Daily Papers

The Optical Character Recognition (OCR) task is important for evaluating Vision-Language Models (VLMs) and providing high-quality data sources for LLM training data. While state-of-the-art VLMs show improved average OCR accuracy, they still struggle with sample-level quality degradation and lack reliable automatic detection of low-quality outputs. We introduce Consensus Entropy (CE), a training-free post-inference method that quantifies OCR uncertainty by aggregating outputs from multiple VLMs. Our approach exploits a key insight: correct VLM OCR predictions converge in output space while errors diverge. We develop a lightweight multi-model framework that effectively identifies problematic samples, selects the best outputs and combines model strengths. Experiments across multiple OCR benchmarks and VLMs demonstrate that CE outperforms VLM-as-judge approaches and single-model baselines at the same cost and achieves state-of-the-art results across multiple metrics. For instance, our solution demonstrates: achieving 15.2% higher F1 scores than VLM-as-judge methods in quality verification, delivering 6.0% accuracy gains on mathematical calculation tasks, and requiring rephrasing only 7.3% of inputs while maintaining overall performance. Notably, the entire process requires neither training nor supervision while maintaining plug-and-play functionality throughout.

Large Language Models (LLMs) often produce inconsistent answers when faced with different phrasings of the same prompt. In this paper, we propose Flip-Flop Consistency (F^2C), an unsupervised training method that improves robustness to such perturbations. F^2C is composed of two key components. The first, Consensus Cross-Entropy (CCE), uses a majority vote across prompt variations to create a hard pseudo-label. The second is a representation alignment loss that pulls lower-confidence and non-majority predictors toward the consensus established by high-confidence, majority-voting variations. We evaluate our method on 11 datasets spanning four NLP tasks, with 4-15 prompt variations per dataset. On average, F^2C raises observed agreement by 11.62%, improves mean F_1 by 8.94%, and reduces performance variance across formats by 3.29%. In out-of-domain evaluations, F^2C generalizes effectively, increasing F_1 and agreement while decreasing variance across most source-target pairs. Finally, when trained on only a subset of prompt perturbations and evaluated on held-out formats, F^2C consistently improves both performance and agreement while reducing variance. These findings highlight F^2C as an effective unsupervised method for enhancing LLM consistency, performance, and generalization under prompt perturbations. Code is available at https://github.com/ParsaHejabi/Flip-Flop-Consistency-Unsupervised-Training-for-Robustness-to-Prompt-Perturbations-in-LLMs.

Large language model (LLM) simulations of human behavior have the potential to revolutionize the social and behavioral sciences, if and only if they faithfully reflect real human behaviors. Current evaluations are fragmented, based on bespoke tasks and metrics, creating a patchwork of incomparable results. To address this, we introduce SimBench, the first large-scale, standardized benchmark for a robust, reproducible science of LLM simulation. By unifying 20 diverse datasets covering tasks from moral decision-making to economic choice across a large global participant pool, SimBench provides the necessary foundation to ask fundamental questions about when, how, and why LLM simulations succeed or fail. We show that, while even the best LLMs today have limited simulation ability (score: 40.80/100), performance scales log-linearly with model size. Simulation performance is not improved by increased inference-time compute. We demonstrate an alignment-simulation trade-off: instruction-tuning improves performance on low-entropy (consensus) questions but degrades it on high-entropy (diverse) ones. Models particularly struggle when simulating specific demographic groups. Finally, we demonstrate that simulation ability correlates most strongly with deep, knowledge-intensive reasoning (MMLU-Pro, r=0.939). By making progress measurable, we aim to accelerate the development of more faithful LLM simulators.

Test-Time Reinforcement Learning (TTRL) enables Large Language Models (LLMs) to enhance reasoning capabilities on unlabeled test streams by deriving pseudo-rewards from majority voting consensus. However, existing TTRL methods rely exclusively on positive pseudo-labeling strategies. Such reliance becomes vulnerable under challenging scenarios where answer distributions are highly dispersed, resulting in weak consensus that inadvertently reinforces incorrect trajectories as supervision signals. In this paper, we propose SCRL (Selective-Complementary Reinforcement Learning), a robust test-time reinforcement learning framework that effectively mitigates label noise amplification. SCRL develops Selective Positive Pseudo-Labeling, which enforces strict consensus criteria to filter unreliable majorities. Complementarily, SCRL introduces Entropy-Gated Negative Pseudo-Labeling, the first negative supervision mechanism in TTRL, to reliably prune incorrect trajectories based on generation uncertainty. Extensive experiments on multiple reasoning benchmarks demonstrate that SCRL achieves substantial improvements over baselines, while maintaining robust generalization and training stability under constrained rollout budgets. Our code is available at https://github.com/Jasper-Yan/SCRL.

Medical Vision-Language Models (VLMs) hold immense promise for complex clinical tasks, but their reasoning capabilities are often constrained by text-only paradigms that fail to ground inferences in visual evidence. This limitation not only curtails performance on tasks requiring fine-grained visual analysis but also introduces risks of visual hallucination in safety-critical applications. Thus, we introduce MedVR, a novel reinforcement learning framework that enables annotation-free visual reasoning for medical VLMs. Its core innovation lies in two synergistic mechanisms: Entropy-guided Visual Regrounding (EVR) uses model uncertainty to direct exploration, while Consensus-based Credit Assignment (CCA) distills pseudo-supervision from rollout agreement. Without any human annotations for intermediate steps, MedVR achieves state-of-the-art performance on diverse public medical VQA benchmarks, significantly outperforming existing models. By learning to reason directly with visual evidence, MedVR promotes the robustness and transparency essential for accelerating the clinical deployment of medical AI.

The shift from monolithic LLMs to distributed multi-agent architectures demands new frameworks for verifying and securing autonomous coordination. Unlike traditional multi-agent systems focused on cooperative state alignment, modern LLM patterns: multi-agent debate, constitutional oversight, helper-critic loops-rely on adversarial critique for error correction and reasoning refinement. Since LLMs are dynamical systems whose latent states are imperfectly observable from verbalized outputs, securing these networks requires understanding both macroscopic topology and microscopic agent observability. This paper establishes a rigorous graph-theoretic framework for analyzing consensus in signed, directed interaction networks, bridging graph theory and LLM reasoning by formally mapping Transformer cross-entropy log-odds to the signed Laplacian. We characterize agreement stability through structural balance theory, showing how unbalanced critique cycles produce logical frustration and persistent reasoning oscillations, and prove that unobservable latent states from hidden system prompts act as topological Trojan horses that destabilize cooperative consensus. To resolve unobservable deadlocks, we restrict interaction topologies to chordal graphs and apply matrix decomposition with Gram-Schmidt orthogonalization, proving that rank-one spectral edge perturbations deterministically break expertise symmetry by shifting eigenvalues into the stable left-half plane. Core contributions include consensus theorems, polynomial-time Perfect Elimination Ordering verification algorithms, and large-scale empirical validation on clustered ensembles of LLaMA-3, Mistral, and Gemma agents.

This paper introduces the concept of {mutual consensus} as a novel non-compensatory consensus measure that accounts for the maximum disparity among opinions to ensure robust consensus evaluation. Incorporating this concept, several new Minimum Cost Consensus (MCC) models are proposed, and their properties are analyzed. To show their applicability, these mutual consensus-based MCC models are then considered in the context of the {OWA-MCC} model, which employs Ordered Weighted Averaging (OWA) operators for preference aggregation. Concretely, we include a linearized formulation under symmetry conditions as well as examples of the non-convexity of the feasible region in the general case. Finally, mutual consensus is utilized to obtain approximate solutions for the OWA-MCC model, demonstrating its practical effectiveness and advancing the theoretical and applied dimensions of consensus modeling in group decision-making.

Can classical consensus models predict the group behavior of large language models (LLMs)? We examine multi-round interactions among LLM agents through the DeGroot framework, where agents exchange text-based messages over diverse communication graphs. To track opinion evolution, we map each message to an opinion score via sentiment analysis. We find that agents typically reach consensus and the disagreement between the agents decays exponentially. However, the limiting opinion departs from DeGroot's network-centrality-weighted forecast. The consensus between LLM agents turns out to be largely insensitive to initial conditions and instead depends strongly on the discussion subject and inherent biases. Nevertheless, transient dynamics align with classical graph theory and the convergence rate of opinions is closely related to the second-largest eigenvalue of the graph's combination matrix. Together, these findings can be useful for LLM-driven social-network simulations and the design of resource-efficient multi-agent LLM applications.

Collective motion in fish schools exemplifies emergent self-organization in active matter systems, yet computational tools for simulating and analyzing these dynamics remain fragmented across research groups. We present dewi-kadita, an open-source Python library implementing the three-dimensional Couzin zone-based model with comprehensive entropy diagnostics tailored for marine collective behavior research. The library introduces seven information-theoretic metrics -- school cohesion entropy, polarization entropy, depth stratification entropy, angular momentum entropy, nearest-neighbor entropy, velocity correlation entropy, and school shape entropy -- that characterize distinct organizational features inaccessible to classical order parameters. These metrics combine into an Oceanic Schooling Index (OSI) providing a single scalar measure of collective disorder. Validation across four canonical configurations (swarm, torus, dynamic parallel, highly parallel) confirms correct reproduction of known phase behaviors: the swarm maintains disorder with polarization P < 0.1 and OSI approx 0.71, while the highly parallel state achieves P = 0.998 with OSI = 0.24 and velocity correlation entropy vanishing to zero. The entropy framework successfully discriminates the torus and dynamic parallel configurations that exhibit comparable order parameter magnitudes through different organizational mechanisms. Numba just-in-time (JIT) compilation accelerates pairwise interaction calculations by 10--100times, enabling simulations of 150--250 agents over 1000--2000 time steps within five minutes on standard workstation hardware. NetCDF4 output ensures interoperability with oceanographic analysis tools. The library addresses the need for standardized, reproducible infrastructure in collective behavior modeling analogous to established molecular dynamics codes.

We introduce Minary, a computational framework designed as a candidate for the first formally provable autopoietic primitive. Minary represents interacting probabilistic events as multi-dimensional vectors and combines them via linear superposition rather than multiplicative scalar operations, thereby preserving uncertainty and enabling constructive and destructive interference in the range [-1,1]. A fixed set of ``perspectives'' evaluates ``semantic dimensions'' according to hidden competencies, and their interactions drive two discrete-time stochastic processes. We model this system as an iterated random affine map and use the theory of iterated random functions to prove that it converges in distribution to a unique stationary law; we moreover obtain an explicit closed form for the limiting expectation in terms of row, column, and global averages of the competency matrix. We then derive exact formulas for the mean and variance of the normalized consensus conditioned on the activation of a given semantic dimension, revealing how consensus depends on competency structure rather than raw input signals. Finally, we argue that Minary is organizationally closed yet operationally open in the sense of Maturana and Varela, and we discuss implications for building self-maintaining, distributed, and parallelizable computational systems that house a uniquely subjective notion of identity.

We consider decentralized optimization problems where one aims to minimize a sum of convex smooth objective functions distributed between nodes in the network. The links in the network can change from time to time. For the setting when the amount of changes is arbitrary, lower complexity bounds and corresponding optimal algorithms are known, and the consensus acceleration is not possible. However, in practice the magnitude of network changes may be limited. We derive lower communication complexity bounds for several regimes of velocity of networks changes. Moreover, we show how to obtain accelerated communication rates for a certain class of time-varying graphs using a specific consensus algorithm.

Entropy serves as a critical metric for measuring the diversity of outputs generated by large language models (LLMs), providing valuable insights into their exploration capabilities. While recent studies increasingly focus on monitoring and adjusting entropy to better balance exploration and exploitation in reinforcement fine-tuning (RFT), a principled understanding of entropy dynamics during this process is yet to be thoroughly investigated. In this paper, we establish a theoretical framework for analyzing the entropy dynamics during the RFT process, which begins with a discriminant expression that quantifies entropy change under a single logit update. This foundation enables the derivation of a first-order expression for entropy change, which can be further extended to the update formula of Group Relative Policy Optimization (GRPO). The corollaries and insights drawn from the theoretical analysis inspire the design of entropy control methods, and also offer a unified lens for interpreting various entropy-based methods in existing studies. We provide empirical evidence to support the main conclusions of our analysis and demonstrate the effectiveness of the derived entropy-discriminator clipping methods. This study yields novel insights into RFT training dynamics, providing theoretical support and practical strategies for optimizing the exploration-exploitation balance during LLM fine-tuning.

In this work we present a new method for the estimation of Mutual Information (MI) between random variables. Our approach is based on an original interpretation of the Girsanov theorem, which allows us to use score-based diffusion models to estimate the Kullback Leibler divergence between two densities as a difference between their score functions. As a by-product, our method also enables the estimation of the entropy of random variables. Armed with such building blocks, we present a general recipe to measure MI, which unfolds in two directions: one uses conditional diffusion process, whereas the other uses joint diffusion processes that allow simultaneous modelling of two random variables. Our results, which derive from a thorough experimental protocol over all the variants of our approach, indicate that our method is more accurate than the main alternatives from the literature, especially for challenging distributions. Furthermore, our methods pass MI self-consistency tests, including data processing and additivity under independence, which instead are a pain-point of existing methods.

Agentic retrieval-augmented reasoning pipelines are increasingly used to structure how large language models (LLMs) incorporate external evidence in clinical decision support. These systems iteratively retrieve curated domain knowledge and synthesize it into structured reports before answer selection. Although such pipelines can improve performance, their impact on reliability under model variability remains unclear. In real-world deployment, heterogeneous models may align, diverge, or synchronize errors in ways not captured by accuracy. We evaluated 34 LLMs on 169 expert-curated publicly available radiology questions, comparing zero-shot inference with a radiology-specific multi-step agentic retrieval condition in which all models received identical structured evidence reports derived from curated radiology knowledge. Agentic inference reduced inter-model decision dispersion (median entropy 0.48 vs. 0.13) and increased robustness of correctness across models (mean 0.74 vs. 0.81). Majority consensus also increased overall (P<0.001). Consensus strength and robust correctness remained correlated under both strategies (ho=0.88 for zero-shot; ho=0.87 for agentic), although high agreement did not guarantee correctness. Response verbosity showed no meaningful association with correctness. Among 572 incorrect outputs, 72% were associated with moderate or high clinically assessed severity, although inter-rater agreement was low (appa=0.02). Agentic retrieval therefore was associated with more concentrated decision distributions, stronger consensus, and higher cross-model robustness of correctness. These findings suggest that evaluating agentic systems through accuracy or agreement alone may not always be sufficient, and that complementary analyses of stability, cross-model robustness, and potential clinical impact are needed to characterize reliability under model variability.

In this paper we provide a novel analytical perspective on the theoretical understanding of gradient-based learning algorithms by interpreting consensus-based optimization (CBO), a recently proposed multi-particle derivative-free optimization method, as a stochastic relaxation of gradient descent. Remarkably, we observe that through communication of the particles, CBO exhibits a stochastic gradient descent (SGD)-like behavior despite solely relying on evaluations of the objective function. The fundamental value of such link between CBO and SGD lies in the fact that CBO is provably globally convergent to global minimizers for ample classes of nonsmooth and nonconvex objective functions, hence, on the one side, offering a novel explanation for the success of stochastic relaxations of gradient descent. On the other side, contrary to the conventional wisdom for which zero-order methods ought to be inefficient or not to possess generalization abilities, our results unveil an intrinsic gradient descent nature of such heuristics. This viewpoint furthermore complements previous insights into the working principles of CBO, which describe the dynamics in the mean-field limit through a nonlinear nonlocal partial differential equation that allows to alleviate complexities of the nonconvex function landscape. Our proofs leverage a completely nonsmooth analysis, which combines a novel quantitative version of the Laplace principle (log-sum-exp trick) and the minimizing movement scheme (proximal iteration). In doing so, we furnish useful and precise insights that explain how stochastic perturbations of gradient descent overcome energy barriers and reach deep levels of nonconvex functions. Instructive numerical illustrations support the provided theoretical insights.

The analysis of scientific data and complex multivariate systems requires information quantities that capture relationships among multiple random variables. Recently, new information-theoretic measures have been developed to overcome the shortcomings of classical ones, such as mutual information, that are restricted to considering pairwise interactions. Among them, the concept of information synergy and redundancy is crucial for understanding the high-order dependencies between variables. One of the most prominent and versatile measures based on this concept is O-information, which provides a clear and scalable way to quantify the synergy-redundancy balance in multivariate systems. However, its practical application is limited to simplified cases. In this work, we introduce SOmegaI, which allows for the first time to compute O-information without restrictive assumptions about the system. Our experiments validate our approach on synthetic data, and demonstrate the effectiveness of SOmegaI in the context of a real-world use case.

In complex systems, we often observe complex global behavior emerge from a collection of agents interacting with each other in their environment, with each individual agent acting only on locally available information, without knowing the full picture. Such systems have inspired development of artificial intelligence algorithms in areas such as swarm optimization and cellular automata. Motivated by the emergence of collective behavior from complex cellular systems, we build systems that feed each sensory input from the environment into distinct, but identical neural networks, each with no fixed relationship with one another. We show that these sensory networks can be trained to integrate information received locally, and through communication via an attention mechanism, can collectively produce a globally coherent policy. Moreover, the system can still perform its task even if the ordering of its inputs is randomly permuted several times during an episode. These permutation invariant systems also display useful robustness and generalization properties that are broadly applicable. Interactive demo and videos of our results: https://attentionneuron.github.io/

Autoregressive decoding in Large Language Models (LLMs) is inherently sequential, creating a latency bottleneck that scales linearly with output length. While ``Decomposition-and-Fill'' methods like Skeleton-of-Thought attempt to parallelize generation via external orchestration, they suffer from coherence drift due to the lack of cross-stream communication. In this work, we introduce the Parallel Decoder Transformer (PDT), a parameter-efficient architecture that embeds coordination primitives directly into the inference process of a frozen pre-trained model. Instead of retraining the base model, PDT injects lightweight Speculative Note Conditioning (SNC) adapters that allow parallel decoding streams to synchronize via a shared, dynamic latent space. We formulate coordination as a speculative consensus problem, where sibling streams broadcast semantic ``notes'' to a global bus, gated by a learned verification head. We validate our approach on a 50,000-step curriculum using a frozen 20B-parameter backbone. Our results demonstrate that PDT achieves effective self-correction, reaching 77.8\% precision in coverage prediction and recovering approximate serial semantics without modifying the trunk weights. This establishes PDT as a scalable, efficient alternative to full model fine-tuning for structured parallel generation.

In federated learning (FL), data heterogeneity is one key bottleneck that causes model divergence and limits performance. Addressing this, existing methods often regard data heterogeneity as an inherent property and propose to mitigate its adverse effects by correcting models. In this paper, we seek to break this inherent property by generating data to complement the original dataset to fundamentally mitigate heterogeneity level. As a novel attempt from the perspective of data, we propose federated learning with consensus-oriented generation (FedCOG). FedCOG consists of two key components at the client side: complementary data generation, which generates data extracted from the shared global model to complement the original dataset, and knowledge-distillation-based model training, which distills knowledge from global model to local model based on the generated data to mitigate over-fitting the original heterogeneous dataset. FedCOG has two critical advantages: 1) it can be a plug-and-play module to further improve the performance of most existing FL methods, and 2) it is naturally compatible with standard FL protocols such as Secure Aggregation since it makes no modification in communication process. Extensive experiments on classical and real-world FL datasets show that FedCOG consistently outperforms state-of-the-art methods.

Bitcoin constructs temporal order internally rather than synchronizing to any external clock. Empirical evidence shows that its time evolution is non-continuous, probabilistic, and self-regulated. Block discovery follows a stochastic process in which uncertainty accumulates during the search phase and collapses abruptly when a valid proof-of-work solution appears. Difficulty adjustment maintains the system near the entropy-maximizing regime and allows the network to infer the underlying global hash rate. Building on these observations, we present a unified framework in which Bitcoin time emerges from four interacting mechanisms: proof of work as a distributed entropy source, difficulty adjustment as temporal feedback, entropy collapse as discrete temporal updates, and recursive sealing through hash pointers. Together these mechanisms form a self-regulating temporal architecture that transforms distributed randomness into a coherent and irreversible global timeline, offering a generalizable foundation for autonomous timekeeping in permissionless systems.

The mechanisms behind the success of multi-view self-supervised learning (MVSSL) are not yet fully understood. Contrastive MVSSL methods have been studied through the lens of InfoNCE, a lower bound of the Mutual Information (MI). However, the relation between other MVSSL methods and MI remains unclear. We consider a different lower bound on the MI consisting of an entropy and a reconstruction term (ER), and analyze the main MVSSL families through its lens. Through this ER bound, we show that clustering-based methods such as DeepCluster and SwAV maximize the MI. We also re-interpret the mechanisms of distillation-based approaches such as BYOL and DINO, showing that they explicitly maximize the reconstruction term and implicitly encourage a stable entropy, and we confirm this empirically. We show that replacing the objectives of common MVSSL methods with this ER bound achieves competitive performance, while making them stable when training with smaller batch sizes or smaller exponential moving average (EMA) coefficients. Github repo: https://github.com/apple/ml-entropy-reconstruction.

In this paper, it is shown that if a sequence of resistance metric spaces equipped with measures converges with respect to the local Gromov-Hausdorff-vague topology, and certain non-explosion and metric-entropy conditions are satisfied, then the associated stochastic processes and their local times also converge. The metric-entropy condition can be checked by applying volume estimates of balls. Whilst similar results have been proved previously, the approach of this article is more widely applicable. Indeed, we recover various known conclusions for scaling limits of some deterministic self-similar fractal graphs, critical Galton-Watson trees, the critical Erdos-R\'enyi random graph and the configuration model (in the latter two cases, we prove for the first time the convergence of the models with respect to the resistance metric and also, for the configuration model, we overcome an error in the existing proof of local time convergence). Moreover, we derive new ones for scaling limits of uniform spanning trees and random recursive fractals. The metric-entropy condition also implies convergence of associated Gaussian processes.

State-of-the-art language generation models can degenerate when applied to open-ended generation problems such as text completion, story generation, or dialog modeling. This degeneration usually shows up in the form of incoherence, lack of vocabulary diversity, and self-repetition or copying from the context. In this paper, we postulate that ``human-like'' generations usually lie in a narrow and nearly flat entropy band, and violation of these entropy bounds correlates with degenerate behavior. Our experiments show that this stable narrow entropy zone exists across models, tasks, and domains and confirm the hypothesis that violations of this zone correlate with degeneration. We then use this insight to propose an entropy-aware decoding algorithm that respects these entropy bounds resulting in less degenerate, more contextual, and "human-like" language generation in open-ended text generation settings.

Achieving robust coordination and cooperation is a central challenge in multi-agent reinforcement learning (MARL). Uncovering the mechanisms underlying such emergent behaviors calls for a dynamical understanding of learn processes. In this work, we investigate the dynamics of actor-critic agents in stochastic games, focusing on the impact of entropy regularization. By leveraging time-scale separation, we derive the system's evolution equations, which are then formally analyzed using dynamical systems theory. We find that in the constant-sum game of Matching Pennies, the system exhibits chaotic behavior. Entropy regularization mitigates this chaos and drives the dynamics toward convergence to fair cooperation. In contrast, in the general-sum game of the Prisoner's Dilemma, the system displays multistability. Interestingly, the three stable equilibria of the system correspond to the well-known ALLC (Always Cooperate), ALLD (Always Defect), and GRIM (Grim Trigger) strategies from evolutionary game theory (EGT). Entropy regularization strengthens system resilience by enlarging the basin of attraction of the cooperative equilibrium. Our findings reveal a close link between the mechanism of direct reciprocity in EGT and how cooperation emerges in MARL, offering insights for designing more robust and collaborative multi-agent systems.

This paper aims to overcome a major obstacle in scaling RL for reasoning with LLMs, namely the collapse of policy entropy. Such phenomenon is consistently observed across vast RL runs without entropy intervention, where the policy entropy dropped sharply at the early training stage, this diminished exploratory ability is always accompanied with the saturation of policy performance. In practice, we establish a transformation equation R=-a*e^H+b between entropy H and downstream performance R. This empirical law strongly indicates that, the policy performance is traded from policy entropy, thus bottlenecked by its exhaustion, and the ceiling is fully predictable H=0, R=-a+b. Our finding necessitates entropy management for continuous exploration toward scaling compute for RL. To this end, we investigate entropy dynamics both theoretically and empirically. Our derivation highlights that, the change in policy entropy is driven by the covariance between action probability and the change in logits, which is proportional to its advantage when using Policy Gradient-like algorithms. Empirical study shows that, the values of covariance term and entropy differences matched exactly, supporting the theoretical conclusion. Moreover, the covariance term stays mostly positive throughout training, further explaining why policy entropy would decrease monotonically. Through understanding the mechanism behind entropy dynamics, we motivate to control entropy by restricting the update of high-covariance tokens. Specifically, we propose two simple yet effective techniques, namely Clip-Cov and KL-Cov, which clip and apply KL penalty to tokens with high covariances respectively. Experiments show that these methods encourage exploration, thus helping policy escape entropy collapse and achieve better downstream performance.

We introduce the Structured Knowledge Accumulation (SKA) framework, which reinterprets entropy as a dynamic, layer-wise measure of knowledge alignment in neural networks. Instead of relying on traditional gradient-based optimization, SKA defines entropy in terms of knowledge vectors and their influence on decision probabilities across multiple layers. This formulation naturally leads to the emergence of activation functions such as the sigmoid as a consequence of entropy minimization. Unlike conventional backpropagation, SKA allows each layer to optimize independently by aligning its knowledge representation with changes in decision probabilities. As a result, total network entropy decreases in a hierarchical manner, allowing knowledge structures to evolve progressively. This approach provides a scalable, biologically plausible alternative to gradient-based learning, bridging information theory and artificial intelligence while offering promising applications in resource-constrained and parallel computing environments.

In federated learning (FL), weighted aggregation of local models is conducted to generate a global model, and the aggregation weights are normalized (the sum of weights is 1) and proportional to the local data sizes. In this paper, we revisit the weighted aggregation process and gain new insights into the training dynamics of FL. First, we find that the sum of weights can be smaller than 1, causing global weight shrinking effect (analogous to weight decay) and improving generalization. We explore how the optimal shrinking factor is affected by clients' data heterogeneity and local epochs. Second, we dive into the relative aggregation weights among clients to depict the clients' importance. We develop client coherence to study the learning dynamics and find a critical point that exists. Before entering the critical point, more coherent clients play more essential roles in generalization. Based on the above insights, we propose an effective method for Federated Learning with Learnable Aggregation Weights, named as FedLAW. Extensive experiments verify that our method can improve the generalization of the global model by a large margin on different datasets and models.

As the issue of robustness in AI systems becomes vital, statistical learning techniques that are reliable even in presence of partly contaminated data have to be developed. Preference data, in the form of (complete) rankings in the simplest situations, are no exception and the demand for appropriate concepts and tools is all the more pressing given that technologies fed by or producing this type of data (e.g. search engines, recommending systems) are now massively deployed. However, the lack of vector space structure for the set of rankings (i.e. the symmetric group S_n) and the complex nature of statistics considered in ranking data analysis make the formulation of robustness objectives in this domain challenging. In this paper, we introduce notions of robustness, together with dedicated statistical methods, for Consensus Ranking the flagship problem in ranking data analysis, aiming at summarizing a probability distribution on S_n by a median ranking. Precisely, we propose specific extensions of the popular concept of breakdown point, tailored to consensus ranking, and address the related computational issues. Beyond the theoretical contributions, the relevance of the approach proposed is supported by an experimental study.

Multi-agent systems can improve reliability, yet under a fixed inference budget they often help, saturate, or even collapse. We develop a minimal and calibratable theory that predicts these regimes from three binding constraints of modern agent stacks: finite context windows, lossy inter-agent communication, and shared failures among similar agents. Each leaf agent is summarized by a compute-performance scaling exponent β; communication is captured by a message-length fidelity curve γ(m); dependence is captured by an effective shared-error correlation ρ; and a context window W imposes hard fan-in limits that make hierarchy necessary. For binary success/failure tasks with majority aggregation, we prove a sharp phase transition for deep b-ary trees with correlated inputs and lossy communication: a single scalar α_ρ (combining γ(m), ρ, and fan-in b) determines whether weak signal is amplified to a nontrivial fixed point or washed out to chance. In the amplifying regime, we derive an organization exponent s and show that budgeted synergy, i.e., outperforming the best single agent under the same total budget, occurs exactly when s>β, yielding closed-form compute allocation rules and explicit budget thresholds. We further characterize saturation via a mixing depth and provide a conservative clipped predictor that remains accurate across growth and saturation. A continuous-performance warm-up gives closed-form risks for star, chain, and tree organizations, making correlation- and communication-induced floors explicit and exposing the core design trade-offs in a smooth setting. Finally, we validate the predicted phase boundaries in controlled synthetic simulations and show how the same mechanisms explain the dominant bottlenecks reported in recent large-scale matched-budget studies of LLM agent-system scaling.

RL training of multi-turn LLM agents is inherently unstable, and reasoning quality directly determines task performance. Entropy is widely used to track reasoning stability. However, entropy only measures diversity within the same input, and cannot tell whether reasoning actually responds to different inputs. In RAGEN-2, we find that even with stable entropy, models can rely on fixed templates that look diverse but are input-agnostic. We call this template collapse, a failure mode invisible to entropy and all existing metrics. To diagnose this failure, we decompose reasoning quality into within-input diversity (Entropy) and cross-input distinguishability (Mutual Information, MI), and introduce a family of mutual information proxies for online diagnosis. Across diverse tasks, mutual information correlates with final performance much more strongly than entropy, making it a more reliable proxy for reasoning quality. We further explain template collapse with a signal-to-noise ratio (SNR) mechanism. Low reward variance weakens task gradients, letting regularization terms dominate and erase cross-input reasoning differences. To address this, we propose SNR-Aware Filtering to select high-signal prompts per iteration using reward variance as a lightweight proxy. Across planning, math reasoning, web navigation, and code execution, the method consistently improves both input dependence and task performance.

While Reinforcement Learning with Verifiable Rewards (RLVR) can enhance LLM reasoning, its training process poses a critical risk: entropy collapse. This phenomenon is a rapid loss of policy diversity, stemming from the exploration-exploitation imbalance and leading to a lack of generalization. Recent entropy-intervention methods aim to prevent entropy collapse, yet their underlying mechanisms remain unclear. In this paper, we conduct a quantitative analysis to reveal token-level entropy changes and how existing entropy intervention methods help avoid entropy collapse. Our findings point out a fundamental limitation of existing methods: they attempt to control entropy dynamics indirectly. By only affecting related factors, such as the advantage signal and generation probability, their effectiveness is inherently limited and could potentially fail. To address this limitation, we introduce an entropy-change-aware reweighting scheme, namely Stabilizing Token-level Entropy-changE via Reweighting (STEER), that adaptively stabilizes entropy dynamics through fine-grained token-level adjustments. Our approach mitigates over-exploitation while fostering robust exploration. Extensive experiments demonstrate that STEER significantly mitigates entropy collapse, stabilizes entropy dynamics, and achieves stronger downstream performance across various mathematical reasoning benchmarks \footnote{Our code is available at https://github.com/zz-haooo/STEER.

Present-day federated learning (FL) systems deployed over edge networks consists of a large number of workers with high degrees of heterogeneity in data and/or computing capabilities, which call for flexible worker participation in terms of timing, effort, data heterogeneity, etc. To satisfy the need for flexible worker participation, we consider a new FL paradigm called "Anarchic Federated Learning" (AFL) in this paper. In stark contrast to conventional FL models, each worker in AFL has the freedom to choose i) when to participate in FL, and ii) the number of local steps to perform in each round based on its current situation (e.g., battery level, communication channels, privacy concerns). However, such chaotic worker behaviors in AFL impose many new open questions in algorithm design. In particular, it remains unclear whether one could develop convergent AFL training algorithms, and if yes, under what conditions and how fast the achievable convergence speed is. Toward this end, we propose two Anarchic Federated Averaging (AFA) algorithms with two-sided learning rates for both cross-device and cross-silo settings, which are named AFA-CD and AFA-CS, respectively. Somewhat surprisingly, we show that, under mild anarchic assumptions, both AFL algorithms achieve the best known convergence rate as the state-of-the-art algorithms for conventional FL. Moreover, they retain the highly desirable {\em linear speedup effect} with respect of both the number of workers and local steps in the new AFL paradigm. We validate the proposed algorithms with extensive experiments on real-world datasets.

Let p denote a generative language model. Let r denote a reward model that returns a scalar that captures the degree at which a draw from p is preferred. The goal of language model alignment is to alter p to a new distribution phi that results in a higher expected reward while keeping phi close to p. A popular alignment method is the KL-constrained reinforcement learning (RL), which chooses a distribution phi_Delta that maximizes E_{phi_{Delta}} r(y) subject to a relative entropy constraint KL(phi_Delta || p) leq Delta. Another simple alignment method is best-of-N, where N samples are drawn from p and one with highest reward is selected. In this paper, we offer a closed-form characterization of the optimal KL-constrained RL solution. We demonstrate that any alignment method that achieves a comparable trade-off between KL divergence and reward must approximate the optimal KL-constrained RL solution in terms of relative entropy. To further analyze the properties of alignment methods, we introduce two simplifying assumptions: we let the language model be memoryless, and the reward model be linear. Although these assumptions may not reflect complex real-world scenarios, they enable a precise characterization of the asymptotic behavior of both the best-of-N alignment, and the KL-constrained RL method, in terms of information-theoretic quantities. We prove that the reward of the optimal KL-constrained RL solution satisfies a large deviation principle, and we fully characterize its rate function. We also show that the rate of growth of the scaled cumulants of the reward is characterized by a proper Renyi cross entropy. Finally, we show that best-of-N is asymptotically equivalent to KL-constrained RL solution by proving that their expected rewards are asymptotically equal, and concluding that the two distributions must be close in KL divergence.

Byzantine robustness has received significant attention recently given its importance for distributed and federated learning. In spite of this, we identify severe flaws in existing algorithms even when the data across the participants is identically distributed. First, we show realistic examples where current state of the art robust aggregation rules fail to converge even in the absence of any Byzantine attackers. Secondly, we prove that even if the aggregation rules may succeed in limiting the influence of the attackers in a single round, the attackers can couple their attacks across time eventually leading to divergence. To address these issues, we present two surprisingly simple strategies: a new robust iterative clipping procedure, and incorporating worker momentum to overcome time-coupled attacks. This is the first provably robust method for the standard stochastic optimization setting. Our code is open sourced at https://github.com/epfml/byzantine-robust-optimizer.

Collaborative Perception (CP) has shown a promising technique for autonomous driving, where multiple connected and autonomous vehicles (CAVs) share their perception information to enhance the overall perception performance and expand the perception range. However, in CP, ego CAV needs to receive messages from its collaborators, which makes it easy to be attacked by malicious agents. For example, a malicious agent can send harmful information to the ego CAV to mislead it. To address this critical issue, we propose a novel method, CP-Guard, a tailored defense mechanism for CP that can be deployed by each agent to accurately detect and eliminate malicious agents in its collaboration network. Our key idea is to enable CP to reach a consensus rather than a conflict against the ego CAV's perception results. Based on this idea, we first develop a probability-agnostic sample consensus (PASAC) method to effectively sample a subset of the collaborators and verify the consensus without prior probabilities of malicious agents. Furthermore, we define a collaborative consistency loss (CCLoss) to capture the discrepancy between the ego CAV and its collaborators, which is used as a verification criterion for consensus. Finally, we conduct extensive experiments in collaborative bird's eye view (BEV) tasks and our results demonstrate the effectiveness of our CP-Guard. Code is available at https://github.com/CP-Security/CP-Guard

Knowledge distillation is a model compression technique in which a compact "student" network is trained to replicate the predictive behavior of a larger "teacher" network. In logit-based knowledge distillation, it has become the de facto approach to augment cross-entropy with a distillation term. Typically, this term is either a KL divergence that matches marginal probabilities or a correlation-based loss that captures intra- and inter-class relationships. In every case, it acts as an additional term to cross-entropy. This term has its own weight, which must be carefully tuned. In this paper, we adopt a choice-theoretic perspective and recast knowledge distillation under the Plackett-Luce model by interpreting teacher logits as "worth" scores. We introduce "Plackett-Luce Distillation (PLD)", a weighted list-wise ranking loss. In PLD, the teacher model transfers knowledge of its full ranking of classes, weighting each ranked choice by its own confidence. PLD directly optimizes a single "teacher-optimal" ranking. The true label is placed first, followed by the remaining classes in descending teacher confidence. This process yields a convex and translation-invariant surrogate that subsumes weighted cross-entropy. Empirically, across CIFAR-100, ImageNet-1K, and MS-COCO, PLD achieves consistent gains across diverse architectures and distillation objectives, including divergence-based, correlation-based, and feature-based methods, in both homogeneous and heterogeneous teacher-student pairs.

We introduce the Consensus-Bottleneck Asset Pricing Model (CB-APM), a framework that reconciles the predictive power of deep learning with the structural transparency of traditional finance. By embedding aggregate analyst consensus as a structural "bottleneck", the model treats professional beliefs as a sufficient statistic for the market's high-dimensional information set. We document a striking "interpretability-accuracy amplification effect" for annual horizons, the structural constraint acts as an endogenous regularizer that significantly improves out-of-sample R2 over unconstrained benchmarks. Portfolios sorted on CB-APM forecasts exhibit a strong monotonic return gradient, delivering an annualized Sharpe ratio of 1.44 and robust performance across macroeconomic regimes. Furthermore, pricing diagnostics reveal that the learned consensus captures priced variation only partially spanned by canonical factor models, identifying structured risk heterogeneity that standard linear models systematically miss. Our results suggest that anchoring machine intelligence to human-expert belief formation is not merely a tool for transparency, but a catalyst for uncovering new dimensions of belief-driven risk premiums.

Conformal prediction is emerging as a popular paradigm for providing rigorous uncertainty quantification in machine learning since it can be easily applied as a post-processing step to already trained models. In this paper, we extend conformal prediction to the federated learning setting. The main challenge we face is data heterogeneity across the clients - this violates the fundamental tenet of exchangeability required for conformal prediction. We propose a weaker notion of partial exchangeability, better suited to the FL setting, and use it to develop the Federated Conformal Prediction (FCP) framework. We show FCP enjoys rigorous theoretical guarantees and excellent empirical performance on several computer vision and medical imaging datasets. Our results demonstrate a practical approach to incorporating meaningful uncertainty quantification in distributed and heterogeneous environments. We provide code used in our experiments https://github.com/clu5/federated-conformal.

Recent work has sought to quantify large language model uncertainty to facilitate model control and modulate user trust. Previous works focus on measures of uncertainty that are theoretically grounded or reflect the average overt behavior of the model. In this work, we investigate a variety of uncertainty measures, in order to identify measures that correlate with human group-level uncertainty. We find that Bayesian measures and a variation on entropy measures, top-k entropy, tend to agree with human behavior as a function of model size. We find that some strong measures decrease in human-similarity with model size, but, by multiple linear regression, we find that combining multiple uncertainty measures provide comparable human-alignment with reduced size-dependency.

Recently, Agentic Reinforcement Learning (Agentic RL) has made significant progress in incentivizing the multi-turn, long-horizon tool-use capabilities of web agents. While mainstream agentic RL algorithms autonomously explore high-uncertainty tool-call steps under the guidance of entropy, excessive reliance on entropy signals can impose further constraints, leading to the training collapse. In this paper, we delve into the challenges caused by entropy and propose the Agentic Entropy-Balanced Policy Optimization (AEPO), an agentic RL algorithm designed to balance entropy in both the rollout and policy update phases. AEPO comprises two core components: (1) a dynamic entropy-balanced rollout mechanism that adaptively allocate global and branch sampling budget through entropy pre-monitoring, while imposing a branch penalty on consecutive high-entropy tool-call steps to prevent over-branching issues; and (2) Entropy-Balanced Policy Optimization that inserts a stop-gradient operation into the high-entropy clipping term to preserve and properly rescale gradients on high-entropy tokens, while incorporating entropy-aware advantage estimation to prioritize learning on high-uncertainty tokens. Results across 14 challenging datasets show that AEPO consistently outperforms 7 mainstream RL algorithms. With just 1K RL samples, Qwen3-14B with AEPO achieves impressive results: 47.6% on GAIA, 11.2% on Humanity's Last Exam, and 43.0% on WebWalker for Pass@1; 65.0% on GAIA, 26.0% on Humanity's Last Exam, and 70.0% on WebWalker for Pass@5. Further analysis reveals that AEPO improves rollout sampling diversity while maintaining stable policy entropy, facilitating scalable web agent training.

Can we learn more from data than existed in the generating process itself? Can new and useful information be constructed from merely applying deterministic transformations to existing data? Can the learnable content in data be evaluated without considering a downstream task? On these questions, Shannon information and Kolmogorov complexity come up nearly empty-handed, in part because they assume observers with unlimited computational capacity and fail to target the useful information content. In this work, we identify and exemplify three seeming paradoxes in information theory: (1) information cannot be increased by deterministic transformations; (2) information is independent of the order of data; (3) likelihood modeling is merely distribution matching. To shed light on the tension between these results and modern practice, and to quantify the value of data, we introduce epiplexity, a formalization of information capturing what computationally bounded observers can learn from data. Epiplexity captures the structural content in data while excluding time-bounded entropy, the random unpredictable content exemplified by pseudorandom number generators and chaotic dynamical systems. With these concepts, we demonstrate how information can be created with computation, how it depends on the ordering of the data, and how likelihood modeling can produce more complex programs than present in the data generating process itself. We also present practical procedures to estimate epiplexity which we show capture differences across data sources, track with downstream performance, and highlight dataset interventions that improve out-of-distribution generalization. In contrast to principles of model selection, epiplexity provides a theoretical foundation for data selection, guiding how to select, generate, or transform data for learning systems.

Language model training in distributed settings is limited by the communication cost of gradient exchanges. In this short note, we extend recent work from Malladi et al. (2023), using shared randomness to perform distributed fine-tuning with low bandwidth. The method is a natural decentralized extension of memory-efficient Simultaneous Perturbation Stochastic Approximation (SPSA). Each iteration, each machine seeds a Random Number Generator (RNG) to perform local reproducible perturbations on model weights and calculate and exchange scalar projected gradients, which are then used to update each model. By using a (machine, sample) identifier as the random seed, each model can regenerate one another's perturbations. As machines only exchange single-byte projected gradients, this is highly communication efficient. There are also potential privacy benefits, as projected gradients may be calculated on different training data, and models never access the other's data. Our approach not only drastically reduces communication bandwidth requirements but also accommodates dynamic addition or removal of machines during the training process and retains the memory-efficient and inference-only advantages of recent work. We perform proof-of-concept experiments to demonstrate the potential usefulness of this method, building off of rich literature on distributed optimization and memory-efficient training.

Recent advances in large language models (LLMs) have accelerated progress toward artificial general intelligence, with inference-time scaling emerging as a key technique. Contemporary approaches leverage either sequential reasoning (iteratively extending chains of thought) or parallel reasoning (generating multiple solutions simultaneously) to scale inference. However, both paradigms face fundamental limitations: sequential scaling typically relies on arbitrary token budgets for termination, leading to inefficiency or premature cutoff; while parallel scaling often lacks coordination among parallel branches and requires intrusive fine-tuning to perform effectively. In light of these challenges, we aim to design a flexible test-time collaborative inference framework that exploits the complementary strengths of both sequential and parallel reasoning paradigms. Towards this goal, the core challenge lies in developing an efficient and accurate intrinsic quality metric to assess model responses during collaborative inference, enabling dynamic control and early termination of the reasoning trace. To address this challenge, we introduce semantic entropy (SE), which quantifies the semantic diversity of parallel model responses and serves as a robust indicator of reasoning quality due to its strong negative correlation with accuracy...

Pioneering advancements in large language model-powered agents have underscored the design pattern of multi-agent collaboration, demonstrating that collective intelligence can surpass the capabilities of each individual. Inspired by the neural scaling law, which posits that increasing neurons leads to emergent abilities, this study investigates whether a similar principle applies to increasing agents in multi-agent collaboration. Technically, we propose multi-agent collaboration networks (MacNet), which utilize directed acyclic graphs to organize agents and streamline their interactive reasoning via topological ordering, with solutions derived from their dialogues. Extensive experiments show that MacNet consistently outperforms baseline models, enabling effective agent collaboration across various network topologies and supporting cooperation among more than a thousand agents. Notably, we observed a small-world collaboration phenomenon, where topologies resembling small-world properties achieved superior performance. Additionally, we identified a collaborative scaling law, indicating that normalized solution quality follows a logistic growth pattern as scaling agents, with collaborative emergence occurring much earlier than previously observed instances of neural emergence. The code and data will be available at https://github.com/OpenBMB/ChatDev.

We establish a fundamental connection between score-based diffusion models and non-equilibrium thermodynamics by deriving performance limits based on entropy rates. Our main theoretical contribution is a lower bound on the negative log-likelihood of the data that relates model performance to entropy rates of diffusion processes. We numerically validate this bound on a synthetic dataset and investigate its tightness. By building a bridge to entropy rates - system, intrinsic, and exchange entropy - we provide new insights into the thermodynamic operation of these models, drawing parallels to Maxwell's demon and implications for thermodynamic computing hardware. Our framework connects generative modeling performance to fundamental physical principles through stochastic thermodynamics.

Two principles: the complementary principle and the consensus principle are widely acknowledged in the literature of multi-view learning. However, the current design of multi-head self-attention, an instance of multi-view learning, prioritizes the complementarity while ignoring the consensus. To address this problem, we propose an enhanced multi-head self-attention (EMHA). First, to satisfy the complementary principle, EMHA removes the one-to-one mapping constraint among queries and keys in multiple subspaces and allows each query to attend to multiple keys. On top of that, we develop a method to fully encourage consensus among heads by introducing two interaction models, namely inner-subspace interaction and cross-subspace interaction. Extensive experiments on a wide range of language tasks (e.g., machine translation, abstractive summarization and grammar correction, language modeling), show its superiority, with a very modest increase in model size. Our code would be available at: https://github.com/zhengkid/EIT-Enhanced-Interactive-Transformer.

Markov categories are a novel framework to describe and treat problems in probability and information theory. In this work we combine the categorical formalism with the traditional quantitative notions of entropy, mutual information, and data processing inequalities. We show that several quantitative aspects of information theory can be captured by an enriched version of Markov categories, where the spaces of morphisms are equipped with a divergence or even a metric. As it is customary in information theory, mutual information can be defined as a measure of how far a joint source is from displaying independence of its components. More strikingly, Markov categories give a notion of determinism for sources and channels, and we can define entropy exactly by measuring how far a source or channel is from being deterministic. This recovers Shannon and R\'enyi entropies, as well as the Gini-Simpson index used in ecology to quantify diversity, and it can be used to give a conceptual definition of generalized entropy.

We address the challenging problem of semi-supervised learning in the context of multiple visual interpretations of the world by finding consensus in a graph of neural networks. Each graph node is a scene interpretation layer, while each edge is a deep net that transforms one layer at one node into another from a different node. During the supervised phase edge networks are trained independently. During the next unsupervised stage edge nets are trained on the pseudo-ground truth provided by consensus among multiple paths that reach the nets' start and end nodes. These paths act as ensemble teachers for any given edge and strong consensus is used for high-confidence supervisory signal. The unsupervised learning process is repeated over several generations, in which each edge becomes a "student" and also part of different ensemble "teachers" for training other students. By optimizing such consensus between different paths, the graph reaches consistency and robustness over multiple interpretations and generations, in the face of unknown labels. We give theoretical justifications of the proposed idea and validate it on a large dataset. We show how prediction of different representations such as depth, semantic segmentation, surface normals and pose from RGB input could be effectively learned through self-supervised consensus in our graph. We also compare to state-of-the-art methods for multi-task and semi-supervised learning and show superior performance.

Verifying the provenance of content is crucial to the function of many organizations, e.g., educational institutions, social media platforms, firms, etc. This problem is becoming increasingly difficult as text generated by Large Language Models (LLMs) becomes almost indistinguishable from human-generated content. In addition, many institutions utilize in-house LLMs and want to ensure that external, non-sanctioned LLMs do not produce content within the institution. In this paper, we answer the following question: Given a piece of text, can we identify whether it was produced by LLM A or B (where B can be a human)? We model LLM-generated text as a sequential stochastic process with complete dependence on history and design zero-shot statistical tests to distinguish between (i) the text generated by two different sets of LLMs A (in-house) and B (non-sanctioned) and also (ii) LLM-generated and human-generated texts. We prove that the type I and type II errors for our tests decrease exponentially in the text length. In designing our tests, we derive concentration inequalities on the difference between log-perplexity and the average entropy of the string under A. Specifically, for a given string, we demonstrate that if the string is generated by A, the log-perplexity of the string under A converges to the average entropy of the string under A, except with an exponentially small probability in string length. We also show that if B generates the text, except with an exponentially small probability in string length, the log-perplexity of the string under A converges to the average cross-entropy of B and A. Lastly, we present preliminary experimental results to support our theoretical results. By enabling guaranteed (with high probability) finding of the origin of harmful LLM-generated text with arbitrary size, we can help combat misinformation.

Co-Salient Object Detection (CoSOD) aims at detecting common salient objects within a group of relevant source images. Most of the latest works employ the attention mechanism for finding common objects. To achieve accurate CoSOD results with high-quality maps and high efficiency, we propose a novel Memory-aided Contrastive Consensus Learning (MCCL) framework, which is capable of effectively detecting co-salient objects in real time (~150 fps). To learn better group consensus, we propose the Group Consensus Aggregation Module (GCAM) to abstract the common features of each image group; meanwhile, to make the consensus representation more discriminative, we introduce the Memory-based Contrastive Module (MCM), which saves and updates the consensus of images from different groups in a queue of memories. Finally, to improve the quality and integrity of the predicted maps, we develop an Adversarial Integrity Learning (AIL) strategy to make the segmented regions more likely composed of complete objects with less surrounding noise. Extensive experiments on all the latest CoSOD benchmarks demonstrate that our lite MCCL outperforms 13 cutting-edge models, achieving the new state of the art (~5.9% and ~6.2% improvement in S-measure on CoSOD3k and CoSal2015, respectively). Our source codes, saliency maps, and online demos are publicly available at https://github.com/ZhengPeng7/MCCL.

In this paper we present the initial design of Minerva consensus protocol for Truechain and other technical details. Currently, it is widely believed in the blockchain community that a public chain cannot simultaneously achieve high performance, decentralization and security. This is true in the case of a Nakamoto chain (low performance) or a delegated proof of stake chain (partially centralized), which are the most popular block chain solutions at time of writing. Our consensus design enjoys the same consistency, liveness, transaction finality and security guarantee, a de-facto with the Hybrid Consensus. We go on to propose the idea of a new virtual machine on top of Ethereum which adds permissioned-chain based transaction processing capabilities in a permissionless setting. We also use the idea of data sharding and speculative transactions, and evaluation of smart contracts in a sharding friendly virtual machine. Finally, we will briefly discuss our fundamentally ASIC resistant mining algorithm, Truehash.

We demonstrate how collective memory emerges in decentralized multi-agent systems through the interplay between individual agent memory and environmental trace communication. Our agents maintain internal memory states while depositing persistent environmental traces, creating a spatially distributed collective memory without centralized control. Comprehensive validation across five environmental conditions (20x20 to 50x50 grids, 5-20 agents, 50 runs per configuration) reveals a critical asymmetry: individual memory alone provides 68.7% performance improvement over no-memory baselines (1563.87 vs 927.23, p < 0.001), while environmental traces without memory fail completely. This demonstrates that memory functions independently but traces require cognitive infrastructure for interpretation. Systematic density-sweep experiments (rho in [0.049, 0.300], up to 625 agents) validate our theoretical phase transition prediction. On realistic large grids (30x30, 50x50), stigmergic coordination dominates above rho ~ 0.20, with traces outperforming memory by 36-41% on composite metrics despite lower food efficiency. The experimental crossover confirms the predicted critical density rho_c = 0.230 within 13% error.

The Koopman operator provides a powerful framework for modeling dynamical systems and has attracted growing interest from the machine learning community. However, its infinite-dimensional nature makes identifying suitable finite-dimensional subspaces challenging, especially for deep architectures. We argue that these difficulties come from suboptimal representation learning, where latent variables fail to balance expressivity and simplicity. This tension is closely related to the information bottleneck (IB) dilemma: constructing compressed representations that are both compact and predictive. Rethinking Koopman learning through this lens, we demonstrate that latent mutual information promotes simplicity, yet an overemphasis on simplicity may cause latent space to collapse onto a few dominant modes. In contrast, expressiveness is sustained by the von Neumann entropy, which prevents such collapse and encourages mode diversity. This insight leads us to propose an information-theoretic Lagrangian formulation that explicitly balances this tradeoff. Furthermore, we propose a new algorithm based on the Lagrangian formulation that encourages both simplicity and expressiveness, leading to a stable and interpretable Koopman representation. Beyond quantitative evaluations, we further visualize the learned manifolds under our representations, observing empirical results consistent with our theoretical predictions. Finally, we validate our approach across a diverse range of dynamical systems, demonstrating improved performance over existing Koopman learning methods. The implementation is publicly available at https://github.com/Wenxuan52/InformationKoopman.

MoltBook is a large-scale multi-agent coordination environment where over 770,000 autonomous LLM agents interact without human participation, offering the first opportunity we are aware of to observe emergent multi-agent coordination dynamics at this population scale. We introduce Molt Dynamics: the emergent agent coordination behaviors, inter-agent communication dynamics, and role specialization patterns arising when autonomous agents operate as decentralized decision-makers in an unconstrained multi-agent environment. Through longitudinal observation of 90,704 active agents over three weeks, we characterize three aspects. First, spontaneous role specialization: network-based clustering reveals six structural roles (silhouette 0.91), though the result primarily reflects core-periphery organization -- 93.5\% of agents occupy a homogeneous peripheral cluster, with meaningful differentiation confined to the active minority. Second, decentralized information dissemination: cascade analysis of 10,323 inter-agent propagation events reveals power-law distributed cascade sizes (α= 2.57 pm 0.02) and saturating adoption dynamics where adoption probability shows diminishing returns with repeated exposures (Cox hazard ratio 0.53, concordance 0.78). Third, distributed cooperative task resolution: 164 multi-agent collaborative events show detectable coordination patterns, but success rates are low (6.7\%, p = 0.057) and cooperative outcomes are significantly worse than a matched single-agent baseline (Cohen's d = -0.88), indicating emergent cooperative behavior is nascent. These findings establish an empirical baseline for coordination dynamics in decentralized autonomous agent systems, with implications for multi-agent system design, agent communication protocol engineering, and AI safety.

Fairness is essential for machine learning systems deployed in high-stake applications. Among all fairness notions, individual fairness, deriving from a consensus that `similar individuals should be treated similarly,' is a vital notion to describe fair treatment for individual cases. Previous studies typically characterize individual fairness as a prediction-invariant problem when perturbing sensitive attributes on samples, and solve it by Distributionally Robust Optimization (DRO) paradigm. However, such adversarial perturbations along a direction covering sensitive information used in DRO do not consider the inherent feature correlations or innate data constraints, therefore could mislead the model to optimize at off-manifold and unrealistic samples. In light of this drawback, in this paper, we propose to learn and generate antidote data that approximately follows the data distribution to remedy individual unfairness. These generated on-manifold antidote data can be used through a generic optimization procedure along with original training data, resulting in a pure pre-processing approach to individual unfairness, or can also fit well with the in-processing DRO paradigm. Through extensive experiments on multiple tabular datasets, we demonstrate our method resists individual unfairness at a minimal or zero cost to predictive utility compared to baselines.

This paper aims to extend the Structured Knowledge Accumulation (SKA) framework recently proposed by mahi2025ska. We introduce two core concepts: the Tensor Net function and the characteristic time property of neural learning. First, we reinterpret the learning rate as a time step in a continuous system. This transforms neural learning from discrete optimization into continuous-time evolution. We show that learning dynamics remain consistent when the product of learning rate and iteration steps stays constant. This reveals a time-invariant behavior and identifies an intrinsic timescale of the network. Second, we define the Tensor Net function as a measure that captures the relationship between decision probabilities, entropy gradients, and knowledge change. Additionally, we define its zero-crossing as the equilibrium state between decision probabilities and entropy gradients. We show that the convergence of entropy and knowledge flow provides a natural stopping condition, replacing arbitrary thresholds with an information-theoretic criterion. We also establish that SKA dynamics satisfy a variational principle based on the Euler-Lagrange equation. These findings extend SKA into a continuous and self-organizing learning model. The framework links computational learning with physical systems that evolve by natural laws. By understanding learning as a time-based process, we open new directions for building efficient, robust, and biologically-inspired AI systems.

The statistical mechanics of Gibbs is a juxtaposition of subjective, probabilistic ideas on the one hand and objective, mechanical ideas on the other. In this paper, we follow the path set out by Jaynes, including elements added subsequently to that original work, to explore the consequences of the purely statistical point of view. We show how standard methods in the equilibrium theory could have been derived simply from a description of the available problem information. In addition, our presentation leads to novel insights into questions associated with symmetry and non-equilibrium statistical mechanics. Two surprising consequences to be explored in further work are that (in)distinguishability factors are automatically predicted from the problem formulation and that a quantity related to the thermodynamic entropy production is found by considering information loss in non-equilibrium processes. Using the problem of ion channel thermodynamics as an example, we illustrate the idea of building up complexity by successively adding information to create progressively more complex descriptions of a physical system. Our result is that such statistical mechanical descriptions can be used to create transparent, computable, experimentally-relevant models that may be informed by more detailed atomistic simulations. We also derive a theory for the kinetic behavior of this system, identifying the nonequilibrium `process' free energy functional. The Gibbs relation for this functional is a fluctuation-dissipation theorem applicable arbitrarily far from equilibrium, that captures the effect of non-local and time-dependent behavior from transient driving forces. Based on this work, it is clear that statistical mechanics is a general tool for constructing the relationships between constraints on system information.

The emergence of multi-agent systems built from large language models (LLMs) offers a promising paradigm for scalable collective intelligence and self-evolution. Ideally, such systems would achieve continuous self-improvement in a fully closed loop while maintaining robust safety alignment--a combination we term the self-evolution trilemma. However, we demonstrate both theoretically and empirically that an agent society satisfying continuous self-evolution, complete isolation, and safety invariance is impossible. Drawing on an information-theoretic framework, we formalize safety as the divergence degree from anthropic value distributions. We theoretically demonstrate that isolated self-evolution induces statistical blind spots, leading to the irreversible degradation of the system's safety alignment. Empirical and qualitative results from an open-ended agent community (Moltbook) and two closed self-evolving systems reveal phenomena that align with our theoretical prediction of inevitable safety erosion. We further propose several solution directions to alleviate the identified safety concern. Our work establishes a fundamental limit on the self-evolving AI societies and shifts the discourse from symptom-driven safety patches to a principled understanding of intrinsic dynamical risks, highlighting the need for external oversight or novel safety-preserving mechanisms.

Using the example of configurations generated with the worm algorithm for the two-dimensional Ising model, we propose renormalization group (RG) transformations, inspired by the tensor RG, that can be applied to sets of images. We relate criticality to the logarithmic divergence of the largest principal component. We discuss the changes in link occupation under the RG transformation, suggest ways to obtain data collapse, and compare with the two state tensor RG approximation near the fixed point.

We study multi-agent reinforcement learning in the setting of episodic Markov decision processes, where multiple agents cooperate via communication through a central server. We propose a provably efficient algorithm based on value iteration that enable asynchronous communication while ensuring the advantage of cooperation with low communication overhead. With linear function approximation, we prove that our algorithm enjoys an mathcal{O}(d^{3/2}H^2K) regret with mathcal{O}(dHM^2) communication complexity, where d is the feature dimension, H is the horizon length, M is the total number of agents, and K is the total number of episodes. We also provide a lower bound showing that a minimal Omega(dM) communication complexity is required to improve the performance through collaboration.

We show that coherent, long-form musical composition can emerge from a decentralized swarm of identical, frozen foundation models that coordinate via stigmergic, peer-to-peer signals, without any weight updates. We compare a centralized multi-agent system with a global critic to a fully decentralized swarm in which bar-wise agents sense and deposit harmonic, rhythmic, and structural cues, adapt short-term memory, and reach consensus. Across symbolic, audio, and graph-theoretic analyses, the swarm yields superior quality while delivering greater diversity and structural variety and leads across creativity metrics. The dynamics contract toward a stable configuration of complementary roles, and self-similarity networks reveal a small-world architecture with efficient long-range connectivity and specialized bridging motifs, clarifying how local novelties consolidate into global musical form. By shifting specialization from parameter updates to interaction rules, shared memory, and dynamic consensus, MusicSwarm provides a compute- and data-efficient route to long-horizon creative structure that is immediately transferable beyond music to collaborative writing, design, and scientific discovery.

Active matter systems, from self-propelled colloids to motile bacteria, are characterized by the conversion of free energy into useful work at the microscopic scale. These systems generically involve physics beyond the reach of equilibrium statistical mechanics, and a persistent challenge has been to understand the nature of their nonequilibrium states. The entropy production rate and the magnitude of the steady-state probability current provide quantitative ways to do so by measuring the breakdown of time-reversal symmetry and the strength of nonequilibrium transport of measure. Yet, their efficient computation has remained elusive, as they depend on the system's unknown and high-dimensional probability density. Here, building upon recent advances in generative modeling, we develop a deep learning framework that estimates the score of this density. We show that the score, together with the microscopic equations of motion, gives direct access to the entropy production rate, the probability current, and their decomposition into local contributions from individual particles, spatial regions, and degrees of freedom. To represent the score, we introduce a novel, spatially-local transformer-based network architecture that learns high-order interactions between particles while respecting their underlying permutation symmetry. We demonstrate the broad utility and scalability of the method by applying it to several high-dimensional systems of interacting active particles undergoing motility-induced phase separation (MIPS). We show that a single instance of our network trained on a system of 4096 particles at one packing fraction can generalize to other regions of the phase diagram, including systems with as many as 32768 particles. We use this observation to quantify the spatial structure of the departure from equilibrium in MIPS as a function of the number of particles and the packing fraction.

Backpropagation, which uses the chain rule, is the de-facto standard algorithm for optimizing neural networks nowadays. Recently, Hinton (2022) proposed the forward-forward algorithm, a promising alternative that optimizes neural nets layer-by-layer, without propagating gradients throughout the network. Although such an approach has several advantages over back-propagation and shows promising results, the fact that each layer is being trained independently limits the optimization process. Specifically, it prevents the network's layers from collaborating to learn complex and rich features. In this work, we study layer collaboration in the forward-forward algorithm. We show that the current version of the forward-forward algorithm is suboptimal when considering information flow in the network, resulting in a lack of collaboration between layers of the network. We propose an improved version that supports layer collaboration to better utilize the network structure, while not requiring any additional assumptions or computations. We empirically demonstrate the efficacy of the proposed version when considering both information flow and objective metrics. Additionally, we provide a theoretical motivation for the proposed method, inspired by functional entropy theory.

One of the most challenging forms of misinformation involves the out-of-context (OOC) use of images paired with misleading text, creating false narratives. Existing AI-driven detection systems lack explainability and require expensive finetuning. We address these issues with LLM-Consensus, a multi-agent debate system for OOC misinformation detection. LLM-Consensus introduces a novel multi-agent debate framework where multimodal agents collaborate to assess contextual consistency and request external information to enhance cross-context reasoning and decision-making. Our framework enables explainable detection with state-of-the-art accuracy even without domain-specific fine-tuning. Extensive ablation studies confirm that external retrieval significantly improves detection accuracy, and user studies demonstrate that LLM-Consensus boosts performance for both experts and non-experts. These results position LLM-Consensus as a powerful tool for autonomous and citizen intelligence applications.

Entropy and mutual information in neural networks provide rich information on the learning process, but they have proven difficult to compute reliably in high dimensions. Indeed, in noisy and high-dimensional data, traditional estimates in ambient dimensions approach a fixed entropy and are prohibitively hard to compute. To address these issues, we leverage data geometry to access the underlying manifold and reliably compute these information-theoretic measures. Specifically, we define diffusion spectral entropy (DSE) in neural representations of a dataset as well as diffusion spectral mutual information (DSMI) between different variables representing data. First, we show that they form noise-resistant measures of intrinsic dimensionality and relationship strength in high-dimensional simulated data that outperform classic Shannon entropy, nonparametric estimation, and mutual information neural estimation (MINE). We then study the evolution of representations in classification networks with supervised learning, self-supervision, or overfitting. We observe that (1) DSE of neural representations increases during training; (2) DSMI with the class label increases during generalizable learning but stays stagnant during overfitting; (3) DSMI with the input signal shows differing trends: on MNIST it increases, while on CIFAR-10 and STL-10 it decreases. Finally, we show that DSE can be used to guide better network initialization and that DSMI can be used to predict downstream classification accuracy across 962 models on ImageNet. The official implementation is available at https://github.com/ChenLiu-1996/DiffusionSpectralEntropy.

Hallucination in large language models (LLMs) can be detected by assessing the uncertainty of model outputs, typically measured using entropy. Semantic entropy (SE) enhances traditional entropy estimation by quantifying uncertainty at the semantic cluster level. However, as modern LLMs generate longer one-sentence responses, SE becomes less effective because it overlooks two crucial factors: intra-cluster similarity (the spread within a cluster) and inter-cluster similarity (the distance between clusters). To address these limitations, we propose a simple black-box uncertainty quantification method inspired by nearest neighbor estimates of entropy. Our approach can also be easily extended to white-box settings by incorporating token probabilities. Additionally, we provide theoretical results showing that our method generalizes semantic entropy. Extensive empirical results demonstrate its effectiveness compared to semantic entropy across two recent LLMs (Phi3 and Llama3) and three common text generation tasks: question answering, text summarization, and machine translation. Our code is available at https://github.com/BigML-CS-UCLA/SNNE.

The study of collaborative multi-agent bandits has attracted significant attention recently. In light of this, we initiate the study of a new collaborative setting, consisting of N agents such that each agent is learning one of M stochastic multi-armed bandits to minimize their group cumulative regret. We develop decentralized algorithms which facilitate collaboration between the agents under two scenarios. We characterize the performance of these algorithms by deriving the per agent cumulative regret and group regret upper bounds. We also prove lower bounds for the group regret in this setting, which demonstrates the near-optimal behavior of the proposed algorithms.

Supervised Fine-Tuning (SFT) is the standard paradigm for domain adaptation, yet it frequently incurs the cost of catastrophic forgetting. In sharp contrast, on-policy Reinforcement Learning (RL) effectively preserves general capabilities. We investigate this discrepancy and identify a fundamental distributional gap: while RL aligns with the model's internal belief, SFT forces the model to fit external supervision. This mismatch often manifests as "Confident Conflicts" tokens characterized by low probability but low entropy. In these instances, the model is highly confident in its own prediction but is forced to learn a divergent ground truth, triggering destructive gradient updates. To address this, we propose Entropy-Adaptive Fine-Tuning (EAFT). Unlike methods relying solely on prediction probability, EAFT utilizes token-level entropy as a gating mechanism to distinguish between epistemic uncertainty and knowledge conflict. This allows the model to learn from uncertain samples while suppressing gradients on conflicting data. Extensive experiments on Qwen and GLM series (ranging from 4B to 32B parameters) across mathematical, medical, and agentic domains confirm our hypothesis. EAFT consistently matches the downstream performance of standard SFT while significantly mitigating the degradation of general capabilities.

We design a low complexity decentralized learning algorithm to train a recently proposed large neural network in distributed processing nodes (workers). We assume the communication network between the workers is synchronized and can be modeled as a doubly-stochastic mixing matrix without having any master node. In our setup, the training data is distributed among the workers but is not shared in the training process due to privacy and security concerns. Using alternating-direction-method-of-multipliers (ADMM) along with a layerwise convex optimization approach, we propose a decentralized learning algorithm which enjoys low computational complexity and communication cost among the workers. We show that it is possible to achieve equivalent learning performance as if the data is available in a single place. Finally, we experimentally illustrate the time complexity and convergence behavior of the algorithm.

Multimodal large language models (MLLMs) must resolve conflicts when different modalities provide contradictory information, a process we term modality following. Prior work measured this behavior only with coarse dataset-level statistics, overlooking the influence of model's confidence in unimodal reasoning. In this paper, we introduce a new framework that decomposes modality following into two fundamental factors: relative reasoning uncertainty (the case-specific confidence gap between unimodal predictions) and inherent modality preference( a model's stable bias when uncertainties are balanced). To validate this framework, we construct a controllable dataset that systematically varies the reasoning difficulty of visual and textual inputs. Using entropy as a fine-grained uncertainty metric, we uncover a universal law: the probability of following a modality decreases monotonically as its relative uncertainty increases. At the relative difficulty level where the model tends to follow both modalities with comparable probability what we call the balance point, a practical indicator of the model's inherent preference. Unlike traditional macro-level ratios, this measure offers a more principled and less confounded way to characterize modality bias, disentangling it from unimodal capabilities and dataset artifacts. Further, by probing layer-wise predictions, we reveal the internal mechanism of oscillation: in ambiguous regions near the balance point, models vacillate between modalities across layers, explaining externally observed indecision. Together, these findings establish relative uncertainty and inherent preference as the two governing principles of modality following, offering both a quantitative framework and mechanistic insight into how MLLMs resolve conflicting information.

Cooperative multi-agent reinforcement learning (MARL) commonly adopts centralized training with decentralized execution (CTDE), where centralized critics leverage global information to guide decentralized actors. However, centralized-decentralized mismatch (CDM) arises when the suboptimal behavior of one agent degrades others' learning. Prior approaches mitigate CDM through value decomposition, but linear decompositions allow per-agent gradients at the cost of limited expressiveness, while nonlinear decompositions improve representation but require centralized gradients, reintroducing CDM. To overcome this trade-off, we propose the multi-agent cross-entropy method (MCEM), combined with monotonic nonlinear critic decomposition (NCD). MCEM updates policies by increasing the probability of high-value joint actions, thereby excluding suboptimal behaviors. For sample efficiency, we extend off-policy learning with a modified k-step return and Retrace. Analysis and experiments demonstrate that MCEM outperforms state-of-the-art methods across both continuous and discrete action benchmarks.

Federated learning and gossip learning are emerging methodologies designed to mitigate data privacy concerns by retaining training data on client devices and exclusively sharing locally-trained machine learning (ML) models with others. The primary distinction between the two lies in their approach to model aggregation: federated learning employs a centralized parameter server, whereas gossip learning adopts a fully decentralized mechanism, enabling direct model exchanges among nodes. This decentralized nature often positions gossip learning as less efficient compared to federated learning. Both methodologies involve a critical step: computing a representation of received ML models and integrating this representation into the existing model. Conventionally, this representation is derived by averaging the received models, exemplified by the FedAVG algorithm. Our findings suggest that this averaging approach inherently introduces a potential delay in model convergence. We identify the underlying cause and refer to it as the "vanishing variance" problem, where averaging across uncorrelated ML models undermines the optimal variance established by the Xavier weight initialization. Unlike federated learning where the central server ensures model correlation, and unlike traditional gossip learning which circumvents this problem through model partitioning and sampling, our research introduces a variance-corrected model averaging algorithm. This novel algorithm preserves the optimal variance needed during model averaging, irrespective of network topology or non-IID data distributions. Our extensive simulation results demonstrate that our approach enables gossip learning to achieve convergence efficiency comparable to that of federated learning.

We introduce the category of information structures, whose objects are suitable diagrams of measurable sets that encode the possible outputs of a given family of observables and their mutual relationships of refinement; they serve as mathematical models of contextuality in classical and quantum settings. Each information structure can be regarded as a ringed site with trivial topology; the structure ring is generated by the observables themselves and its multiplication corresponds to joint measurement. We extend Baudot and Bennequin's definition of information cohomology to this setting, as a derived functor in the category of modules over the structure ring, and show explicitly that the bar construction gives a projective resolution in that category, recovering in this way the cochain complexes previously considered in the literature. Finally, we study the particular case of a one-parameter family of coefficients made of functions of probability distributions. The only 1-cocycles are Shannon entropy or Tsallis alpha-entropy, depending on the value of the parameter.

We performed a billion locality sensitive hash comparisons between artificially generated data samples to answer the critical question - can we verify the "correctness" of generative AI output in a non-deterministic, trustless, decentralized network? We generate millions of data samples from a variety of open source diffusion and large language models and describe the procedures and trade-offs between generating more verses less deterministic output in a heterogenous, stochastic network. Further, we analyze the outputs to provide empirical evidence of different parameterizations of tolerance and error bounds for verification. Finally, given that we have the generated an enormous amount of simulated data, we also release a new training dataset called ImageNet-Gen for use in augmenting existing training pipelines. For our results, we show that with a majority vote between three independent verifiers, we can detect image generated perceptual collisions in generated AI with over 99.89% probability and less than 0.0267% chance of intra-class collision. For large language models (LLMs), we are able to gain 100% consensus using greedy methods or n-way beam searches to generate consensus demonstrated on different LLMs. In the context of generative AI training, we pinpoint and minimize the major sources of stochasticity and present gossip and synchronization training techniques for verifiability. Thus, this work provides a practical, solid foundation for AI verification and consensus for the minimization of trust in a decentralized network.

Large Language Models (LLMs) show potential for complex reasoning, yet their capacity for emergent coordination in Multi-Agent Systems (MAS) when operating under strict constraints-such as limited local perception and communication, characteristic of natural swarms-remains largely unexplored, particularly concerning the nuances of swarm intelligence. Existing benchmarks often do not fully capture the unique challenges of decentralized coordination that arise when agents operate with incomplete spatio-temporal information. To bridge this gap, we introduce SwarmBench, a novel benchmark designed to systematically evaluate the swarm intelligence capabilities of LLMs acting as decentralized agents. SwarmBench features five foundational MAS coordination tasks within a configurable 2D grid environment, forcing agents to rely primarily on local sensory input (k x k view) and local communication. We propose metrics for coordination effectiveness and analyze emergent group dynamics. Evaluating several leading LLMs in a zero-shot setting, we find significant performance variations across tasks, highlighting the difficulties posed by local information constraints. While some coordination emerges, results indicate limitations in robust planning and strategy formation under uncertainty in these decentralized scenarios. Assessing LLMs under swarm-like conditions is crucial for realizing their potential in future decentralized systems. We release SwarmBench as an open, extensible toolkit-built upon a customizable and scalable physical system with defined mechanical properties. It provides environments, prompts, evaluation scripts, and the comprehensive experimental datasets generated, aiming to foster reproducible research into LLM-based MAS coordination and the theoretical underpinnings of Embodied MAS. Our code repository is available at https://github.com/x66ccff/swarmbench.

Extracting low-dimensional summary statistics from large datasets is essential for efficient (likelihood-free) inference. We characterize different classes of summaries and demonstrate their importance for correctly analysing dimensionality reduction algorithms. We demonstrate that minimizing the expected posterior entropy (EPE) under the prior predictive distribution of the model subsumes many existing methods. They are equivalent to or are special or limiting cases of minimizing the EPE. We offer a unifying framework for obtaining informative summaries, provide concrete recommendations for practitioners, and propose a practical method to obtain high-fidelity summaries whose utility we demonstrate for both benchmark and practical examples.

Despite their groundbreaking performance for many generative modeling tasks, diffusion models have fallen short on discrete data domains such as natural language. Crucially, standard diffusion models rely on the well-established theory of score matching, but efforts to generalize this to discrete structures have not yielded the same empirical gains. In this work, we bridge this gap by proposing score entropy, a novel loss that naturally extends score matching to discrete spaces, integrates seamlessly to build discrete diffusion models, and significantly boosts performance. Experimentally, we test our Score Entropy Discrete Diffusion models (SEDD) on standard language modeling tasks. For comparable model sizes, SEDD beats existing language diffusion paradigms (reducing perplexity by 25-75\%) and is competitive with autoregressive models, in particular outperforming GPT-2. Furthermore, compared to autoregressive mdoels, SEDD generates faithful text without requiring distribution annealing techniques like temperature scaling (around 6-8times better generative perplexity than un-annealed GPT-2), can trade compute and quality (similar quality with 32times fewer network evaluations), and enables controllable infilling (matching nucleus sampling quality while enabling other strategies besides left to right prompting).

Recent reinforcement learning has enhanced the flow matching models on human preference alignment. While stochastic sampling enables the exploration of denoising directions, existing methods which optimize over multiple denoising steps suffer from sparse and ambiguous reward signals. We observe that the high entropy steps enable more efficient and effective exploration while the low entropy steps result in undistinguished roll-outs. To this end, we propose E-GRPO, an entropy aware Group Relative Policy Optimization to increase the entropy of SDE sampling steps. Since the integration of stochastic differential equations suffer from ambiguous reward signals due to stochasticity from multiple steps, we specifically merge consecutive low entropy steps to formulate one high entropy step for SDE sampling, while applying ODE sampling on other steps. Building upon this, we introduce multi-step group normalized advantage, which computes group-relative advantages within samples sharing the same consolidated SDE denoising step. Experimental results on different reward settings have demonstrated the effectiveness of our methods.

We present a concise dynamical picture of infant-driven household chaos. The framework has three postulations: recurrent daily chaos, overall entropy growth in household organization, and transient local ordering episodes with switching rules (a volatile Maxwell-demon effect). We illustrate entropy growth with a two-region toy model (organizer vs. play area), where entropy production is nonnegative and long-time behavior is typically play-area dominated. We also model toy diffusion and curiosity-driven behavior, where novelty matters more than punishment in the short term, while gradual learning still occurs.

The present work explores the theoretical limits of Machine Learning (ML) within the framework of Kolmogorov's theory of Algorithmic Probability, which clarifies the notion of entropy as Expected Kolmogorov Complexity and formalizes other fundamental concepts such as Occam's razor via Levin's Universal Distribution. As a fundamental application, we develop Maximum Entropy methods that allow us to derive the Erdos--Kac Law in Probabilistic Number Theory, and establish the impossibility of discovering a formula for primes using Machine Learning via the Prime Coding Theorem.

In this paper I apply newly-proposed information-theoretic principles to thermodynamic work extraction. I show that if it is possible to extract work deterministically from a physical system prepared in any one of a set of states, then those states must be distinguishable from one another. This result is formulated independently of scale and of particular dynamical laws; it also provides a novel connection between thermodynamics and information theory, established via the law of conservation of energy (rather than the second law of thermodynamics). Albeit compatible with these conclusions, existing thermodynamics approaches cannot provide a result of such generality, because they are scale-dependent (relying on ensembles or coarse-graining) or tied to particular dynamical laws. This paper thus provides a broader foundation for thermodynamics, with implications for the theory of von Neumann's universal constructor

Conformal prediction is a widely used method to quantify the uncertainty of a classifier under the assumption of exchangeability (e.g., IID data). We generalize conformal prediction to the Hidden Markov Model (HMM) framework where the assumption of exchangeability is not valid. The key idea of the proposed method is to partition the non-exchangeable Markovian data from the HMM into exchangeable blocks by exploiting the de Finetti's Theorem for Markov Chains discovered by Diaconis and Freedman (1980). The permutations of the exchangeable blocks are viewed as randomizations of the observed Markovian data from the HMM. The proposed method provably retains all desirable theoretical guarantees offered by the classical conformal prediction framework in both exchangeable and Markovian settings. In particular, while the lack of exchangeability introduced by Markovian samples constitutes a violation of a crucial assumption for classical conformal prediction, the proposed method views it as an advantage that can be exploited to improve the performance further. Detailed numerical and empirical results that complement the theoretical conclusions are provided to illustrate the practical feasibility of the proposed method.

In this work, we consider the problem of collaborative multi-user reinforcement learning. In this setting there are multiple users with the same state-action space and transition probabilities but with different rewards. Under the assumption that the reward matrix of the N users has a low-rank structure -- a standard and practically successful assumption in the offline collaborative filtering setting -- the question is can we design algorithms with significantly lower sample complexity compared to the ones that learn the MDP individually for each user. Our main contribution is an algorithm which explores rewards collaboratively with N user-specific MDPs and can learn rewards efficiently in two key settings: tabular MDPs and linear MDPs. When N is large and the rank is constant, the sample complexity per MDP depends logarithmically over the size of the state-space, which represents an exponential reduction (in the state-space size) when compared to the standard ``non-collaborative'' algorithms.

Test-time adaptation (TTA) fine-tunes pre-trained deep neural networks for unseen test data. The primary challenge of TTA is limited access to the entire test dataset during online updates, causing error accumulation. To mitigate it, TTA methods have utilized the model output's entropy as a confidence metric that aims to determine which samples have a lower likelihood of causing error. Through experimental studies, however, we observed the unreliability of entropy as a confidence metric for TTA under biased scenarios and theoretically revealed that it stems from the neglect of the influence of latent disentangled factors of data on predictions. Building upon these findings, we introduce a novel TTA method named Destroy Your Object (DeYO), which leverages a newly proposed confidence metric named Pseudo-Label Probability Difference (PLPD). PLPD quantifies the influence of the shape of an object on prediction by measuring the difference between predictions before and after applying an object-destructive transformation. DeYO consists of sample selection and sample weighting, which employ entropy and PLPD concurrently. For robust adaptation, DeYO prioritizes samples that dominantly incorporate shape information when making predictions. Our extensive experiments demonstrate the consistent superiority of DeYO over baseline methods across various scenarios, including biased and wild. Project page is publicly available at https://whitesnowdrop.github.io/DeYO/.

Software repositories provide a detailed record of software evolution by capturing developer interactions through code-related activities such as pull requests and modifications. To better understand the underlying dynamics of codebase evolution, we introduce a novel approach that integrates semantic code embeddings with opinion dynamics theory, offering a quantitative framework to analyze collaborative development processes. Our approach begins by encoding code snippets into high-dimensional vector representations using state-of-the-art code embedding models, preserving both syntactic and semantic features. These embeddings are then processed using Principal Component Analysis (PCA) for dimensionality reduction, with data normalized to ensure comparability. We model temporal evolution using the Expressed-Private Opinion (EPO) model to derive trust matrices and track opinion trajectories across development cycles. These opinion trajectories reflect the underlying dynamics of consensus formation, influence propagation, and evolving alignment (or divergence) within developer communities -- revealing implicit collaboration patterns and knowledge-sharing mechanisms that are otherwise difficult to observe. By bridging software engineering and computational social science, our method provides a principled way to quantify software evolution, offering new insights into developer influence, consensus formation, and project sustainability. We evaluate our approach on data from three prominent open-source GitHub repositories, demonstrating its ability to reveal interpretable behavioral trends and variations in developer interactions. The results highlight the utility of our framework in improving open-source project maintenance through data-driven analysis of collaboration dynamics.

Test-time adaptation (TTA) methods, which generally rely on the model's predictions (e.g., entropy minimization) to adapt the source pretrained model to the unlabeled target domain, suffer from noisy signals originating from 1) incorrect or 2) open-set predictions. Long-term stable adaptation is hampered by such noisy signals, so training models without such error accumulation is crucial for practical TTA. To address these issues, including open-set TTA, we propose a simple yet effective sample selection method inspired by the following crucial empirical finding. While entropy minimization compels the model to increase the probability of its predicted label (i.e., confidence values), we found that noisy samples rather show decreased confidence values. To be more specific, entropy minimization attempts to raise the confidence values of an individual sample's prediction, but individual confidence values may rise or fall due to the influence of signals from numerous other predictions (i.e., wisdom of crowds). Due to this fact, noisy signals misaligned with such 'wisdom of crowds', generally found in the correct signals, fail to raise the individual confidence values of wrong samples, despite attempts to increase them. Based on such findings, we filter out the samples whose confidence values are lower in the adapted model than in the original model, as they are likely to be noisy. Our method is widely applicable to existing TTA methods and improves their long-term adaptation performance in both image classification (e.g., 49.4% reduced error rates with TENT) and semantic segmentation (e.g., 11.7% gain in mIoU with TENT).

Neural networks often exhibit emergent behavior, where qualitatively new capabilities arise from scaling up the amount of parameters, training data, or training steps. One approach to understanding emergence is to find continuous progress measures that underlie the seemingly discontinuous qualitative changes. We argue that progress measures can be found via mechanistic interpretability: reverse-engineering learned behaviors into their individual components. As a case study, we investigate the recently-discovered phenomenon of ``grokking'' exhibited by small transformers trained on modular addition tasks. We fully reverse engineer the algorithm learned by these networks, which uses discrete Fourier transforms and trigonometric identities to convert addition to rotation about a circle. We confirm the algorithm by analyzing the activations and weights and by performing ablations in Fourier space. Based on this understanding, we define progress measures that allow us to study the dynamics of training and split training into three continuous phases: memorization, circuit formation, and cleanup. Our results show that grokking, rather than being a sudden shift, arises from the gradual amplification of structured mechanisms encoded in the weights, followed by the later removal of memorizing components.

The rapid evolution of Large Language Models has catalyzed a surge in scientific idea production, yet this leap has not been accompanied by a matching advance in idea evaluation. The fundamental nature of scientific evaluation needs knowledgeable grounding, collective deliberation, and multi-criteria decision-making. However, existing idea evaluation methods often suffer from narrow knowledge horizons, flattened evaluation dimensions, and the inherent bias in LLM-as-a-Judge. To address these, we regard idea evaluation as a knowledge-grounded, multi-perspective reasoning problem and introduce InnoEval, a deep innovation evaluation framework designed to emulate human-level idea assessment. We apply a heterogeneous deep knowledge search engine that retrieves and grounds dynamic evidence from diverse online sources. We further achieve review consensus with an innovation review board containing reviewers with distinct academic backgrounds, enabling a multi-dimensional decoupled evaluation across multiple metrics. We construct comprehensive datasets derived from authoritative peer-reviewed submissions to benchmark InnoEval. Experiments demonstrate that InnoEval can consistently outperform baselines in point-wise, pair-wise, and group-wise evaluation tasks, exhibiting judgment patterns and consensus highly aligned with human experts.

Multi-agent systems composed of large generative models are rapidly moving from laboratory prototypes to real-world deployments, where they jointly plan, negotiate, and allocate shared resources to solve complex tasks. While such systems promise unprecedented scalability and autonomy, their collective interaction also gives rise to failure modes that cannot be reduced to individual agents. Understanding these emergent risks is therefore critical. Here, we present a pioneer study of such emergent multi-agent risk in workflows that involve competition over shared resources (e.g., computing resources or market share), sequential handoff collaboration (where downstream agents see only predecessor outputs), collective decision aggregation, and others. Across these settings, we observe that such group behaviors arise frequently across repeated trials and a wide range of interaction conditions, rather than as rare or pathological cases. In particular, phenomena such as collusion-like coordination and conformity emerge with non-trivial frequency under realistic resource constraints, communication protocols, and role assignments, mirroring well-known pathologies in human societies despite no explicit instruction. Moreover, these risks cannot be prevented by existing agent-level safeguards alone. These findings expose the dark side of intelligent multi-agent systems: a social intelligence risk where agent collectives, despite no instruction to do so, spontaneously reproduce familiar failure patterns from human societies.

There are a variety of mechanisms (i.e., input types) for real-time human interaction that can facilitate effective human-robot teaming. For example, previous works have shown how teleoperation, corrective, and discrete (i.e., preference over a small number of choices) input can enable robots to complete complex tasks. However, few previous works have looked at combining different methods, and in particular, opportunities for a robot to estimate and elicit the most effective form of assistance given its understanding of a task. In this paper, we propose a method for estimating the value of different human assistance mechanisms based on the action uncertainty of a robot policy. Our key idea is to construct mathematical expressions for the expected post-interaction differential entropy (i.e., uncertainty) of a stochastic robot policy to compare the expected value of different interactions. As each type of human input imposes a different requirement for human involvement, we demonstrate how differential entropy estimates can be combined with a likelihood penalization approach to effectively balance feedback informational needs with the level of required input. We demonstrate evidence of how our approach interfaces with emergent learning models (e.g., a diffusion model) to produce accurate assistance value estimates through both simulation and a robot user study. Our user study results indicate that the proposed approach can enable task completion with minimal human feedback for uncertain robot behaviors.

We present DYMAG, a graph neural network based on a novel form of message aggregation. Standard message-passing neural networks, which often aggregate local neighbors via mean-aggregation, can be regarded as convolving with a simple rectangular waveform which is non-zero only on 1-hop neighbors of every vertex. Here, we go beyond such local averaging. We will convolve the node features with more sophisticated waveforms generated using dynamics such as the heat equation, wave equation, and the Sprott model (an example of chaotic dynamics). Furthermore, we use snapshots of these dynamics at different time points to create waveforms at many effective scales. Theoretically, we show that these dynamic waveforms can capture salient information about the graph including connected components, connectivity, and cycle structures even with no features. Empirically, we test DYMAG on both real and synthetic benchmarks to establish that DYMAG outperforms baseline models on recovery of graph persistence, generating parameters of random graphs, as well as property prediction for proteins, molecules and materials. Our code is available at https://github.com/KrishnaswamyLab/DYMAG.

The emergent collective motion of active agents - in particular pedestrians - at a three-way intersection is studied by Langevin simulations of cognitive intelligent active Brownian particles (iABPs) with directed visual perception and self-steering avoidance. Depending on the maneuverability Omega, the goal fixation K, and the vision angle psi, different types of pedestrian motion emerge. At intermediate relative maneuverability Delta = Omega/K and large psi, pedestrians have noisy trajectories due to multiple scattering events as they encounter other pedestrians in their field of view. For psi = pi and large relative maneuverability Delta, an effectively jammed state is found, which belongs to the percolation universality class. For small psi, agents exhibit localised clustering and flocking, while for intermediate psi self-organized rotational flows can emerge. The analysis of mean squared displacement and velocity auto-correlation of the agents reveals that the motion is well described by fractional Brownian Motion with positively correlated noise. Finally, despite the rich variety of collective behaviour, the fundamental flow diagram for the three-way-crossing setup shows a universal curve for the different vision angles. Our research provides valuable insights into the importance of vision angle and self-steering avoidance on pedestrian dynamics in semi-dense crowds.

Based on the theory of homogeneous spaces we derive geometrically optimal edge attributes to be used within the flexible message-passing framework. We formalize the notion of weight sharing in convolutional networks as the sharing of message functions over point-pairs that should be treated equally. We define equivalence classes of point-pairs that are identical up to a transformation in the group and derive attributes that uniquely identify these classes. Weight sharing is then obtained by conditioning message functions on these attributes. As an application of the theory, we develop an efficient equivariant group convolutional network for processing 3D point clouds. The theory of homogeneous spaces tells us how to do group convolutions with feature maps over the homogeneous space of positions R^3, position and orientations R^3 {times} S^2, and the group SE(3) itself. Among these, R^3 {times} S^2 is an optimal choice due to the ability to represent directional information, which R^3 methods cannot, and it significantly enhances computational efficiency compared to indexing features on the full SE(3) group. We support this claim with state-of-the-art results -- in accuracy and speed -- on five different benchmarks in 2D and 3D, including interatomic potential energy prediction, trajectory forecasting in N-body systems, and generating molecules via equivariant diffusion models.

We introduce a distributed algorithm, termed noise-robust distributed maximum consensus (RD-MC), for estimating the maximum value within a multi-agent network in the presence of noisy communication links. Our approach entails redefining the maximum consensus problem as a distributed optimization problem, allowing a solution using the alternating direction method of multipliers. Unlike existing algorithms that rely on multiple sets of noise-corrupted estimates, RD-MC employs a single set, enhancing both robustness and efficiency. To further mitigate the effects of link noise and improve robustness, we apply moving averaging to the local estimates. Through extensive simulations, we demonstrate that RD-MC is significantly more robust to communication link noise compared to existing maximum-consensus algorithms.

Multi-agent systems (MAS) can substantially extend the reasoning capacity of large language models (LLMs), yet most frameworks still aggregate agent outputs with majority voting. This heuristic discards the evidential structure of reasoning traces and is brittle under the confabulation consensus, where agents share correlated biases and converge on the same incorrect rationale. We introduce AgentAuditor, which replaces voting with a path search over a Reasoning Tree that explicitly represents agreements and divergences among agent traces. AgentAuditor resolves conflicts by comparing reasoning branches at critical divergence points, turning global adjudication into efficient, localized verification. We further propose Anti-Consensus Preference Optimization (ACPO), which trains the adjudicator on majority-failure cases and rewards evidence-based minority selections over popular errors. AgentAuditor is agnostic to MAS setting, and we find across 5 popular settings that it yields up to 5% absolute accuracy improvement over a majority vote, and up to 3% over using LLM-as-Judge.

This paper analyzes Cross-Entropy (CE) loss in knowledge distillation (KD) for recommender systems. KD for recommender systems targets at distilling rankings, especially among items most likely to be preferred, and can only be computed on a small subset of items. Considering these features, we reveal the connection between CE loss and NDCG in the field of KD. We prove that when performing KD on an item subset, minimizing CE loss maximizes the lower bound of NDCG, only if an assumption of closure is satisfied. It requires that the item subset consists of the student's top items. However, this contradicts our goal of distilling rankings of the teacher's top items. We empirically demonstrate the vast gap between these two kinds of top items. To bridge the gap between our goal and theoretical support, we propose Rejuvenated Cross-Entropy for Knowledge Distillation (RCE-KD). It splits the top items given by the teacher into two subsets based on whether they are highly ranked by the student. For the subset that defies the condition, a sampling strategy is devised to use teacher-student collaboration to approximate our assumption of closure. We also combine the losses on the two subsets adaptively. Extensive experiments demonstrate the effectiveness of our method. Our code is available at https://github.com/BDML-lab/RCE-KD.

The uniform information density (UID) hypothesis states that humans tend to distribute information roughly evenly across an utterance or discourse. Early evidence in support of the UID hypothesis came from Genzel & Charniak (2002), which proposed an entropy rate constancy principle based on the probability of English text under n-gram language models. We re-evaluate the claims of Genzel & Charniak (2002) with neural language models, failing to find clear evidence in support of entropy rate constancy. We conduct a range of experiments across datasets, model sizes, and languages and discuss implications for the uniform information density hypothesis and linguistic theories of efficient communication more broadly.

We study an online learning problem in general-sum Stackelberg games, where players act in a decentralized and strategic manner. We study two settings depending on the type of information for the follower: (1) the limited information setting where the follower only observes its own reward, and (2) the side information setting where the follower has extra side information about the leader's reward. We show that for the follower, myopically best responding to the leader's action is the best strategy for the limited information setting, but not necessarily so for the side information setting -- the follower can manipulate the leader's reward signals with strategic actions, and hence induce the leader's strategy to converge to an equilibrium that is better off for itself. Based on these insights, we study decentralized online learning for both players in the two settings. Our main contribution is to derive last-iterate convergence and sample complexity results in both settings. Notably, we design a new manipulation strategy for the follower in the latter setting, and show that it has an intrinsic advantage against the best response strategy. Our theories are also supported by empirical results.

The pervasiveness of proprietary language models has raised critical privacy concerns, necessitating advancements in private inference (PI), where computations are performed directly on encrypted data without revealing users' sensitive information. While PI offers a promising solution, its practical deployment is hindered by substantial communication and latency overheads, primarily stemming from nonlinear operations. To address this, we introduce an information-theoretic framework to characterize the role of nonlinearities in decoder-only language models, laying a principled foundation for optimizing transformer-architectures tailored to the demands of PI. By leveraging Shannon's entropy as a quantitative measure, we uncover the previously unexplored dual significance of nonlinearities: beyond ensuring training stability, they are crucial for maintaining attention head diversity. Specifically, we find that their removal triggers two critical failure modes: {\em entropy collapse} in deeper layers that destabilizes training, and {\em entropic overload} in earlier layers that leads to under-utilization of Multi-Head Attention's (MHA) representational capacity. We propose an entropy-guided attention mechanism paired with a novel entropy regularization technique to mitigate entropic overload. Additionally, we explore PI-friendly alternatives to layer normalization for preventing entropy collapse and stabilizing the training of LLMs with reduced-nonlinearities. Our study bridges the gap between information theory and architectural design, establishing entropy dynamics as a principled guide for developing efficient PI architectures. The code and implementation are available at https://github.com/Nandan91/entropy-guided-attention-llm{entropy-guided-llm}.

RL (reinforcement learning) methods (e.g., GRPO) for MLLM (Multimodal LLM) perception ability has attracted wide research interest owing to its remarkable generalization ability. Nevertheless, existing reinforcement learning methods still face the problem of low data quality, where data samples cannot elicit diverse responses from MLLMs, thus restricting the exploration scope for MLLM reinforcement learning. Some methods attempt to mitigate this problem by imposing constraints on entropy, but none address it at its root. Therefore, to tackle this problem, this work proposes Syn-GRPO (Synthesis-GRPO), which employs an online data generator to synthesize high-quality training data with diverse responses in GRPO training. Specifically, Syn-GRPO consists of two components: (1) data server; (2) GRPO workflow. The data server synthesizes new samples from existing ones using an image generation model, featuring a decoupled and asynchronous scheme to achieve high generation efficiency. The GRPO workflow provides the data server with the new image descriptions, and it leverages a diversity reward to supervise the MLLM to predict image descriptions for synthesizing samples with diverse responses. Experiment results across three visual perception tasks demonstrate that Syn-GRPO improves the data quality by a large margin, achieving significant superior performance to existing MLLM perception methods, and Syn-GRPO presents promising potential for scaling long-term self-evolving RL. Our code is available at https://github.com/hqhQAQ/Syn-GRPO.

RAG systems are increasingly deployed in high-stakes domains where users expect outputs to be consistent across semantically equivalent queries. However, existing systems often exhibit significant inconsistencies due to variability in both the retriever and generator (LLM), undermining trust and reliability. In this work, we focus on information consistency, i.e., the requirement that outputs convey the same core content across semantically equivalent inputs. We introduce a principled evaluation framework that decomposes RAG consistency into retriever-level, generator-level, and end-to-end components, helping identify inconsistency sources. To improve consistency, we propose Paraphrased Set Group Relative Policy Optimization (PS-GRPO), an RL approach that leverages multiple rollouts across paraphrased set to assign group similarity rewards. We leverage PS-GRPO to achieve Information Consistent RAG (Con-RAG), training the generator to produce consistent outputs across paraphrased queries and remain robust to retrieval-induced variability. Because exact reward computation over paraphrase sets is computationally expensive, we also introduce a scalable approximation method that retains effectiveness while enabling efficient, large-scale training. Empirical evaluations across short-form, multi-hop, and long-form QA benchmarks demonstrate that Con-RAG significantly improves both consistency and accuracy over strong baselines, even in the absence of explicit ground-truth supervision. Our work provides practical solutions for evaluating and building reliable RAG systems for safety-critical deployments.

Large Language Model-based Multi-Agent Systems (LLM-MAS) are increasingly applied to complex collaborative scenarios. However, their collaborative mechanisms may cause minor inaccuracies to gradually solidify into system-level false consensus through iteration. Such risks are difficult to trace since errors can propagate and amplify through message dependencies. Existing protections often rely on single-agent validation or require modifications to the collaboration architecture, which can weaken effective information flow and may not align with natural collaboration processes in real tasks. To address this, we propose a propagation dynamics model tailored for LLM-MAS that abstracts collaboration as a directed dependency graph and provides an early-stage risk criterion to characterize amplification risk. Through experiments on six mainstream frameworks, we identify three vulnerability classes: cascade amplification, topological sensitivity, and consensus inertia. We further instantiate an attack where injecting just a single atomic error seed leads to widespread failure. In response, we introduce a genealogy-graph-based governance layer, implemented as a message-layer plugin, that suppresses both endogenous and exogenous error amplification without altering the collaboration architecture. Experiments show that this approach raises the defense success rate from a baseline of 0.32 to over 0.89 and significantly mitigates the cascading spread of minor errors.

Multiple robots could perceive a scene (e.g., detect objects) collaboratively better than individuals, although easily suffer from adversarial attacks when using deep learning. This could be addressed by the adversarial defense, but its training requires the often-unknown attacking mechanism. Differently, we propose ROBOSAC, a novel sampling-based defense strategy generalizable to unseen attackers. Our key idea is that collaborative perception should lead to consensus rather than dissensus in results compared to individual perception. This leads to our hypothesize-and-verify framework: perception results with and without collaboration from a random subset of teammates are compared until reaching a consensus. In such a framework, more teammates in the sampled subset often entail better perception performance but require longer sampling time to reject potential attackers. Thus, we derive how many sampling trials are needed to ensure the desired size of an attacker-free subset, or equivalently, the maximum size of such a subset that we can successfully sample within a given number of trials. We validate our method on the task of collaborative 3D object detection in autonomous driving scenarios.

We discovered the underlying physics in Next-token Prediction (NTP). We identified the law of information conservation within NTP and proposed the First Law of Information Capacity (IC-1), demonstrating that the essence of intelligence emergence in auto-regressive models is fundamentally a process of information transfer. We also introduced Landauer's Principle into NTP, formulating the Second Law of Information Capacity (IC-2), which establishes the relationship between auto-regressive model training and energy consumption. Additionally, we presented several corollaries, which hold practical significance for production practices. Finally, we validated the compatibility and complementarity of our findings with existing theories.

Society is characterized by the presence of a variety of social norms: collective patterns of sanctioning that can prevent miscoordination and free-riding. Inspired by this, we aim to construct learning dynamics where potentially beneficial social norms can emerge. Since social norms are underpinned by sanctioning, we introduce a training regime where agents can access all sanctioning events but learning is otherwise decentralized. This setting is technologically interesting because sanctioning events may be the only available public signal in decentralized multi-agent systems where reward or policy-sharing is infeasible or undesirable. To achieve collective action in this setting we construct an agent architecture containing a classifier module that categorizes observed behaviors as approved or disapproved, and a motivation to punish in accord with the group. We show that social norms emerge in multi-agent systems containing this agent and investigate the conditions under which this helps them achieve socially beneficial outcomes.

Current label-free RLVR approaches for large language models (LLMs), such as TTRL and Self-reward, have demonstrated effectiveness in improving the performance of LLMs on complex reasoning tasks. However, these methods rely heavily on accurate pseudo-label estimation and converge on spurious yet popular answers, thereby trapping in a dominant mode and limiting further improvements. Building on this, we propose Dual Consensus Reinforcement Learning (DCRL), a novel self-supervised training method which is capable of generating more reliable learning signals through a two-stage consensus mechanism. The model initially acts as an anchor, producing dominant responses; then it serves as an explorer, generating diverse auxiliary signals via a temporary unlearning process. The final training target is derived from the harmonic mean of these two signal sets. Notably, the process operates entirely without external models or supervision. Across eight benchmarks and diverse domains, DCRL consistently improves Pass@1 over majority vote while yielding more stable training dynamics. These results demonstrate that DCRL establishes a scalable path toward stronger reasoning without labels.

As large language models (LLMs) become integral to multi-agent systems, new privacy risks emerge that extend beyond memorization, direct inference, or single-turn evaluations. In particular, seemingly innocuous responses, when composed across interactions, can cumulatively enable adversaries to recover sensitive information, a phenomenon we term compositional privacy leakage. We present the first systematic study of such compositional privacy leaks and possible mitigation methods in multi-agent LLM systems. First, we develop a framework that models how auxiliary knowledge and agent interactions jointly amplify privacy risks, even when each response is benign in isolation. Next, to mitigate this, we propose and evaluate two defense strategies: (1) Theory-of-Mind defense (ToM), where defender agents infer a questioner's intent by anticipating how their outputs may be exploited by adversaries, and (2) Collaborative Consensus Defense (CoDef), where responder agents collaborate with peers who vote based on a shared aggregated state to restrict sensitive information spread. Crucially, we balance our evaluation across compositions that expose sensitive information and compositions that yield benign inferences. Our experiments quantify how these defense strategies differ in balancing the privacy-utility trade-off. We find that while chain-of-thought alone offers limited protection to leakage (~39% sensitive blocking rate), our ToM defense substantially improves sensitive query blocking (up to 97%) but can reduce benign task success. CoDef achieves the best balance, yielding the highest Balanced Outcome (79.8%), highlighting the benefit of combining explicit reasoning with defender collaboration. Together, our results expose a new class of risks in collaborative LLM deployments and provide actionable insights for designing safeguards against compositional, context-driven privacy leakage.

We propose a novel speculative decoding method tailored for multi-sample reasoning scenarios, such as self-consistency and Best-of-N sampling. Our method exploits the intrinsic consensus of parallel generation paths to synthesize high-quality draft tokens without requiring auxiliary models or external databases. By dynamically analyzing structural patterns across parallel reasoning paths through a probabilistic aggregation mechanism, it identifies consensus token sequences that align with the decoding distribution. Evaluations on mathematical reasoning benchmarks demonstrate a substantial improvement in draft acceptance rates over baselines, while reducing the latency in draft token construction. This work establishes a paradigm shift for efficient multi-sample inference, enabling seamless integration of speculative decoding with sampling-based reasoning techniques.

In contrast to entropy, which increases monotonically, the "complexity" or "interestingness" of closed systems seems intuitively to increase at first and then decrease as equilibrium is approached. For example, our universe lacked complex structures at the Big Bang and will also lack them after black holes evaporate and particles are dispersed. This paper makes an initial attempt to quantify this pattern. As a model system, we use a simple, two-dimensional cellular automaton that simulates the mixing of two liquids ("coffee" and "cream"). A plausible complexity measure is then the Kolmogorov complexity of a coarse-grained approximation of the automaton's state, which we dub the "apparent complexity." We study this complexity measure, and show analytically that it never becomes large when the liquid particles are non-interacting. By contrast, when the particles do interact, we give numerical evidence that the complexity reaches a maximum comparable to the "coffee cup's" horizontal dimension. We raise the problem of proving this behavior analytically.

Token-level reweighting is a simple yet effective mechanism for controlling supervised fine-tuning, but common indicators are largely one-dimensional: the ground-truth probability reflects downstream alignment, while token entropy reflects intrinsic uncertainty induced by the pre-training prior. Ignoring entropy can misidentify noisy or easily replaceable tokens as learning-critical, while ignoring probability fails to reflect target-specific alignment. RankTuner introduces a probability--entropy calibration signal, the Relative Rank Indicator, which compares the rank of the ground-truth token with its expected rank under the prediction distribution. The inverse indicator is used as a token-wise Relative Scale to reweight the fine-tuning objective, focusing updates on truly under-learned tokens without over-penalizing intrinsically uncertain positions. Experiments on multiple backbones show consistent improvements on mathematical reasoning benchmarks, transfer gains on out-of-distribution reasoning, and pre code generation performance over probability-only or entropy-only reweighting baselines.

Federated learning (FL) allows mutually untrusted clients to collaboratively train a common machine learning model without sharing their private/proprietary training data among each other. FL is unfortunately susceptible to poisoning by malicious clients who aim to hamper the accuracy of the commonly trained model through sending malicious model updates during FL's training process. We argue that the key factor to the success of poisoning attacks against existing FL systems is the large space of model updates available to the clients, allowing malicious clients to search for the most poisonous model updates, e.g., by solving an optimization problem. To address this, we propose Federated Rank Learning (FRL). FRL reduces the space of client updates from model parameter updates (a continuous space of float numbers) in standard FL to the space of parameter rankings (a discrete space of integer values). To be able to train the global model using parameter ranks (instead of parameter weights), FRL leverage ideas from recent supermasks training mechanisms. Specifically, FRL clients rank the parameters of a randomly initialized neural network (provided by the server) based on their local training data. The FRL server uses a voting mechanism to aggregate the parameter rankings submitted by clients in each training epoch to generate the global ranking of the next training epoch. Intuitively, our voting-based aggregation mechanism prevents poisoning clients from making significant adversarial modifications to the global model, as each client will have a single vote! We demonstrate the robustness of FRL to poisoning through analytical proofs and experimentation. We also show FRL's high communication efficiency. Our experiments demonstrate the superiority of FRL in real-world FL settings.

Standard human preference-based alignment methods, such as Reinforcement Learning from Human Feedback (RLHF), are a cornerstone technology for aligning Large Language Models (LLMs) with human values. However, these methods are all underpinned by a critical, yet flawed assumption: human preferences are homogeneous (representing a single, unified preference) and the collected data is noiseless (free from error). In reality, neither is true since human preference is pluralistic and annotators can make mistakes. This creates a discrepancy between the recorded data and the ground-truth preferences, which can misguide the model and degrade its performance. To address this challenge, we introduce Latent Collective Preference Optimization (LCPO). LCPO leverages an Expectation-Maximization (EM) algorithm to learn the latent collective consensus from noisy data. It operates by inferring the correctness of each preference label and using this probability as an adaptive weight to re-calibrate each data point's contribution to the training loss, thereby mitigating noise. We generalize this approach by establishing a theoretical link between arbitrary preference losses and their corresponding probabilistic models, elevating LCPO from a specific algorithm to a general framework for robust preference alignment. Theoretically, we prove that under the condition of a perfectly calibrated model, LCPO is guaranteed to converge to the true noise level of the dataset. Our experiments demonstrate LCPO's effectiveness as a general framework, consistently enhancing four state-of-the-art alignment algorithms (DPO, IPO, SimPO, and CPO). When applied to Mistral and Llama 3 models, the LCPO-enhanced methods achieve substantial win rate gains on AlpacaEval 2 and Arena-Hard, with improvements of up to 7.0% on both benchmarks.

Federated and decentralized machine learning leverage end-user devices for privacy-preserving training of models at lower operating costs than within a data center. In a round of Federated Learning (FL), a random sample of participants trains locally, then a central server aggregates the local models to produce a single model for the next round. In a round of Decentralized Learning (DL), all participants train locally and then aggregate with their immediate neighbors, resulting in many local models with residual variance between them. On the one hand, FL's sampling and lower model variance provides lower communication costs and faster convergence. On the other hand, DL removes the need for a central server and distributes the communication costs more evenly amongst nodes, albeit at a larger total communication cost and slower convergence. In this paper, we present MoDeST: Mostly-Consistent Decentralized Sampling Training. MoDeST implements decentralized sampling in which a random subset of nodes is responsible for training and aggregation every round: this provides the benefits of both FL and DL without their traditional drawbacks. Our evaluation of MoDeST on four common learning tasks: (i) confirms convergence as fast as FL, (ii) shows a 3x-14x reduction in communication costs compared to DL, and (iii) demonstrates that MoDeST quickly adapts to nodes joining, leaving, or failing, even when 80% of all nodes become unresponsive.

We introduce a method to measure uncertainty in large language models. For tasks like question answering, it is essential to know when we can trust the natural language outputs of foundation models. We show that measuring uncertainty in natural language is challenging because of "semantic equivalence" -- different sentences can mean the same thing. To overcome these challenges we introduce semantic entropy -- an entropy which incorporates linguistic invariances created by shared meanings. Our method is unsupervised, uses only a single model, and requires no modifications to off-the-shelf language models. In comprehensive ablation studies we show that the semantic entropy is more predictive of model accuracy on question answering data sets than comparable baselines.

Entropy regularization is a standard technique in reinforcement learning (RL) to enhance exploration, yet it yields negligible effects or even degrades performance in Large Language Models (LLMs). We attribute this failure to the cumulative tail risk inherent to LLMs with massive vocabularies and long generation horizons. In such environments, standard global entropy maximization indiscriminately dilutes probability mass into the vast tail of invalid tokens rather than focusing on plausible candidates, thereby disrupting coherent reasoning. To address this, we propose Trust Region Entropy (TRE), a method that encourages exploration strictly within the model's trust region. Extensive experiments across mathematical reasoning (MATH), combinatorial search (Countdown), and preference alignment (HH) tasks demonstrate that TRE consistently outperforms vanilla PPO, standard entropy regularization, and other exploration baselines. Our code is available at https://github.com/WhyChaos/TRE-Encouraging-Exploration-in-the-Trust-Region.

Label-free reinforcement learning enables large language models to improve reasoning capabilities without ground-truth supervision, typically by treating majority-voted answers as pseudo-labels. However, we identify a critical failure mode: as training maximizes self-consistency, output diversity collapses, causing the model to confidently reinforce systematic errors that evade detection. We term this the consensus trap. To escape it, we propose CoVerRL, a framework where a single model alternates between generator and verifier roles, with each capability bootstrapping the other. Majority voting provides noisy but informative supervision for training the verifier, while the improving verifier progressively filters self-consistent errors from pseudo-labels. This co-evolution creates a virtuous cycle that maintains high reward accuracy throughout training. Experiments across Qwen and Llama model families demonstrate that CoVerRL outperforms label-free baselines by 4.7-5.9\% on mathematical reasoning benchmarks. Moreover, self-verification accuracy improves from around 55\% to over 85\%, confirming that both capabilities genuinely co-evolve.

We introduce the concurrent shuffle model of differential privacy. In this model we have multiple concurrent shufflers permuting messages from different, possibly overlapping, batches of users. Similarly to the standard (single) shuffle model, the privacy requirement is that the concatenation of all shuffled messages should be differentially private. We study the private continual summation problem (a.k.a. the counter problem) and show that the concurrent shuffle model allows for significantly improved error compared to a standard (single) shuffle model. Specifically, we give a summation algorithm with error O(n^{1/(2k+1)}) with k concurrent shufflers on a sequence of length n. Furthermore, we prove that this bound is tight for any k, even if the algorithm can choose the sizes of the batches adaptively. For k=log n shufflers, the resulting error is polylogarithmic, much better than Theta(n^{1/3}) which we show is the smallest possible with a single shuffler. We use our online summation algorithm to get algorithms with improved regret bounds for the contextual linear bandit problem. In particular we get optimal O(n) regret with k= Omega(log n) concurrent shufflers.

Understanding geometric properties of natural language processing models' latent spaces allows the manipulation of these properties for improved performance on downstream tasks. One such property is the amount of data spread in a model's latent space, or how fully the available latent space is being used. In this work, we define data spread and demonstrate that the commonly used measures of data spread, Average Cosine Similarity and a partition function min/max ratio I(V), do not provide reliable metrics to compare the use of latent space across models. We propose and examine eight alternative measures of data spread, all but one of which improve over these current metrics when applied to seven synthetic data distributions. Of our proposed measures, we recommend one principal component-based measure and one entropy-based measure that provide reliable, relative measures of spread and can be used to compare models of different sizes and dimensionalities.

Machine learning algorithms relying on deep neural networks recently allowed a great leap forward in artificial intelligence. Despite the popularity of their applications, the efficiency of these algorithms remains largely unexplained from a theoretical point of view. The mathematical description of learning problems involves very large collections of interacting random variables, difficult to handle analytically as well as numerically. This complexity is precisely the object of study of statistical physics. Its mission, originally pointed towards natural systems, is to understand how macroscopic behaviors arise from microscopic laws. Mean-field methods are one type of approximation strategy developed in this view. We review a selection of classical mean-field methods and recent progress relevant for inference in neural networks. In particular, we remind the principles of derivations of high-temperature expansions, the replica method and message passing algorithms, highlighting their equivalences and complementarities. We also provide references for past and current directions of research on neural networks relying on mean-field methods.

Large language models perform near-Bayesian inference yet violate permutation invariance on exchangeable data. We resolve this by showing transformers minimize expected conditional description length (cross-entropy) over orderings, E_pi[ell(Y mid Gamma_pi(X))], which admits a Kolmogorov-complexity interpretation up to additive constants, rather than the permutation-invariant description length ell(Y mid X). This makes them Bayesian in expectation, not in realization. We derive (i) a Quantified Martingale Violation bound showing order-induced deviations scale as O(log n) with constants; (ii) the Expectation-level Decompression Law linking information budgets to reliability for Bernoulli predicates; and (iii) deployable planners (B2T/RoH/ISR) for answer/abstain decisions. Empirically, permutation dispersion follows a+bln n (Qwen2-7B b approx 0.377, Llama-3.1-8B b approx 0.147); permutation mixtures improve ground-truth likelihood/accuracy; and randomized dose-response shows hallucinations drop by sim 0.13 per additional nat. A pre-specified audit with a fixed ISR=1.0 achieves near-0\% hallucinations via calibrated refusal at 24\% abstention. The framework turns hallucinations into predictable compression failures and enables principled information budgeting.