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General Machine Learning · Methodology

Yuqing Zhang, Changli Zhou, Binghuang Huang, Hui Tian

Data heterogeneity is a fundamental challenge in Federated Learning (FL), where induced model drift often results in "negative gains" for global models on data-abundant clients, with performance falling below that of local training. To address this issue, we propose FedGain, a novel framework that optimizes collaborative client clustering to mitigate the negative gain. We are the first to develop a modified Scaling Law to quantify the "reduction" in data utility caused by heterogeneity and define Effective Federated Capacity to align clients with the highest potential collaboration gains. Extensive experiments demonstrate that our modified SL strictly adheres to the power-law learning discipline in non-IID scenarios. FedGain effectively suppresses negative gains to a negligible level across various FL algorithms and outperforms other Clustered FL methods.

General Machine Learning · Methodology

Daisuke Yamada, Qijun Zhang, Travis Pence, Barbara Bendlin, Federico Rey, Vikas Singh

Compositional data---vectors encoding relative proportions---arise across scientific domains, including ecology, geochemistry, and genomics. The features in these data often come with known hierarchical structure (e.g., taxonomies, phylogenies, ontologies), yet existing methods either ignore this structure, discard the intrinsic Aitchison geometry, require assumptions such as binary trees, or yield incomplete coordinate systems. We describe *PolyILR*, a canonical orthonormal decomposition of the Aitchison tangent space aligned with any tree topology. Our construction defines a weighted local geometry at each internal node capturing full branching structure, then lifts these to a global orthonormal basis where every coordinate corresponds to a specific tree location. On microbiome and single-cell benchmarks, PolyILR yields stable, interpretable features and enables inference at multiscale tree resolution. We also establish a novel theoretical connection to softmax classifiers, suggesting possible applications to probabilistic modeling.

General Machine Learning · Methodology

Hanlin Zhang, Jikai Jin, Vasilis Syrgkanis, Sham Kakade

For deploying foundation models, practitioners increasingly need prescriptive scaling laws: given a pre-training compute budget, what downstream accuracy is attainable with contemporary post-training practice, and how stable is that mapping as the field evolves? Using large-scale observational evaluations with 5k observational and 2k newly sampled data on model performance, we estimate capability boundaries—high conditional quantiles of benchmark scores as a function of log pre-training FLOPs, via smoothed quantile regression with a monotone, saturating sigmoid parameterization. We validate the temporal reliability by fitting on earlier model generations and evaluating on later releases. Across various tasks, the estimated boundaries are mostly stable, with the exception of math reasoning that exhibits a consistently advancing boundary over time. We then extend our approach to analyze task-dependent saturation and to probe contamination-related shifts on math reasoning tasks. Finally, we introduce an efficient algorithm that recovers near-full-data frontiers using roughly 20% of evaluation budget. Together, our work releases the Proteus-2k, the latest model performance evaluation dataset, and introduces a practical methodology for translating compute budgets into reliable performance expectations and for monitoring when capability boundaries move.

Theory · Game Theory

Kira Goldner, Divyarthi Mohan, Thodoris Tsilivis

We study consumer utility maximization in an online random-order model where strategic agents arrive sequentially. To circumvent strong impossibility results for utility maximization, we turn to the framework of learning-augmented mechanism design. Crucially, we show that the types of predictions commonly used in learning-augmented mechanism design (such as predictions of agent values or the optimal value) are not useful for utility maximization, where payments are directly at odds with the objective. Instead, we identify that a qualitatively different kind of prediction suffices: the identity of the highest-valued agent. First, we provide a deterministic truthful mechanism for our online setting by adapting offline randomized techniques. Then, we augment our mechanism with predictions. When the predictions are correct, we achieve a constant approximation to the optimal solution under full information (consistency), and even when predictions are arbitrarily bad, we guarantee a constant approximation to the best implementable solution (robustness).

General Machine Learning · Data

Emmanuel J Candes, Andrew Ilyas, Tijana Zrnic

Obtaining high-quality labeled datasets is often costly, requiring either human annotation or expensive experiments. In theory, powerful pre-trained AI models provide an opportunity to automatically label datasets and save costs. Unfortunately, these models provide no guarantees on their accuracy, making wholesale replacement of manual labeling impractical. In this work, we propose a method for leveraging pre-trained AI models to curate cost-effective and high-quality datasets. In particular, our approach results in probably approximately correct labels: with high probability, the overall labeling error is small. Our method is nonasymptotically valid under minimal assumptions on the dataset or the AI model being studied, and thus enables rigorous yet efficient dataset curation using modern AI models. We demonstrate the benefits of the methodology through text annotation with large language models, image labeling with pre-trained vision models, and protein folding analysis with AlphaFold.

Theory · Game Theory

Lingxiao Huang, Nisheeth K. Vishnoi, Wenyang Xiao

As AI systems enter institutional workflows, workers must decide whether to delegate task execution to AI and how much effort to invest in verifying AI outputs, while institutions evaluate workers using outcome-based standards that may misalign with workers’ private costs. We model delegation and verification as the solution to a rational worker’s optimization problem, and define worker quality by evaluating an institution-centered utility (distinct from the worker’s objective) at the resulting optimal action. We formally characterize optimal worker workflows and show that AI induces *phase transitions*, where arbitrarily small differences in verification ability lead to sharply different behaviors. As a result, AI can amplify workers with strong verification reliability while degrading institutional worker quality for others who rationally over-delegate and reduce oversight, even when baseline task success improves and no behavioral biases are present. These results identify a structural mechanism by which AI reshapes institutional worker quality and amplifies quality disparities between workers with different verification reliability.

Theory · Game Theory

Ziyuan Huang, Lina Alkarmi, Mingyan Liu

Strategic classification studies the problem where self-interested individuals or agents manipulate their response to obtain favorable decision outcomes made by classifiers, typically turning to dishonest actions when they are less costly than genuine efforts. While existing studies on sequential strategic classification primarily focus on optimizing dynamic classifier weights, we depart from these weight-centric approaches by analyzing the design of classifier thresholds and difficulty progression within a multi-level promotion-relegation framework. Our model captures the critical inter-temporal incentives driven by an agent's farsightedness, skill retention, and a "leg-up" effect where qualification and attainment can be self-reinforcing. We characterize the agent’s optimal long-term strategy and demonstrate that a principal can design a sequence of thresholds to effectively incentivize honest effort. Crucially, we prove that under mild conditions, this mechanism enables agents to reach arbitrarily high levels solely through genuine improvement efforts.

General Machine Learning · Evaluation

Tejas Agrawal, Vu Le, Sumit Gulwani, Gust Verbruggen

Predictive code completion greatly accelerates how quickly developers work. In spreadsheets, despite being much more common, such auto-completion features are virtually non-existent. To address this gap, we introduce a benchmark for systems that observe a sequence of user actions in a spreadsheet and predict future actions. Two challenges are (1) the absence of edit histories in public spreadsheet corpora and (2) the complex space of spreadsheet actions (spatial, temporal, composite). To address (1) we symbolically generate action sequences using parametrized heuristics and refine them (LLM + human) to create 58 sequences consisting of 13K actions from publicly available spreadsheets. To address (2) we propose an online evaluation that expects a prediction after each user action, accepts or rejects that prediction, updates the future actions upon acceptance, and repeats this until the target spreadsheet is obtained. We use LMs as baseline predictive systems and analyze different properties that our benchmark teaches us, including but not limited to: properties of saved actions and false positives, efficiency, effect of user profiles, effect of triggers, effect of context, and effect of prediction length.

Theory · Deep Learning

Sejun Park, Yeachan Park, Geonho Hwang

Theoretical studies show that for any differentiable function on a compact domain, there exists a neural network that approximates both the function values and gradients. However, such a result cannot be used in practice since it assumes real parameters and exact internal operations. In contrast, real implementations only use a finite subset of reals and machine operations with round-off errors. In this work, we investigate whether a similar result holds for neural networks under floating-point arithmetic, when the gradient with respect to the input is computed by the automatic differentiation algorithm $D^\mathtt{AD}$. We first show that given a floating-point function $\phi$ (e.g., a loss function), arbitrary function values and gradients can be represented by a floating-point network $f$ and $D^\mathtt{AD}(\phi\circ f)$, respectively. We further extend this result: given $\phi_1,\dots,\phi_n$, $D^\mathtt{AD}(\phi_i\circ f)$ can simultaneously represent arbitrary gradients while $f$ represents the target values, under mild conditions. Our results hold for practical activation functions, e.g., ReLU, ELU, GELU, Swish, Sigmoid, and tanh.

Reinforcement Learning · Multi-agent

Joseph Fioresi, Ashmal Vayani, Parth Parag Kulkarni, Song Wang, Mubarak Shah

Agentic systems solve complex tasks by coordinating multiple agents that iteratively reason, invoke tools, and exchange intermediate results. To improve robustness and solution quality, recent approaches deploy multiple agent teams running in parallel to explore diverse reasoning trajectories. However, parallel execution comes at a significant computational cost: when different teams independently reason about similar sub-problems or execute analogous steps, they repeatedly perform substantial overlapping computation. To address these limitations, in this paper, we propose Learning to Share (LTS), a learned shared-memory mechanism for parallel agentic frameworks that enables selective cross-team information reuse while controlling context growth. LTS introduces a global memory bank accessible to all teams and a lightweight controller that decides whether intermediate agent steps should be added to memory or not. The controller is trained using stepwise reinforcement learning with usage-aware credit assignment, allowing it to identify information that is globally useful across parallel executions. Experiments on the AssistantBench and GAIA benchmarks show that LTS significantly reduces overall runtime while matching or improving task performance compared to memory-free parallel baselines, demonstrating that learned memory admission is an effective strategy for improving the efficiency of parallel agentic systems.

Theory · Deep Learning

Haodong Qin, Tatyana Sharpee

We present a general theoretical framework for analyzing how information about past inputs is encoded in recurrent networks into evolving dynamics rather than being represented as convergence to static attractors. Using dynamic mean-field theory and diffusion from physics, we derive a Fisher information diffusion operator that links network connectivity structure to the time-resolved propagation of information across interacting subpopulations. The analysis reveals that operating near criticality (spectral radius near one) is necessary but not sufficient for reliable memory in structured or non-normal recurrent networks; effective information retention requires alignment between input–output structure and stable dynamical subspaces. The theory yields principled initialization rules that balance stability and sensitivity, mitigating vanishing and exploding gradients. Experiments on the copy task and sequential MNIST show faster convergence and higher accuracy than standard random initialization. Together, these results provide both principled design guidelines for recurrent networks and new theoretical insight into how information can be preserved over time in their dynamics.

Theory · Deep Learning

Yu-Han Wu, Quentin Berthet, Gérard Biau, Claire Boyer, Romuald Elie, Pierre Marion

We identify and analyze a surprising phenomenon of $\textit{Latent}$ Diffusion Models (LDMs) where the final steps of the diffusion can $\textit{degrade}$ sample quality. In contrast to conventional arguments that justify early stopping for numerical stability, this phenomenon is intrinsic to the dimensionality reduction in LDMs. We provide a principled explanation by analyzing the interaction between latent dimension and stopping time. Under a Gaussian framework with linear autoencoders, we characterize the conditions under which early stopping is needed to minimize the distance between generated and target distributions. More precisely, we show that lower-dimensional representations benefit from earlier termination, whereas higher-dimensional latent spaces require later stopping time. We further establish that the latent dimension interplays with other hyperparameters of the problem such as constraints in the parameters of score matching. Crucially, this framework suggests that the reconstruction quality of the autoencoder alone can serve as a proxy to estimate the potential performance of the full LDM. Experiments on synthetic and real datasets illustrate these properties, underlining that early stopping can improve generative quality. Together, our results offer a theoretical foundation for understanding how the latent dimension influences the sample quality, and highlight stopping time as a key hyperparameter in LDMs.

Reinforcement Learning · Everything Else

Abhishek Vijaya Kumar, Bhaskar Kataria, Byungsoo Oh, Emaad Manzoor, Rachee Singh

In RL post-training of LLM agents, calls to ex ternal tools take several seconds or even min- utes, leaving allocated GPUs idle and inflating post-training time and cost. While many tool invocations repeat across parallel rollouts and could in principle be cached, naively caching their outputs for reuse is incorrect since tool outputs depend on the environment state induced by prior agent interactions. We present TVCACHE, a stateful tool-value cache for LLM agent post- training. TVCACHE maintains a tree of observed tool-call sequences and performs longest-prefix matching for cache lookups: a hit occurs only when the agent’s full tool history matches a previ- ously executed sequence, guaranteeing identical environment state. On three diverse workloads— terminal-based tasks, SQL generation, and video understanding—TVCACHE achieves cache hit rates of up to 70% and reduces median tool call execution time by up to 6.9×, with no degradation in post-training reward accumulation.

Theory · Deep Learning

Connall Garrod, Jonathan Keating

Low-dimensional structures appear ubiquitously in the eigenspectra of deep-learning matrices in classification networks trained in the overparameterized regime. While theoretical advances have aimed to explain this phenomenology, they typically succeed only in capturing subsets of the full behavior or rely on assumptions that cannot hold in practice. In this work, we provide an analytic explanation for the bulk–outlier structure of several canonical deep-learning matrices, including the Hessian, gradients, and weights. We achieve this using unconstrained feature models (UFMs), a now-common tool for studying the emergence of deep neural collapse (DNC). We show that DNC is the source of these low-dimensional eigenspectra: in each case, the eigenvalues and eigenvectors can be constructed from feature means, the characterizing objects of DNC. This provides a unifying analytic explanation for a wide range of spectral phenomena in deep learning and goes beyond empirical characterizations—which typically focus on eigenvalues—by providing a detailed analysis of eigenvectors. We prove that our results hold for both linear and ReLU networks and provide numerical validation in both the modeling context and standard deep-network architectures on canonical datasets.

Theory · Deep Learning

George Wang, Daniel Murfet

Mechanistic interpretability aims to understand how neural networks generalize beyond their training data by reverse-engineering their internal structures. We introduce patterning as the dual problem: given a desired form of generalization, determine what training data produces it. Our approach is based on susceptibilities, which measure how posterior expectation values of observables respond to infinitesimal shifts in the data distribution. Inverting this linear response relationship yields the data intervention that steers the model toward a target internal configuration. We demonstrate patterning in a small language model, showing that re-weighting training data along principal susceptibility directions can accelerate or delay the formation of structure, such as the induction circuit. In a synthetic parentheses balancing task where multiple algorithms achieve perfect training accuracy, we show that patterning can select which algorithm the model learns by targeting the local learning coefficient of each solution. These results establish that the same mathematical framework used to read internal structure can be inverted to write it.

Theory · Deep Learning

Magamed Taimeskhanov, Samuel Vaiter, Damien Garreau

A popular approach to post-training control of large language models (LLMs) is the steering of intermediate latent representations. Namely, identify a well-chosen direction depending on the task at hand and perturbs representations along this direction at inference time. While many propositions exist to pick this direction, considerably less is understood about how to choose the magnitude of the move, whereas its importance is clear: too little and the intended behavior does not emerge, too much and the model's performance degrades beyond repair. In this work, we propose the first theoretical analysis of steering strength. We characterize its effect on next token probability, presence of a concept, and cross-entropy, deriving precise qualitative laws governing these quantities. Our analysis reveals surprising behaviors, including non-monotonic effects of steering strength. We validate our theoretical predictions empirically on eleven language models, ranging from a small GPT architecture to modern models.

Yuan Feng, Junlin Lv, Haoyu Guo, Yukun Cao, Xike Xie, S Kevin Zhou

Large language models have revolutionized natural language processing but face significant challenges of high storage and runtime costs, due to the transformer architecture's reliance on self-attention, particularly the large KV cache for long-sequence inference. Recent efforts to reduce KV cache size by pruning less critical entries based on attention weights remain empirical and lack formal grounding. This paper presents a formal study on identifying critical KV cache entries by analyzing attention output perturbation. Our analysis reveals that, beyond attention weights, the value states within KV entries and pretrained parameter matrices are also crucial. Based on this, we propose a perturbation-constrained selection algorithm that optimizes the worst-case output perturbation to identify critical entries. We demonstrate that our algorithm is a universal, plug-and-play enhancement that incurs negligible computational overhead. When integrated with three state-of-the-art cache eviction methods on three distinct LLMs, our algorithm significantly reduces the compression loss by more than \textit{half} on average across 29 datasets from the Ruler and LongBench benchmarks. Further perturbation analysis, at both the head and layer levels, confirms the principles underlying our effectiveness. This work offers a new, formally grounded perspective to cache eviction , opening promising avenues for future research.

Jiakang Yuan, Tianshuo Peng, Yilei Jiang, Yiting Lu, Renrui Zhang, Kaituo Feng, Chaoyou Fu, Tao Chen, LEI BAI, Bo Zhang

Logical reasoning is a fundamental aspect of human intelligence and an essential capability for multimodal large language models (MLLMs). Despite the significant advancement in multimodal reasoning, existing benchmarks fail to comprehensively evaluate their reasoning abilities due to the lack of explicit categorization for logical reasoning types and an unclear understanding of reasoning. To address these issues, we introduce MME-Reasoning, a comprehensive benchmark designed to evaluate the reasoning ability of MLLMs, which covers all three types of reasoning (i.e., inductive, deductive, and abductive). We carefully curate the data to ensure that each question effectively evaluates reasoning ability rather than perceptual skills or knowledge breadth, and extend the evaluation protocols to cover the evaluation of diverse questions. Our evaluation reveals substantial limitations of SoTA MLLMs when subjected to holistic assessments of logical reasoning capabilities. Even the most advanced MLLMs show limited performance in comprehensive logical reasoning, with notable performance imbalances across reasoning types. In addition, we conducted an in-depth analysis of approaches such as ``thinking mode'' and Rule-based RL, which are commonly believed to enhance reasoning abilities. We hope the community can pay more attention to the comprehensive reasoning capabilities of MLLMs instead of only focusing on its subset.

Social Aspects · Accountability, Transparency, and Interpretability

Rebecca Salganik, Guillaume Salha-Galvan, Adelaida Afilipoaie, Gustavo Ferreira, Valdy Wiratama, Anson Kahng, Jian Kang, Heritiana Ranaivoson

Recent AI regulation has largely focused on algorithmic components such as recommender models, ranking systems, and profiling mechanisms. At the same time, cultural and digital policy agendas increasingly frame discovery as a key objective, aiming to promote exposure diversity and cultural representation. We argue that these outcomes cannot be effectively governed through algorithm-centric approaches alone. Discovery does not arise from individual algorithms in isolation, but from interactions among models, interfaces, user behavior, economic incentives, and cultural norms. We introduce the Cultural Expressions Discovery Circuit (CEDC), an interdisciplinary framework that models discovery as an emergent socio-technical process. Through this lens, we illustrate how certain regulatory approaches struggle to align with broader cultural objectives. Furthermore, we highlight how socio-technical analysis can help inform both technical research and the governance of cultural expressions in online platforms.

General Machine Learning · Unsupervised and Semi-supervised Learning

Wei Zheng, Zijie Wang, Xin Li, Bin Gong, Yuqing Sun

We address the challenge of unsupervised coreset selection for few-shot in-context learning (ICL). The goal is to select a small subset of examples under a fixed annotation budget to yield effective prompts for large language models. Existing geometry-based methods often yield coresets that suffer from a skewed distribution, due to the oversampling of peripheral examples and high local redundancy. To address these issues, we propose a process-aware framework for coreset selection. It jointly optimizes the diversity and representativeness of selected samples via a submodular objective. It ensures representativeness by selecting samples based on local density awareness, while promoting diversity by imposing a redundancy penalty relative to the evolving selected set. Thus, it performs progress-aware balancing of representativeness and diversity based on the selection context. Extensive experiments on 7 NLP datasets demonstrate that our method consistently outperforms state-of-the-art coreset selection methods in downstream ICL performance. Further analysis validates that our approach better balances diversity and representativeness throughout the selection process, while retaining the theoretical guarantees of submodular optimization.