This paper investigates the entropy dynamics of Chain-of-Thought (CoT) and uncovers a consistent two-phase structure: an ***Uncertainty Region*** of exploration transitioning sharply to a ***Confidence Region*** of convergence. We demonstrate that the Confidence Region possesses two critical properties: 1) ***High Reliability***—answers in confidence region become highly accurate and stable, and 2) ***High Redundancy***—models generate unnecessary tokens long after reaching the correct answer. These properties unlock more efficient and reliable inference strategies: 1) ***Early Exit*** leverages reliability and redundancy to terminate computation safely when returns diminish, and 2) ***Test-Time Scaling*** uses the Confidence Region signal to prioritize converged trajectories. To operationalize these insights, we formulate Confidence Region detection as a sequential change-point detection problem, being the first to apply classical change-point methods to monitor CoT reasoning. Using the Cumulative Sum (CUSUM) algorithm, a statistically optimal change-point detector, we develop a training-free framework for real-time inference control. Experiments show our approach establishes a superior Pareto-frontier for early exit. CUSUM achieves 63.06% accuracy with 11.1% token reduction, outperforming DEER and Dynasor by 3.28% and 4.36% in accuracy respectively. For test-time scaling, CUSUM-weighted voting consistently outperforms self-consistency.
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General Machine Learning · Unsupervised and Semi-supervised Learning
The goal of single-channel source separation is to reconstruct $K$ sources given their mixture. In supervised settings where vast amounts of clean source data are available, this challenging, ill-posed problem has been addressed successfully by generative diffusion and flow-based prior models. However, access to such clean source samples is often limited. To bridge this gap, we present Separation via Unsupervised Remixing Flow (\textbf{SURF}), an unsupervised flow matching approach for source separation that learns directly from observed mixtures. This method relies on a novel combination of state-of-the-art supervised flow matching and regression-based self-supervised techniques. At a high level, starting from a teacher model, we utilize a ``remixing'' step to bootstrap the learning of a student flow model from the teacher's estimates. We provide insights into the objectives optimized by this approach and draw a novel connection to the Wake-Sleep algorithm. Empirical evaluations on image and audio benchmarks demonstrate that \textbf{SURF} establishes a new state-of-the-art, significantly outperforming existing unsupervised methods.
Deep Learning · Large Language Models
Alignment of large language models remains a central challenge in natural language processing. Preference optimization has emerged as a popular and effective method for improving alignment, typically through training-time or prompt-based interventions. In this paper, we introduce alignment-aware decoding (AAD), a method to enhance model alignment directly at inference. Theoretically, AAD can be interpreted as implicit reward optimization, yet it requires no specialized training beyond the standard DPO setup. Empirically, AAD consistently outperforms strong baselines across diverse alignment benchmarks and model scales. Moreover, in data-constrained settings, AAD can produce high-quality synthetic data to improve alignment under standard decoding, providing a practical solution when labeled data is limited.
Theory · Optimization
We present learning-augmented algorithms for two general classes of online minimization problems: metrical task systems and laminar set cover. Both algorithms achieve improved theoretical guarantees using machine-learned predictions of an optimal solution to the dual linear program. Unlike optimal primal solutions, which can change drastically under tiny instance perturbations, these dual solutions are much more stable, which ensures the existence of good (and learnable) predictions for families of similar instances. While previous work has used dual predictions in offline settings and for online maximization problems, our algorithms are, to the best of our knowledge, the first demonstration that such dual predictions can be effective for online minimization. Our theoretical results are complemented by experiments on the $k$-server problem and the parking permit problem.
Deep Learning · Large Language Models
Linear attention architectures based on the Delta rule, such as DeltaNet and RWKV-7, combine Transformers' training scalability with RNNs' inference efficiency and can provably solve regular language tasks. However, due to their fixed-size state, these models fundamentally struggle to capture the recursive, hierarchical structures that are intrinsic to natural languages. To bridge this gap, we introduce DeltaStack, a novel architecture that augments the associative memory of DeltaNet with a lightweight, differentiable stack. Unlike prior stack-augmented approaches that rely on sequential recurrence, DeltaStack formulates stack operations as linear delta-rule updates. This novel formulation enables a hardware-aware implementation that is fully parallelizable over sequence length, preserving the training efficiency of linear transformers. Theoretically, we prove that DeltaStack extends the expressivity of DeltaNet to model both regular and hierarchical languages. Empirically, our method outperforms DeltaNet and Stack-Attention on comprehensive formal language benchmarks. Furthermore, a 340M-parameter DeltaStack model trained on 15B tokens surpasses strong DeltaNet baselines in both perplexity and zero-shot downstream performance.
Deep Learning · Generative Models and Autoencoders
Training-free diffusion guidance offers a flexible framework for leveraging off-the-shelf classifiers without additional training. Yet, current approaches hinge on posterior approximations via Tweedie’s formula, which often yield unreliable guidance, particularly in low-density regions. Stochastic optimal control (SOC), in contrast, enables principled posterior sampling but remains computationally prohibitive for efficient inference. In this work, we reconcile the strengths of these paradigms by introducing Stein Diffusion Guidance (SDG), a novel training-free framework grounded in a surrogate SOC objective. We establish a new theoretical bound on the SOC value function, revealing the necessity of correcting approximate posteriors to reflect true diffusion dynamics. Building on Stein variational inference, SDG computes the steepest descent direction that minimizes the Kullback-Leibler divergence between approximate and true posteriors. By integrating a principled Stein correction mechanism along with a novel running cost functional, SDG enables effective guidance in low-density regions. Our experiments on diverse image-guidance tasks and on challenging small-ligand sampling for protein docking suggest that SDG consistently outperforms standard training-free guidance methods and highlights its potential for broader posterior sampling problems beyond high-density regimes.
Deep Learning · Large Language Models
Retrieval augmented generation (RAG) has enhanced large language models by enabling access to external knowledge, with graph-based RAG emerging as a powerful paradigm for structured retrieval and reasoning. However, existing graph-based methods often over-rely on surface-level node matching and lack explicit causal modeling, leading to unfaithful or spurious answers. Prior attempts to incorporate causality are typically limited to local or single-document contexts and also suffer from information isolation that arises from modular graph structures, which hinders scalability and cross-module causal reasoning. To address these challenges, we propose HugRAG, a framework that rethinks knowledge organization for graph-based RAG through causal gating across hierarchical modules. HugRAG explicitly models causal relationships to suppress spurious correlations while enabling scalable reasoning over large-scale knowledge graphs. Extensive experiments demonstrate that HugRAG consistently outperforms competitive graph-based RAG baselines across multiple datasets and evaluation metrics. Our work establishes a principled foundation for structured, scalable, and causally grounded RAG systems.
Deep Learning · Large Language Models
We study the in-context universal approximation and compositional generalization of softmax Transformers. We prove an in-context universality result: a fixed-weight softmax Transformer approximates a broad class of continuous sequence-to-sequence functions. Building on this universality, we establish a composition theorem: by concatenating prompts associated with simple ``subprograms,'' the same fixed Transformer executes their composition, and thereby synthesizes more complex programs on-the-fly. These results support a principled view of prompts as programs and fixed-weight Transformers as program interpreters. Moreover, we provide a concrete mechanism by which GPT-style models both execute and assemble algorithms in context.
Deep Learning · Theory
This article initiates the study of a basic question about model pruning. Given a vector s of importance scores assigned to model components, how many of the scored components could be discarded without sacrificing performance? We propose Effective Model Pruning (EMP), which derives the desired sparsity directly from the score distribution using the notion of effective sample size from particle filtering, also known as the inverse Simpson index. Rather than prescribe a pruning criterion, EMP supplies a universal adaptive threshold derived from the distribution of the score $s$ over the model components: EMP maps $s$ to a number $N_{eff} = N_{eff} (s)$, called the effective sample size. The $N − N_{eff}$ lowest scoring components are discarded. A tight lower bound on the preserved mass fraction seff (the sum of retained normalized scores) in terms of $N_{eff}$ is derived. This process yields models with a provable upper bound on the loss change relative to the original dense model. Numerical experiments are performed demonstrating this phenomenon across a variety of network architectures including MLPs, CNNs, Transformers, LLMs, and KAN. It is also shown that EMP addresses a rich set of pruning criteria such as weight magnitude, attention score, KAN importance score, and even feature-level signals such as image pixels.
General Machine Learning · Unsupervised and Semi-supervised Learning
Verification of model outputs is rapidly emerging as a key primitive for both training and real-world deployment of large language models (LLMs). In practice, this often involves using imperfect LLM judges and reward models since ground truth acquisition can be time-consuming and expensive. We introduce Fully Unsupervised Score Ensembling (FUSE), a method for improving verification quality by ensembling verifiers without access to ground truth correctness labels. The key idea behind FUSE is to control conditional dependencies between verifiers in a manner that improves the unsupervised performance of a class of spectral algorithms from the ensembling literature. Despite requiring zero ground truth labels, FUSE typically matches or improves upon semi-supervised alternatives in test-time scaling experiments with diverse sets of generator models, verifiers, and benchmarks. In particular, we validate our method on both conventional academic benchmarks such as GPQA Diamond and on frontier, unsaturated benchmarks such as Humanity's Last Exam and IMO Shortlist questions.
General Machine Learning · Unsupervised and Semi-supervised Learning
Many methods aim to enhance the performance of vision-language models (VLMs) at test time. Among them, transduction has emerged as a promising paradigm due to its strong compatibility and efficiency. However, realistic evaluations often involve highly imbalanced class distributions, which cause performance degradation or even collapse. In this work, we systematically revisit transduction from the perspective of penalized likelihood estimation (PLE), showing that PLE with a KL-divergence anchor term naturally yields an adaptive shrinkage behavior between prior anchors and empirical estimates. From this viewpoint, the brittleness of transductive methods can be attributed to the absence of anchoring mechanism and static modeling of the shrinkage strength. Therefore, we propose Mixture of Von Mises-Fisher Models with Dynamic Shrinkage (MOON). MOON is based on a mixture of von Mises-Fisher distributions to model feature representations on the unit hypersphere. To handle imbalance, MOON dynamically adjusts the shrinkage strength using zero-shot priors at both instance and class levels. Thus, it suppresses unreliable assignments and prevents harmful updates from outlier classes, thereby mitigating negative transfer. MOON is model-agnostic, training-free, and requires no task-specific hyperparameter tuning. Extensive experiments further validate the advantage of MOON in both performance and efficiency.
General Machine Learning · Causality
We study off-policy evaluation (OPE) under strategic behavior where decision subjects (or agents) respond to a decision maker's policy by strategically modifying their covariates. Such behavior induces a policy-dependent covariate shift, breaking the standard assumption in existing methods that covariates are exogenous to the policy. Related work addresses this challenge by imposing strong assumptions such as repeated interactions or full knowledge of agents’ response behavior, substantially limiting its applicability to OPE. In contrast, we consider a one-shot OPE setting where the decision maker has only partial knowledge of the agents' response behavior. Our key insight is that disclosing local information through post-hoc explanations reveals agents’ pre-strategic covariates prior to adaptation, mitigating the information loss induced by strategic behavior. Leveraging this structure, we estimate a statistical model for the agents’ responses and construct a doubly robust estimator for policy value. By assuming that the agents' cost sensitivity follows a conditional log-normal distribution, we establish consistency of the proposed estimator and validate our approach empirically. More broadly, our results highlight how interaction design can mitigate information asymmetry by revealing otherwise hidden structure in agents' strategic responses.
Theory · Learning Theory
Performative predictions influence the very outcomes they aim to forecast. We study performative predictions that affect a sample (e.g., only existing users of an app) and/or the whole population (e.g., all potential app users). This raises the question of how well models generalize under performativity. For example, how well can we draw insights about new app users based on existing users when both of them react to the app's predictions? We address this question by embedding performative predictions into statistical learning theory. We prove generalization bounds under performative effects on the sample, on the population, and on both. A key intuition behind our proofs is that in the worst case, the population negates predictions, while the sample deceptively fulfills them. We cast such self-negating and self-fulfilling predictions as min-max and min-min risk functionals in Wasserstein space, respectively. Our analysis reveals both a fundamental trade-off between performatively changing the world and learning from it, as well as a surprising insight on how to improve generalization guarantees by retraining on performatively distorted samples. We illustrate our bounds using real data on prediction-informed assignments to job trainings.
Optimization · Large Scale, Parallel and Distributed
LLM-based multi-agent simulations are increasingly adopted across application domains, but remain difficult to scale due to GPU memory pressure. Each agent maintains private GPU-resident states, including models, prefix caches, and adapters, which quickly exhaust device memory as the agent count grows. We identify two key properties of these workloads: sparse agent activation and an estimable agent invocation order. Based on an analysis of representative workload classes, we introduce invocation distance, a unified abstraction that estimates the relative order in which agents will issue future LLM requests. Leveraging this abstraction, we present ScaleSim, a memory-efficient LLM serving system for large-scale multi-agent simulations. ScaleSim enables proactive prefetching and priority-based eviction, supports diverse agent-specific memory through a modular interface, and achieves up to 1.74$\times$ speedup over SGLang on simulation benchmarks.
Deep Learning · Large Language Models
In-context learning (ICL) is highly sensitive to which demonstrations appear in the prompt, but selecting them is expensive because candidate contexts must be validated with repeated LLM calls. We argue that demonstration selection is \emph{easier to judge than to find}: predicting whether a specific query--context pair $(q,D)$ will succeed is cheaper and more general than searching for an optimal $D^\star$. Based on this insight, we propose DiSP, a sample-and-judge framework that stratifies queries by difficulty. DiSP runs random demonstration trials to estimate each training query's success rate, trains a lightweight router to predict difficulty from the query, and trains level-specific judges to score sampled contexts. At inference, DiSP performs stop-on-acceptance judging under an explicit budget and typically makes a single LLM call, emitting diagnostic risk tags when no suitable context is found. Across five classification datasets with Llama 3–8B and Qwen 2.5–7B, DiSP achieves the best average accuracy, improving over strong learned selection baselines by up to 3.4%, while achieving up to 23× end-to-end wall-clock speedup.
Autonomous agents powered by large language models (LLMs) promise to accelerate scientific discovery, but rigorously evaluating their capacity for verifiable discovery remains a central challenge. Existing benchmarks face a trade-off: they either rely on LLM-as-judge evaluations of automatically generated papers, or optimize isolated performance metrics that provide only coarse proxies for scientific insight. To address this, we introduce FIRE-Bench (Full-cycle Insight Rediscovery Evaluation), a benchmark that evaluates agents through the rediscovery of established findings from recent, high-impact machine learning research. Agents are given only a high-level research question from a published study and must autonomously design experiments, implement code, execute their plans, and derive conclusions supported by empirical evidence. We evaluate a range of state-of-the-art agents with frontier model backbones, such as gpt-5, on FIRE-Bench. Our results show that full-cycle scientific research remains challenging for current agent systems: even the strongest agents achieve limited rediscovery success, exhibit high variance across runs, and display recurring failure modes in experimental design, execution, and evidence-based reasoning. Overall, FIRE-Bench provides a rigorous and diagnostic framework for measuring progress toward reliable agent-driven scientific discovery.
Deep Learning · Generative Models and Autoencoders
Existing diffusion models have made significant progress in generating realistic images. However, their direct adaptation to remote sensing imagery often disregards intrinsic physical laws. This oversight frequently leads to spectral distortion and radiometric inconsistency, severely limiting the scientific utility of generated data. To address this issue, this paper introduces AnyBand-Diff, a novel spectral-prior-guided diffusion framework tailored for robust spectral reconstruction. Specifically, we design a Masked Conditional Diffusion backbone integrated with a dual stochastic masking strategy, empowering the model to recover complete spectral information from arbitrary band subsets. Subsequently, to ensure radiometric fidelity, a Physics-Guided Sampling mechanism is proposed, leveraging gradients from a differentiable physical model to explicitly steer the denoising trajectory toward the manifold of physically plausible solutions. Furthermore, a Multi-Scale Physical Loss is formulated to enforce rigorous constraints across pixel, region, and global levels in a joint manner. Extensive experiments confirm the effectiveness of AnyBand-Diff in generating reliable imagery and achieving accurate spectral reconstruction, contributing to the advancement of physics-aware generative methods for Earth observation.
Reinforcement Learning · Multi-agent
LLM-based multi-agent systems (MAS) promise scalable collaboration, yet adding agents often *reduces* reliability. This position paper argues that many MAS failures are fundamentally **concurrency control problems**: agents concurrently read and write shared state, and long LLM inference windows amplify the risk of stale reads, lost updates, and inconsistent outcomes. Failure modes commonly attributed to "coordination" or "communication" breakdowns can be mapped directly onto classical concurrency anomalies. Rather than treating these as emergent behaviors to be solved by better prompting or more capable models, we contend that MAS frameworks should incorporate explicit concurrency control mechanisms: conflict detection, isolation guarantees, and structured access to shared resources. Concurrency control should be a first-class design concern, not an afterthought.
Deep Learning · Large Language Models
Reinforcement learning (RL) has demonstrated potential for enhancing reasoning in large language models (LLMs). However, effective RL training, which requires medium-difficulty training samples, faces two fundamental challenges: Effective Data Scarcity and Dynamic Difficulty Shifts, where medium-difficulty samples are scarce and become trivial as models improve. Existing methods mitigate this scarcity to some extent by generating training samples. However, these approaches suffer from anchor-free generation, ignoring co-evolution, and difficulty mismatch. To address these issues, we propose D²Evo, a Dual Difficulty-aware self-Evolution RL framework. In each iteration, our method mines medium-difficulty anchors based on the current Solver's capability, trains the Questioner to generate diverse questions at appropriate difficulty levels, and jointly optimizes both components to enable progressive reasoning gains. Extensive experiments demonstrate that D²Evo outperforms existing methods on mathematical reasoning benchmarks with fewer than 2K real mathematical samples, and exhibits strong generalization on general reasoning benchmarks.
Deep Learning · Sequential Models, Time series
Stochastic differential equations (SDEs) and stochastic partial differential equations (SPDEs) are fundamental for modeling stochastic dynamics across the natural sciences and modern machine learning. Learning their solution operators with deep learning models promises fast solvers and new perspectives on classical learning tasks. In this work, we build on Wiener–chaos expansions (WCE) to design neural operator (NO) architectures for SDEs and SPDEs: we project driving noise paths onto orthonormal Wick–Hermite features and use NOs to parameterize the resulting chaos coefficients, enabling reconstruction of full trajectories from noise in a single forward pass. We also make the underlying WCE structure explicit for multi-dimensional SDEs and semilinear SPDEs by showing the coupled deterministic ODE/PDE systems governing these coefficients. Empirically, we achieve competitive accuracy across several tasks, including standard SPDE benchmarks and SDE-based diffusion one-step image sampling, topological graph interpolation, financial extrapolation, parameter estimation, and manifold SDE flood forecasting. These results suggest WCE-based neural operators are a practical and scalable approach to learning SDE/SPDE solution operators across domains.