\tilde{O}(k\varepsilon^{-2}\min(\sqrt{k},\varepsilon^{-2}))$ points while preserving the $k$-means cost for \emph{any} candidate solution up to a $(1\pm \varepsilon)$ factor [CLSSS NeurIPS 2022]. While this bound is reasonably small, most empirical work on coresets suggest that smaller coreset sizes are sufficient. In this paper, we offer an explanation of this phenomenon. We show that a coreset size of $\tilde{O}(k \varepsilon^{-3})$ is sufficient that retains the approximation guarantee up to a $(1+\varepsilon)$ factor of any approximation algorithm used to compute a solution. These \emph{approximation preserving coresets} have a weaker guarantee than that of strong coresets, which apply to all solutions, while having stronger guarantees than weak coresets which only apply to the optimum solution. Thus, in some sense, worst case solutions inducing large strong coresets are solutions that most reasonable algorithms will not consider. We further extend the notion of approximation preserving coresets to \emph{arbitrary} metrics, showing that the approximation guarantee can be retained up to a factor $4+\varepsilon$ with a coreset of size $\tilde{O}(k\varepsilon^{-2})$. We complement this result by showing that a very small distortion on the approximation factor cannot admit coresets of this size. Our implementation with popular approximation algorithms such as $k$-means++ and local search confirm our theoretical findings also in practice.

Deep Learning · Large Language Models

Jinrui Liu, Kai Hua, Xuanguang Pan, Ge Zhang, Yong Wang, Shuai Ma, Chongyang Tao

LLMs achieve remarkable multi-step reasoning capabilities, yet effectively transferring these skills via post-training distillation remains challenging. Existing data selection methods, ranging from manual curation to heuristics based on length, entropy, or overall loss, fail to capture the causal importance of individual reasoning steps, limiting distillation efficiency. To address this, we propose Attention Influence for Reasoning (AIR), a principled, unsupervised and training-free framework that leverages mechanistic insights of the retrieval head to select high-value post-training data. AIR first identifies reasoning-critical attention heads of an off-the-shelf model, then constructs a weakened reference model with disabled head influence, and finally quantifies the resulting loss divergence as the Attention Influence Score. This score enables fine-grained assessment at both the step and sample levels, supporting step-level weighted fine-tuning and global sample selection. Experiments across multiple reasoning benchmarks show that AIR consistently improves reasoning accuracy, surpassing heuristic baselines and effectively isolating the most critical steps and samples. Our work establishes a mechanism-driven, data-efficient approach for reasoning distillation in LLMs.

Optimization · Large Scale, Parallel and Distributed

Xinwen Zhang, Yihan Zhang, Hongchang Gao, Heng Huang

In recent years, decentralized optimization has gained significant attention for solving machine learning problems where data are distributed across multiple devices. However, existing decentralized optimization algorithms are primarily designed for single-level and two-level optimization tasks, limiting their application to more complex problems such as decentralized stochastic $K$-level optimization, where $K>2$. In this work, we propose a novel decentralized stochastic $K$-level variance-reduced gradient descent algorithm to address the significant computation and communication overhead caused by the multi-level structure in decentralized stochastic $K$-level optimization problems. Moreover, we propose a novel theoretical analysis to tackle the recursive dependence issue caused by the multi-level structure when establishing the convergence rate of our algorithm. Finally, the experimental results confirm the effectiveness of our proposed algorithm.

Theory · Game Theory

Alon Eden, Kira Goldner, Eldar Kerner, Thodoris Tsilivis

We study mechanism design for the budget-feasible procurement problem, a natural problem that arises when a buyer wants to procure goods or services from multiple strategic sellers who each have a cost to provide that service, the buyer has a value for each service procured, but is constrained by a budget. In contrast to prior work, which has focused on buyer value maximization for this problem, we solve for optimal and approximately-optimal mechanisms for the objectives of buyer utility (value of procured services minus payments), welfare (value minus production costs), and generalizations of the two. For welfare, we design a simple mechanism that obtains a constant-factor approximation for the prior-free (worst-case) setting. As prior-free mechanisms fail to provide any guarantee for utility, even for a single seller, we consider Bayesian settings, where the buyer has distributional knowledge over sellers' costs. We first provide a utility-optimal mechanism that satisfies the buyer's budget constraint *in expectation*, then we show how to modify the mechanism to satisfy the budget constraint *ex-post*, for every realization of seller costs, while still obtaining near-optimal utility guarantees. Finally, we generalize our mechanisms to other objectives.

Deep Learning · Large Language Models

Yang Zhang, Xiaoshuai Sun, Rui Zhao, Wujin Sun, Yidong Chen, Jiayi Ji, Qian Chen, Rongrong Ji

Existing multimodal reasoning approaches predominantly follow two paradigms: converting visual inputs into text prior to reasoning, or performing end-to-end reasoning within a unified vision–language representation space. Despite their empirical progress, both paradigms suffer from fundamental structural limitations. The former relies on static visual-to-text conversion, which tends to compress and lose fine-grained visual details. The latter is prone to linguistic dominance induced by joint optimization and attention mechanisms, leading to systematically weakened faithfulness to visual evidence during reasoning. In this work, we argue that a central challenge is how and when visual evidence is introduced into the reasoning process. Motivated by this insight, we propose CSMR, a multimodal reasoning framework in which a language model controls the reasoning process by deciding when to invoke an independent visual perception module to acquire task-relevant visual evidence. Experiments across multiple multimodal reasoning benchmarks show that CSMR consistently outperforms representative baseline methods in accuracy under a zero-shot setting. Further experimental analysis confirms that these advantages primarily arise from the proposed cognitive scheduling mechanism.

Deep Learning · Generative Models and Autoencoders

Etrit Haxholli, Yeti Z. Gurbuz, Oğul Can, Eli Waxman

Discrete flow matching, a recent framework for modeling categorical data, has shown competitive performance with autoregressive models. However, unlike continuous flow matching, the rectification strategy cannot be applied due to the stochasticity of discrete paths, necessitating alternative methods to minimize state transitions. We propose a dynamic-optimal-transport-like minimization objective and derive its Kantorovich formulation for discrete flows with convex interpolants, where transport cost depends solely on inter-state similarity and can be optimized via minibatch strategies. We show that such methods can reduce the number of transitions up to 8 times (1024 to 128) to reach the same generative perplexity without compromising diversity. Additionally, path nondeterminism in discrete flows precludes an instantaneous change-of-variables analogue, preventing precise probability estimation available to continuous flows. We therefore propose two upper bounds on perplexity, enabling principled training, evaluation and model comparison. Finally, we introduce Multimask Flows which outperform masked flows in generative perplexity without compromising diversity, particularly when utilizing minibatch Optimal Transport.

Deep Learning · Large Language Models

Tianhao Gao, Jun Fang, Xiaohui Zhang, Zhiyuan Liu, Chao Liu, Pengzhang Liu, Qixia Jiang

Recent advances have empowered large language models (LLMs) with remarkable fine-grained instruction-following capabilities in text generation tasks. However, embedding methods typically rely solely on the hidden state of the input's last token, limiting their ability to capture complete semantic signals distributed across the full output tokens. Moreover, existing discrete-to-continuous re-encoding approaches introduce semantic discontinuity. To address these limitations, we propose $\textbf{InstEmb}$, a novel instruction following embedding framework. InstEmb jointly optimizes two key aspects: (1) Input-Intrinsic semantic information, achieved by employing contrastive learning focused on the representation of the last input token, and (2) Output-Aware semantic information, captured through representation self-distillation leveraging learnable look-ahead tokens without introducing additional decoding latency. Additionally, we introduce $\textbf{Dual-Anchor Alignment Pooling (DAAP)}$, explicitly aligned with our dual training objectives. Extensive experiments demonstrate that InstEmb achieves state-of-the-art performance across multiple instruction following benchmarks without benchmark-specific supervised data.

Social Aspects · Privacy

Yanhao Wei, Xiaokang Zhao, Boheng Li, Yang Zhang, Run Wang

Text-to-Image diffusion models have achieved remarkable success in image generation and are increasingly fine-tuned for personalized use cases. However, many personalized models may incorporate unauthorized data (e.g., copyrighted materials) during the fine-tuning process, raising growing concerns about potential copyright infringements. Existing methods either require intrusive modifications to the images to be protected, which not only fail to safeguard previously released images but may also degrade image quality, or rely on the availability of the pre-fine-tuned model, thereby limiting their applicability. To bridge this gap, in this paper, we propose the first non-intrusive copyright authentication framework without pre-fine-tuned model. We reveal that if a model is fine-tuned on a specific image, it learns the denoising trajectory of that image across varying noise levels, allowing it to stably reconstruct the image even under noise perturbations. Based on this insight, we propose Reliable dEteCtion Of unauthorized data usage via inVErsion Robustness (RECOVER), an effective non-intrusive detection method without pre-fine-tuned model. Unlike existing methods that rely on external watermarks or discrepancies between the suspect and pre-fine-tuned models, RECOVER directly leverages the robustness observed during the inversion–reconstruction process of the suspect model to determine whether an image was used for fine-tuning. Extensive experiments demonstrate that RECOVER is effective across a wide range of scenarios, consistently outperforming existing methods.

General Machine Learning · Representation Learning

Yuchen Guan, Xiao Li, Zongyu Guo, Xiaoyi Zhang, Xiulian Peng, Chun Yuan, Yan Lu

We propose a new paradigm for long video understanding by treating a long video as a Neural Knowledge Representation (NKR). NKR represent video contents neither as a stream of tokens or pre-organized databases, but as an individual small portion of network weights attached to the VLM backbone. The NKR weights is optimized to encapsulate the video's semantic content via a novel Agentic Knowledge Distillation (AKD) process, where an agent automatically synthesizes dense descriptions and question-answer pairs to distill the video's knowledge into the NKR. While AKD serves as a comprehensive, one-time encoding phase, the resulting NKR transforms the video into a portable, reusable asset. At inference, the lightweight NKR is mounted onto a frozen Vision-Language Model (VLM), enabling direct, query-based understanding without reloading or re-encoding the the original video. This approach decouples video length from inference cost, offering high amortized efficiency for multi-turn video understanding. Experiments on the LVBench benchmark show our method achieves performance comparable to state-of-the-art approaches while reducing end-to-end latency by over two orders of magnitude, opening new possibilities for interactive long-video understanding.

Deep Learning · Large Language Models

Jianwei Zhong, Yijun Mo, Quanxin Liu, Ruida Xu, Yuxi Yang, Ming Chi

Schema Linking serves as the foundational perception layer in Text-to-SQL, tasked with grounding natural language queries into relevant schema elements. However, existing retrieval-based approaches suffer from a critical *structural blindness*: by prioritizing elements with high textual similarity, they inadvertently prune semantically-thin but topologically-critical bridge tables, thereby severing relational pathways necessary for multi-hop joins. To bridge this gap, we propose Graph-Link, a novel framework that reformulates schema linking from an independent retrieval task into a constrained subgraph induction problem. We argue that generating executable SQL necessitates a connected subgraph that satisfies both semantic relevance and structural constraints. Accordingly, Graph-Link employs a hierarchical schema graph to model the search space across multiple granularities, and then applies a Steiner-tree-based optimization for subgraph induction that guarantees the topological connectivity while maximizing the signal-to-noise ratio for downstream LLMs. Extensive experiments on BIRD and Spider 2.0 demonstrate that Graph-Link achieves state-of-the-art schema linking performance, improving recall and hit rates by up to 7.0\% over competitive baselines, and boosts downstream SQL generation accuracy on complex queries by 13.8\%.

Applications · Neuroscience, Cognitive Science

Zijie Xu, Zihan Huang, Yiting Dong, Kang Chen, Wenxuan Liu, Zhaofei Yu

Spiking Neural Networks (SNNs) can achieve competitive performance by converting already existing well-trained Artificial Neural Networks (ANNs), avoiding further costly training. This property is particularly attractive in Reinforcement Learning (RL), where training through environment interaction is expensive and potentially unsafe. However, existing conversion methods perform poorly in continuous control, where suitable baselines are largely absent. We identify error amplification as the key cause: small action approximation errors become temporally correlated across decision steps, inducing cumulative state distribution shift and severe performance degradation. To address this issue, we propose Cross-Step Residual Potential Initialization (CRPI), a lightweight training-free mechanism that carries over residual membrane potentials across decision steps to suppress temporally correlated errors. Experiments on continuous control benchmarks with both vector and visual observations demonstrate that CRPI can be integrated into existing conversion pipelines and substantially recovers lost performance. Our results highlight continuous control as a critical and challenging benchmark for ANN-to-SNN conversion, where small errors can be strongly amplified and impact performance.

Reinforcement Learning · Inverse

Locke Cai, Max Ryabinin, Ivan Provilkov

Training Large Language Models (LLMs) to reason often relies on Reinforcement Learning (RL) with task-specific verifiers. However, many real-world reasoning-intensive tasks lack verifiers, despite offering abundant expert demonstrations that remain underutilized for reasoning-focused training. We introduce **RARO** (Relativistic Adversarial Reasoning Optimization), which learns strong reasoning capabilities from expert demonstrations alone via **Inverse Reinforcement Learning**. Our method sets up an adversarial game between a **policy** and a **relativistic critic**: the policy learns to mimic expert answers, while the critic aims to identify the expert among (expert, policy) answer pairs. Both the policy and the critic are trained jointly and continuously via RL, and we identify key stabilization techniques required for robust learning. Empirically, RARO significantly outperforms strong verifier-free baselines across all evaluation tasks—achieving $+13.7$\% accuracy on Countdown ($1.5\text{B}$), $+8.2$\% on DeepMath ($7\text{B}$), and a $+19.1$\% win-rate on Poetry Writing ($7\text{B}$) against expert poems. RARO also exhibits the same robust scaling trends as RL with verifiers. These results demonstrate that our method effectively elicits strong reasoning performance from expert demonstrations alone, enabling robust reasoning learning even when task-specific verifiers are unavailable.

Deep Learning · Large Language Models

Tianyu Fu, Yichen You, Zekai Chen, Guohao Dai, Huazhong Yang, Yu Wang

Improving reasoning abilities of Large Language Models (LLMs), especially under parameter constraints, is crucial for real-world applications. Looped transformers address this by performing multiple latent iterations to refine each token beyond a single forward pass. However, we identify a latent overthinking phenomenon: most token predictions are already correct after the first pass, but are sometimes revised into errors in later iterations. In this work, we ask whether selectively skipping latent iterations may improve accuracy. We reveal significant potential with an oracle iteration policy that boosts model performance by up to 7.3%. Motivated by this, we propose Think-at-Hard (TaH), a looped transformer optimized for selective iteration. TaH employs a lightweight neural decider to trigger latent iteration only at tokens that are likely incorrect after the standard forward pass. During latent iterations, depth-aware Low-Rank Adaptation (LoRA) modules shift the LLM's objective from general next-token prediction to focused hard-token refinement. A duo-causal attention mechanism extends attention from the token sequence dimension to an additional iteration depth dimension, enabling cross-iteration information flow with full sequential parallelism. Experiments on nine benchmarks show consistent gains across math, QA, and coding tasks. With identical parameter counts, TaH outperforms always-iterate baselines by 3.8-4.4% while skipping iterations on 93% of tokens, and exceeds single-iteration Qwen3 baselines by 3.0-3.8%. When allowing <3% more parameters from LoRA and decider modules, the gains further increase to 5.3-6.2% and 6.1-6.8%, respectively.

Applications · Chemistry, Physics, and Earth Sciences

Aleksander Krasowski, Jonas Naujoks, Moritz Weckbecker, Galip Yolcu, Thomas Wiegand, Sebastian Lapuschkin, Wojciech Samek, René P. Klausen

Physics-informed neural networks (PINNs) have emerged as a powerful deep learning approach for solving partial differential equations (PDEs) in the physical sciences, yet their behavior remains largely opaque and is typically understood through failure mode analyses rather than explicit interpretability. To address this issue, we introduce PINNfluence, a training data attribution framework for interpreting PINNs based on influence functions. By extending influence functions to composite physics-informed training objectives, we enable fine-grained attribution between predictions, loss components, and training data points. Through benchmark experiments across various PDEs, we demonstrate that influence patterns provide granular diagnostics that distinguish different PINN failure modes. PINNfluence thus opens a new avenue for understanding and improving the reliability of PINNs through the lens of their data.

Theory · Learning Theory

Kejiang Qian, Amos Storkey, Fengxiang He

This paper proposes a suite of rationality measures and associated theory for reinforcement learning agents, a property increasingly critical yet rarely explored. We define an action in deployment to be perfectly rational if it maximises the hidden true value function in the steepest direction. The expected value discrepancy of a policy's actions against their rational counterparts, culminating over the trajectory in deployment, is defined to be expected rational risk; an empirical average version in training is also defined. Their difference, termed as rational risk gap, is decomposed into (1) an extrinsic component caused by environment shifts between training and deployment, and (2) an intrinsic one due to the algorithm's generalisability in a dynamic environment. They are upper bounded by, respectively, (1) the $1$-Wasserstein distance between transition kernels and initial state distributions in training and deployment, and (2) the empirical Rademacher complexity of the value function class. Our theory suggests hypotheses on the benefits from regularisers (including layer normalisation, $\ell_2$ regularisation, and weight normalisation) and domain randomisation, as well as the harm from environment shifts. Experiments are in full agreement with these hypotheses.

Reinforcement Learning · Multi-agent

Hao Xiang Li, Michael Amir, Amanda Prorok

The agent-environment co-design paradigm jointly optimises agent policies and environment configurations in search of improved system performance, promising to fundamentally reshape how we deploy multi-agent systems in domains such as warehouse logistics and windfarm management. However, current co-design methods collapse under high dimensional environment design spaces and suffer from sample inefficiency when addressing moving targets inherent to joint optimisation. We address this by developing **Diffusion Co-Design** (DiCoDe), a scalable and sample-efficient co-design framework incorporating two core innovations. We introduce Projected Universal Guidance (PUG), enabling exploration of constraint-satisfying reward-maximising environments, and devise a critic distillation mechanism to transfer knowledge from the reinforcement learning loop to a guided diffuision model. Together, these improvements lead to superior environment-policy pairs when validated on challenging multi-agent co-design benchmarks, for example, exceeding state-of-the art in a warehouse setting with 39% higher rewards and 66% fewer simulation steps.

Deep Learning · Large Language Models

Kevin Zhai, Sabbir Mollah, Zhenyi Wang, Mubarak Shah

Standard decoding in Masked Diffusion Models (MDMs) is hindered by context rigidity: tokens are retained based on transient high confidence, often ignoring that early predictions lack full context. This creates cascade effects where initial inconsistencies misguide the remaining generation. Existing revision strategies attempt to mitigate this by relying on static confidence scores, but these signals are inherently myopic; inconsistent tokens frequently appear confident to the model itself. To address this, we propose Context-Robust Remasking (CoRe), a training-free framework for inference-time revision. We introduce a new selection paradigm: rather than trusting static token probabilities, we identify *context-brittle* tokens by probing their sensitivity to adversarial perturbations. We formalize revision as a robust optimization problem targeting worst-case context shifts. CoRe efficiently approximates this objective to expose unstable tokens, prioritizing them for revision. On LLaDA-8B-Base, CoRe delivers consistent improvements across reasoning and code benchmarks, outperforming compute-matched baselines and boosting performance on code generation (MBPP) by up to $+9.2\\%$.

Applications · Health / Medicine

Yang Song, Yixuan Zhang, Lingfa Meng, Tongyuan Hu, Haizhou Shi, Hao Wang, Samir Bhatt, Hengguan Huang

Reliable microbiome-based diagnosis is critical for precision medicine at scale in inflammatory diseases, yet current post-training pipelines in LLMs often overlook the interaction structure that governs microbial ecosystems. In inflammatory bowel disease (IBD), disease signals arise not only from species-level abundance shifts but also from latent microbe–microbe cross-talk. We propose iLoRA, a parameter-efficient Bayesian LoRA framework that infers latent interaction graphs from microbiome inputs and integrates them into adaptation, enabling joint clinical prediction and interaction discovery. Unlike correlation-based post hoc analysis, iLoRA models microbial interactions as latent variables learned end-to-end, yielding uncertainty-aware estimates of cross-talk. We evaluate iLoRA on (i) interactive question answering with human-annotated interaction graphs to quantify structural recovery and (ii) gut microbiome cohorts for IBD diagnosis. Across both domains, iLoRA consistently improves accuracy over strong LoRA baselines while producing interpretable interaction graphs consistent with annotated relations and conventional microbiome association networks.

Applications · Neuroscience, Cognitive Science

Yicheng Feng, Hairong Chen, Chenyu Liu, Samir Bhatt, Hengguan Huang

Alzheimer’s disease (AD) alters brain electrophysiology and disrupts multichannel EEG dynamics, making accurate and clinically useful EEG-based diagnosis increasingly important for screening and disease monitoring. However, many existing approaches rely on black-box classifiers and do not explicitly model the underlying dynamics that generate observed signals. To address these limitations, we propose LERD, an end-to-end Bayesian electrophysiological neural dynamical system that infers latent neural events and their relational structure directly from multichannel EEG without event or interaction annotations. LERD combines a continuous-time event inference module with a stochastic event-generation process to capture flexible temporal patterns, while incorporating an electrophysiology-inspired dynamical prior to guide learning in a principled way. We further provide theoretical analysis that yields a tractable bound for training and stability guarantees for the inferred relational dynamics. Extensive experiments on synthetic benchmarks and two real-world AD EEG cohorts demonstrate that LERD consistently outperforms strong baselines and yields physiology-aligned latent summaries that help characterize group-level dynamical differences.

Deep Learning · Large Language Models

Zhengping Jiang, Mehran Khodabandeh, Akash Bharadwaj, Manik Bhandari, Mayur Srungarapu, Anqi Liu, Benjamin Van Durme, Li Chen

Aligning large language models (LLMs) to heterogeneous and rapidly evolving safety requirements remains a critical challenge. Existing instruction-tuned LLMs and standalone safety classifiers often fail to generalize to new safety configurations, motivating the need for Reward Models (RMs) that are explicitly configurable to changing specifications. We introduce the Configurable Safety Reward Model (CSRM), which is jointly optimized for calibrated safety compliance and reward modeling. Our approach is supported by configuration-targeted data augmentation that enforces instruction adherence while preserving relative severity structure. The resulting RM is sensitive to fine-grained safety configurations and conversational nuances, substantially improving generalization to previously unseen safety configurations. CSRM achieves state-of-the-art performance on recent configurable safety benchmarks, including CoSApien (94.6\% F1) and DynaBench (75.8\% F1), without requiring additional human annotation. When used for downstream safety alignment, CSRM yields LLMs with a significantly improved helpfulness–safety tradeoff compared to existing baselines.