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Deep Learning · Attention Mechanisms

Jingkun Liu, Yisong Yue, Max Welling, Yue Song

Self-attention in Transformers relies on globally normalized softmax weights, causing all tokens to compete for influence at every layer. When composed across depth, this interaction pattern induces strong synchronization dynamics that favor convergence toward a dominant mode, a behavior associated with representation collapse and attention sink phenomena. We introduce $\textbf{Krause Attention}$, a principled attention mechanism inspired by bounded-confidence consensus dynamics. Krause Attention replaces similarity-based global aggregation with distance-based, localized, and selectively sparse interactions, promoting structured local synchronization instead of global mixing. We relate this behavior to recent theory modeling Transformer dynamics as interacting particle systems, and show how bounded-confidence interactions naturally moderate attention concentration and alleviate attention sinks. Restricting interactions to local neighborhoods also reduces runtime complexity from quadratic to linear in sequence length. Experiments across vision (ViT on CIFAR/ImageNet), autoregressive generation (MNIST/CIFAR-10), and large language models (Llama/Qwen) demonstrate consistent gains with substantially reduced computation, highlighting bounded-confidence dynamics as a scalable and effective inductive bias for attention.

General Machine Learning · Evaluation

Yatong Chen, Guanhua Zhang, Moritz Hardt

Influential benchmarks incentivize competing model builders to strategically allocate post-training resources towards improvements on the leaderboard, a phenomenon dubbed \emph{benchmaxxing} or \emph{training on the test task}. In this work, we initiate a principled study of the incentive structure that benchmarks induce. We model benchmarking as a Stackelberg game between a benchmark designer who chooses an evaluation protocol and multiple model providers who compete simultaneously in a subgame given by the designer’s choice. Each competitor has a model of unknown latent quality and can inflate its observed score by allocating resources to benchmark-specific improvements. First, we prove that current benchmarks induce games for which no Nash equilibrium between model developers exists. This result suggests one explanation for why current practice leads to misaligned incentives, prompting model providers to strategize in opaque ways. However, we prove that under mild conditions, a recently proposed evaluation protocol, called tune-before-test, induces a benchmark with a unique Nash equilibrium that ranks models by latent quality. This positive result demonstrates that benchmarks need not set bad incentives, even if current evaluations do.

Optimization · Large Scale, Parallel and Distributed

Rustem Islamov, Michael Crawshaw, Jeremy Cohen, Robert Gower

The Edge of Stability (EoS) is a phenomenon where the sharpness (largest eigenvalue) of the Hessian converges to $2/\eta$ during training with gradient descent (GD) with a step-size $\eta$. Despite violating classical smoothness assumptions, EoS has been widely observed in deep learning, but its theoretical foundations remain incomplete. We propose a framework for analyzing EoS of non-Euclidean GD using directional smoothness (Mishkin et al., 2024), which naturally extends to non-Euclidean norms. This approach allows us to characterize EoS beyond the standard Euclidean setting, encompassing methods such as $\ell_{\infty}$-descent, Block CD, Spectral GD, and Muon without momentum. We derive the appropriate measure of the generalized sharpness under an arbitrary norm. Our generalized sharpness measure includes previously studied vanilla GD and preconditioned GD as special cases. Through analytical results and experiments on neural networks, we show that non-Euclidean GD also exhibits progressive sharpening followed by oscillations around the threshold $2/\eta$. Practically, our framework provides a single, geometry-aware spectral measure that works across optimizers, bridging the gap between empirical observations and deep learning theory.

Optimization · Non-Convex

Rustem Islamov, Michael Crawshaw, Jeremy Cohen, Robert Gower

The Edge of Stability (EoS) is a phenomenon where the sharpness (largest eigenvalue) of the Hessian converges to $2/\eta$ during training with gradient descent (GD) with a step-size $\eta$. Despite violating classical smoothness assumptions, EoS has been widely observed in deep learning, but its theoretical foundations remain incomplete. We propose a framework for analyzing EoS of non-Euclidean GD using directional smoothness (Mishkin et al., 2024), which naturally extends to non-Euclidean norms. This approach allows us to characterize EoS beyond the standard Euclidean setting, encompassing methods such as $\ell_{\infty}$-descent, Block CD, Spectral GD, and Muon without momentum. We derive the appropriate measure of the generalized sharpness under an arbitrary norm. Our generalized sharpness measure includes previously studied vanilla GD and preconditioned GD as special cases. Through analytical results and experiments on neural networks, we show that non-Euclidean GD also exhibits progressive sharpening followed by oscillations around the threshold $2/\eta$. Practically, our framework provides a single, geometry-aware spectral measure that works across optimizers, bridging the gap between empirical observations and deep learning theory.

Applications · Everything Else

Zhiyuan Su, Naihe Feng, Zhen (Luther) Qin, Ga Wu

Sequential recommendation models, while powerful, have limited flexibility in responding to immediate user requests, making it difficult to adapt their recommendations to the user's timely interests. Unfortunately, existing user request adaptation methods often incur high computational overhead due to either 1) retraining the entire backbone network or 2) leveraging the inference ability of large language models (a.k.a. prompt engineering), limiting their applicability in large-scale recommendation services. This paper presents **C**ontrol via **R**equest-**A**ware **M**asking for **E**diting **R**ecommenders (**CRAMER**), a framework that takes users' natural-language requests to immediately change sequential recommendation models' behavior. Specifically, inspired by the model control theory, CRAMER treats user requests as control signals to modulate frozen backbone parameters through masking, achieving instant adaptation to diverse requests while avoiding costly retraining. Experiments on multiple large-scale benchmark datasets show that CRAMER outperforms four state-of-the-art request-aware baselines across multiple recommendation metrics while achieving minimal overhead. Moreover, the proposed framework exhibits enhanced controllability and cross-domain adaptability, establishing a new paradigm for request-aware sequential recommendation.

Deep Learning · Large Language Models

Jinyuan Li, Chengsong Huang, Langlin Huang, Shaoyang Xu, Haolin Liu, Wenxuan Zhang, Jiaxin Huang

Multimodal Process Reward Models (MPRMs) are central to step-level supervision for visual reasoning in MLLMs. Training MPRMs typically requires large-scale Monte Carlo (MC)-annotated corpora, incurring substantial training cost. This paper studies the data efficiency for MPRM training. Our preliminary experiments reveal that MPRM training quickly saturates under random subsampling of the training data, indicating substantial redundancy within existing MC-annotated corpora. To explain this, we formalize a theoretical framework and reveal that informative gradient updates depend on two factors: label mixtures of positive/negative steps and label reliability (average MC scores of positive steps). Guided by these insights, we propose the Balanced-Information Score (BIS), which prioritizes both mixture and reliability based on existing MC signals at the rollout level, without incurring any additional cost. Across two backbones (InternVL2.5-8B and Qwen2.5-VL-7B) on VisualProcessBench, BIS-selected subsets consistently match and even surpass the full-data performance at small fractions. Notably, the BIS subset reaches full-data performance using only 10% of the training data, improving over random subsampling by a relative 4.1%.

Theory · Game Theory

Chris Hays, Rachel Li, Bailey Flanigan, Manish Raghavan

AI arenas, which rank models from pairwise preferences of users, are an industry-standard evaluation mechanism for generative models. In a recent paper, Singh et al. (2025) demonstrate that widely-used mechanisms are not clone-robust: In particular, they submitted multiple copies of the same model and showed that the higher-ranked copy was several positions above the lower-ranked one. In this paper, we begin by showing, both theoretically and in simulations calibrated to data from LMArena, that producers can benefit substantially from submitting clones. We then propose a new mechanism for ranking models based on pairwise comparisons, called You-Rank-We-Rank (YRWR). It uses producers’ rankings over their own models to correct statistical estimates of model quality. We prove that this mechanism is approximately clone-robust, in the sense that a producer cannot gain much utility by doing anything other than submitting each of their unique models exactly once. Moreover, to the extent that model producers are able to correctly rank their own models, YRWR improves overall ranking accuracy. We validate our theory with further semisynthetic experiments.

Deep Learning · Foundation Models

Vanya Cohen, Ray Mooney

Entity state tracking is a necessary component of world modeling that requires maintaining coherent representations of entities over time. Previous work has benchmarked entity tracking performance in purely text-based tasks. We introduce MET-Bench, a multimodal entity tracking benchmark designed to evaluate vision-language models' ability to track entity states across modalities. Using two structured domains, we assess how effectively current models integrate textual and image-based state updates. Our findings reveal a significant performance gap between text-based and image-based entity tracking. We empirically show this discrepancy primarily stems from deficits in visual reasoning rather than perception. We further show that explicit text-based reasoning strategies improve performance, yet limitations remain in long-horizon multimodal tasks. We develop a reinforcement learning method to improve performance on MET-Bench. Applying our method to open-source VLMs achieves competitive performance with advanced closed models. Our results highlight the need for improved multimodal representations and reasoning techniques to bridge the gap between textual and visual entity tracking.

Deep Learning · Large Language Models

Yudi Zhang, Meng Fang, Zhenfang Chen, Mykola Pechenizkiy

Large Language Models (LLMs) have recently emerged as powerful controllers for interactive agents in complex environments, yet training them to perform reliable long-horizon decision making remains a fundamental challenge. A key difficulty lies in the sparsity and delay of supervision: agents often receive feedback only at episode termination, leading to severe credit assignment issues. In this work, we propose a self-evolving framework for LLM agents that unifies automatic process-reward labeling and in-distribution policy learning within a principled offline reinforcement learning paradigm. Our method learns an in-distribution critic from a hybrid offline dataset that combines expert demonstrations with agent-generated trajectories, stabilizing Bellman backups in sparse-reward settings via a weighted Implicit Q-Learning objective. The learned value function is then used to derive step-wise process rewards through advantage estimation, enabling dense and reliable supervision without environment backtracking or human annotation. Leveraging these signals, we perform behavior-proximal policy optimization that evolves the agent while remaining strictly within the data support, allowing iterative self-improvement without exacerbating distribution shift. We evaluate our method on long-horizon interactive benchmarks, including AlfWorld, WebShop, and ScienceWorld, where it consistently outperforms strong baselines in sample efficiency, robustness, and overall task performance. Our results demonstrate that stable self-evolution of LLM agents is achievable by grounding process-level supervision and policy improvement within a shared in-distribution learning loop.

Probabilistic Methods · Monte Carlo and Sampling Methods

Youguang Chen, George Biros

Independent Metropolis–Hastings (IMH) algorithms are widely used in Bayesian inference, but their efficiency deteriorates when proposal distributions are constructed from inaccurate or approximate models. We introduce Proximal-IMH, an IMH method that enhances proposal distributions through a proximal posterior correction. Given an approximate posterior sample, each proposal is generated by minimizing a quadratically regularized surrogate objective, producing a local correction that balances fidelity to the exact model with stability around the approximate state. We analyze the resulting proposals from an optimization and probabilistic perspective, showing how the proximal correction improves alignment between approximate and exact posteriors and leads to improved acceptance and mixing behavior. The proposed framework applies to both linear and nonlinear forward operators, and is particularly well suited to Bayesian inverse problems where exact posterior sampling is computationally prohibitive. Numerical experiments on inverse problems with approximate forward models, including nonlinear operators, demonstrate that Proximal-IMH consistently outperforms existing IMH variants while retaining their simplicity and scalability.

Reinforcement Learning · Deep RL

Daegyeong Roh, Juho Bae, Han-Lim Choi

Many visual reinforcement learning (RL) algorithms learn representations by matching latent distances to a behavioral distance induced by reward and transition similarity. In practice, the choice of the latent distance can strongly affect performance: using a fixed, pre-specified global norms (e.g., $\ell_p$ norms or other hand-designed metrics) may be overly restrictive to capture the behavioral distance. In contrast, unconstrained pairwise distances may admit degenerate solutions that drive the metric loss down without improving the representation. To address this gap, we introduce *PAMD: Pairwise Adaptive Mahalanobis Distance*, which parameterizes a positive-definite, pair-conditioned metric for measuring latent state similarity. PAMD is a simple plug-in for existing bisimulation-based methods, offering a more expressive yet structured alternative to fixed, pre-specified latent distances. We empirically validate our method on visual MuJoCo continuous-control tasks, where final performance of several recent bisimulation-based RL algorithms is substantially improved when equipped with the distance we propose.

Deep Learning · Large Language Models

Jonathan Su

Cross-layer reuse of early attention projections can improve optimization and data efficiency, but it creates a structural conflict: the first layer must simultaneously act as a stable, reusable anchor for all deeper layers and as an effective computational block. We demonstrate that this tension constrains the performance of internal-anchor designs. We propose ExoFormer, which resolves the conflict by learning exogenous anchor projections outside the sequential layer stack. We introduce a unified normalized mixing framework that mixes queries, keys, values, and gate logits using learnable coefficients (exploring coefficient granularities: elementwise, headwise, and scalar), and we show that normalizing anchor sources is key to stable reuse. ExoFormer variants consistently outperform their internal-anchor counterparts, and the dynamic variant yields 1.5x downstream accuracy points while matching validation loss using 1.5x fewer tokens than Gated Attention. We explain this efficacy via an Offloading Hypothesis: external anchors preserve essential token identity, allowing layers to specialize exclusively in feature transformation. We release code and models to facilitate future research.

Deep Learning · Large Language Models

Mohammad Albinhassan, Pranava Madhyastha, Alessandra Russo

Ensuring both syntactic and semantic correctness in Large Language Model (LLM) outputs remains a significant challenge, despite being critical for real-world deployment. In this paper, we introduce $\texttt{SEM-CTRL}$, a unified approach that allows for enforcing rich context-sensitive constraints, and task and instance specific semantics directly on the LLM decoder. Our approach integrates token-level MCTS which is guided by specific syntactic and semantic constraints. The constraints over desired outputs are expressed using Answer Set Grammars, which is a logic-based formalism that generalizes context sensitive grammars while incorporating background knowledge to represent task-specific semantics. We show that our approach helps guarantee valid completions for any off-the-shelf LLM without the need for fine-tuning. We evaluate $\texttt{SEM-CTRL}$ on a range of tasks, including synthetic grammar synthesis, combinatorial reasoning, JSON parsing, and planning. Our experimental results demonstrate that $\texttt{SEM-CTRL}$ allows even small pre-trained LLMs to efficiently outperform larger variants and state-of-the-art reasoning models (e.g., $\text{\textit{o4-mini}}$) while simultaneously guaranteeing semantic validity.

Deep Learning · Large Language Models

Jiangrui Zhao, Xiaoting Du

Large Language Models demonstrate remarkable syntactic fluency, yet the optimization dynamics governing their acquisition of deep semantic dependencies remain poorly understood. We propose a mechanistic framework that models this learning process as a competition between Surface Statistics and Deep Semantics. Our theoretical analysis identifies a ``Gradient Starvation" phenomenon where the error signals for sparse semantic dependencies are actively suppressed during early optimization. This suppression impedes the learning of structural reasoning and causes its emergence to manifest as a sudden phase transition. Furthermore, this framework offers a mechanistic basis for the effectiveness of Chain-of-Thought (CoT) strategies. By externalizing intermediate reasoning steps into concrete tokens, CoT effectively bypasses the suppression regime inherent to implicit reasoning. We validate these findings across scales ranging from toy transformers to production models (Llama-3.1-8B, Qwen2.5-Coder-7B). Finally, guided by this theory, we propose a topology-aligned contrastive objective that explicitly rectifies the gradient geometry. Experiments on variable binding tasks demonstrate that our method achieves an improvement that is over 2× larger than that obtained via standard cross-entropy fine-tuning.

Deep Learning · Graph Neural Networks

Geon Lee, Sunwoo Kim, Kyungho Kim, Kijung Shin

Graph collaborative filtering (GCF) is a dominant paradigm in recommender systems, where contrastive learning (CL) objectives such as the Sampled Softmax (SSM) loss are widely used for optimization. However, it remains unclear how CL interacts with the prediction mechanism of GCF. By unfolding the prediction mechanism of GCF, we show that the user-item prediction score is computed by aggregating learnable weights over a large number of neighbor pairs formed by the multi-hop neighbors of the user and the item. This analysis implies that effective optimization critically depends on which neighbor pairs are upweighted during training. Empirically, we find that effective recommendation is achievable by selectively upweighting only a small subset of neighbor pairs whose constituent neighbors are structurally similar to the target user and item, and that the effect of such selective upweighting varies across different neighbor pair types. Based on these findings, we analyze SSM and identify key limitations in its neighbor pair weight update dynamics. To address these limitations, we propose NT-SSM, an effective and principled CL objective that induces type-aware neighbor pair weight update dynamics. Experiments demonstrate consistent performance improvements over SSM across multiple datasets and GCF models.

Applications · Health / Medicine

Jieun Sung, Wankyu Kim

Single-cell foundation models trained on millions of cells can learn gene expression patterns across diverse contexts. However, for predicting genetic perturbation effects they often underperform simple regression models. We hypothesize two potential limitations: targets defined on dropout-prone absolute expression, and pretraining focused on reconstructing absolute expression within cells, which captures static co-expression patterns but may not encode how genes co-regulate in response to expression changes. We introduce $\textbf{scDEBART}$, a foundation model pretrained to predict log fold-changes (logFC) conditioned on basal expression, thereby learning how gene sets co-vary across basal states at scale. To obtain reliable estimates of expression change under technical sparsity, we compute logFC from scVI-denoised expression and restrict pretraining to genes with robust detection. Pretrained on 6.28 million expression-change profiles from 66.6 million human cells and fine-tuned on five Perturb-seq datasets, scDEBART achieves mean enrichment factor (EF) of 11.96, 4--7$\times$ higher than scGPT and GEARS (mean EF 1.74--2.99), and 42.8\% top-1 accuracy for reverse perturbation identification compared to near-zero accuracy for prior models. In cross-modal transfer to drug perturbations (SCIPLEX), the model shows dose-dependent enrichment (EF 2.03--4.31), suggesting partial transfer of learned regulatory patterns across modalities. Overall, these results indicate that large-scale pretraining on scVI-stabilized expression-change profiles provides a useful inductive bias for perturbation prediction.

Optimization · Discrete and Combinatorial Optimization

Aravind Srinivasan, Arushi Srinivasan, Jiayi Wu

We study the \maxecc\ problem, where given an edge-colored hypergraph with $k$ colors and edge size $r$, we seek to color the vertices of the graph in order to maximize the number of satisfied edges (edges having the same color as their extremities): this is an effective mechanism for clustering (coloring) objects based on their multi-way interactions with one another in a system, providing significant applications in machine learning, clustering, and data mining. We exponentially improve upon the approximation ratio of an existing algorithm, by Crane et al. present in ICML 2025, to $\frac{1}{r+1}$, present another novel dependent-rounding algorithm with an approximation ratio of $1/ \lceil \frac{k}{2}\rceil$, and modify the initial algorithm via analytical scaling techniques in order to achieve an approximation factor of $(1-e^{-r})/r$. We then apply our scaling algorithm to graph \maxecc\ and improve the best-known approximation factor for all hypergraphs: in particular, our algorithm provides an approximation factor of $0.43$ as opposed to the previously-known $0.38$ factor for graphs.

Deep Learning · Self-Supervised Learning

Heejeong Nam, Quentin Le Lidec, Lucas Maes, Yann LeCun, Randall Balestriero

World models require robust relational understanding to support prediction, reasoning, and control. While object-centric representations provide a useful abstraction, they are not sufficient to capture interaction-dependent dynamics. We therefore propose C-JEPA, a simple and flexible object-centric world model that extends masked joint embedding prediction from image patches to object-centric representations. By applying object-level masking that requires an object’s state to be inferred from other objects, C-JEPA induces latent interventions with counterfactual-like effects and prevents shortcut solutions, making interaction reasoning essential. Empirically, C-JEPA leads to consistent gains in visual question answering, with an absolute improvement of about 20\% in counterfactual reasoning over the same architecture without object-level masking. On agent control tasks, C-JEPA enables substantially more efficient planning by using only 1\% of the total latent input features required by patch-based world models, while achieving comparable performance. Finally, we provide a formal analysis demonstrating that object-level masking induces a causal inductive bias via latent interventions. Code will be available at *anonymous*.

Ritik Mishra, Vanshika Gupta, M. Sajid, M. Tanveer

Large Multimodal Models (LMMs) integrate unimodal encoders with Large Language Models (LLMs) to execute complex multimodal tasks. Despite progress in the field, understanding the internal representations of these models through interpretable logic remains an open problem. To address this, we present a framework utilizing a Human-Inspired (Neuro-fuzzy) approach for learning token representations. In this method, we leverage fuzzy rules to compute activation firing strengths, which are subsequently defuzzified to extract distinct concepts. This mechanism allows for the interpretation of learned representations directly through explicit logic. Consequently, we derive "multimodal concepts" that are both semantically coherent and interpretable. We validate our approach through rigorous qualitative and quantitative experiments, demonstrating the utility of these concepts in interpreting test samples. Additionally, we evaluate the disentanglement of the learned concepts and the efficacy of their grounding in both visual and textual domains.

Probabilistic Methods · Monte Carlo and Sampling Methods

Krzysztof Choromanski, Kumar Avinava Dubey, Arijit Sehanobish, Isaac Reid

We propose *refined GRFs* (GRFs++), a new class of *Graph Random Features* (GRFs) for efficient and accurate computations involving kernels defined on the nodes of a graph. GRFs++ resolve some of the long-standing limitations of regular GRFs, including difficulty modeling relationships between more distant nodes. They reduce dependence on sampling long graph random walks via a novel *walk-stitching* technique, concatenating several shorter walks without breaking unbiasedness. By applying these techniques, GRFs++ inherit the approximation quality provided by longer walks but with greater efficiency, trading sequential inefficient sampling of a long walk for parallel computation of short walks and matrix-matrix multiplication. Furthermore, GRFs++ extend the simplistic GRFs walk termination mechanism (Bernoulli schemes with fixed halting probabilities) to a broader class of strategies, applying general distributions on the walks' lengths. This improves approximation accuracy of graph kernels, without incurring extra computational cost. We provide empirical evaluations to showcase our claims and complement our results with theoretical analysis.