Daily Papers

State-of-the-art (SOTA) reinforcement learning (RL) methods enable the vision-language agents to learn from interactions with the environment without human supervision. However, they struggle with learning inefficiencies in tackling real-world complex sequential decision-making tasks, especially with sparse reward signals and long-horizon dependencies. To effectively address the issue, we introduce Variational Subgoal-Conditioned RL (VSC-RL), which reformulates the vision-language sequential decision-making task as a variational goal-conditioned RL problem, allowing us to leverage advanced optimization methods to enhance learning efficiency. Specifically, VSC-RL optimizes the SubGoal Evidence Lower BOund (SGC-ELBO), which consists of (a) maximizing the subgoal-conditioned return via RL and (b) minimizing the subgoal-conditioned difference with the reference policy. We theoretically demonstrate that SGC-ELBO is equivalent to the original optimization objective, ensuring improved learning efficiency without sacrificing performance guarantees. Additionally, for real-world complex decision-making tasks, VSC-RL leverages the vision-language model to autonomously decompose the goal into feasible subgoals, enabling efficient learning. Across various benchmarks, including challenging real-world mobile device control tasks, VSC-RL significantly outperforms the SOTA vision-language agents, achieving superior performance and remarkable improvement in learning efficiency.

The Evidence Lower Bound (ELBO) is a quantity that plays a key role in variational inference. It can also be used as a criterion in model selection. However, though extremely popular in practice in the variational Bayes community, there has never been a general theoretic justification for selecting based on the ELBO. In this paper, we show that the ELBO maximization strategy has strong theoretical guarantees, and is robust to model misspecification while most works rely on the assumption that one model is correctly specified. We illustrate our theoretical results by an application to the selection of the number of principal components in probabilistic PCA.

Formal theorem proving, a field at the intersection of mathematics and computer science, has seen renewed interest with advancements in large language models (LLMs). This paper introduces SubgoalXL, a novel approach that synergizes subgoal-based proofs with expert learning to enhance LLMs' capabilities in formal theorem proving within the Isabelle environment. SubgoalXL addresses two critical challenges: the scarcity of specialized mathematics and theorem-proving data, and the need for improved multi-step reasoning abilities in LLMs. By optimizing data efficiency and employing subgoal-level supervision, SubgoalXL extracts richer information from limited human-generated proofs. The framework integrates subgoal-oriented proof strategies with an expert learning system, iteratively refining formal statement, proof, and subgoal generators. Leveraging the Isabelle environment's advantages in subgoal-based proofs, SubgoalXL achieves a new state-of-the-art performance of 56.1\% in Isabelle on the standard miniF2F dataset, marking an absolute improvement of 4.9\%. Notably, SubgoalXL successfully solves 41 AMC12, 9 AIME, and 3 IMO problems from miniF2F. These results underscore the effectiveness of maximizing limited data utility and employing targeted guidance for complex reasoning in formal theorem proving, contributing to the ongoing advancement of AI reasoning capabilities. The implementation is available at https://github.com/zhaoxlpku/SubgoalXL.

The problems of detecting and recovering planted structures/subgraphs in Erdős-Rényi random graphs, have received significant attention over the past three decades, leading to many exciting results and mathematical techniques. However, prior work has largely focused on specific ad hoc planted structures and inferential settings, while a general theory has remained elusive. In this paper, we bridge this gap by investigating the detection of an arbitrary planted subgraph Γ= Γ_n in an Erdős-Rényi random graph G(n, q_n), where the edge probability within Γ is p_n. We examine both the statistical and computational aspects of this problem and establish the following results. In the dense regime, where the edge probabilities p_n and q_n are fixed, we tightly characterize the information-theoretic and computational thresholds for detecting Γ, and provide conditions under which a computational-statistical gap arises. Most notably, these thresholds depend on Γ only through its number of edges, maximum degree, and maximum subgraph density. Our lower and upper bounds are general and apply to any value of p_n and q_n as functions of n. Accordingly, we also analyze the sparse regime where q_n = Θ(n^{-α}) and p_n-q_n =Θ(q_n), with αin[0,2], as well as the critical regime where p_n=1-o(1) and q_n = Θ(n^{-α}), both of which have been widely studied, for specific choices of Γ. For these regimes, we show that our bounds are tight for all planted subgraphs investigated in the literature thus farand many more. Finally, we identify conditions under which detection undergoes sharp phase transition, where the boundaries at which algorithms succeed or fail shift abruptly as a function of q_n.

Large language models (LLMs) have recently demonstrated remarkable progress in formal theorem proving. Yet their ability to serve as practical assistants for mathematicians, filling in missing steps within complex proofs, remains underexplored. We identify this challenge as the task of subgoal completion, where an LLM must discharge short but nontrivial proof obligations left unresolved in a human-provided sketch. To study this problem, we introduce FormalML, a Lean 4 benchmark built from foundational theories of machine learning. Using a translation tactic that converts procedural proofs into declarative form, we extract 4937 problems spanning optimization and probability inequalities, with varying levels of difficulty. FormalML is the first subgoal completion benchmark to combine premise retrieval and complex research-level contexts. Evaluation of state-of-the-art provers highlights persistent limitations in accuracy and efficiency, underscoring the need for more capable LLM-based theorem provers for effective subgoal completion,

Efficiently tackling combinatorial reasoning problems, particularly the notorious NP-hard tasks, remains a significant challenge for AI research. Recent efforts have sought to enhance planning by incorporating hierarchical high-level search strategies, known as subgoal methods. While promising, their performance against traditional low-level planners is inconsistent, raising questions about their application contexts. In this study, we conduct an in-depth exploration of subgoal-planning methods for combinatorial reasoning. We identify the attributes pivotal for leveraging the advantages of high-level search: hard-to-learn value functions, complex action spaces, presence of dead ends in the environment, or using data collected from diverse experts. We propose a consistent evaluation methodology to achieve meaningful comparisons between methods and reevaluate the state-of-the-art algorithms.

Multimodal Large Language Models (MLLMs) struggle with complex geometric reasoning, largely because "black box" outcome-based supervision fails to distinguish between lucky guesses and rigorous deduction. To address this, we introduce a paradigm shift towards subgoal-level evaluation and learning. We first construct GeoGoal, a benchmark synthesized via a rigorous formal verification data engine, which converts abstract proofs into verifiable numeric subgoals. This structure reveals a critical divergence between reasoning quality and outcome accuracy. Leveraging this, we propose the Sub-Goal Verifiable Reward (SGVR) framework, which replaces sparse signals with dense rewards based on the Skeleton Rate. Experiments demonstrate that SGVR not only enhances geometric performance (+9.7%) but also exhibits strong generalization, transferring gains to general math (+8.0%) and other general reasoning tasks (+2.8%), demonstrating broad applicability across diverse domains.

We introduce a variational reasoning framework for language models that treats thinking traces as latent variables and optimizes them through variational inference. Starting from the evidence lower bound (ELBO), we extend it to a multi-trace objective for tighter bounds and propose a forward-KL formulation that stabilizes the training of the variational posterior. We further show that rejection sampling finetuning and binary-reward RL, including GRPO, can be interpreted as local forward-KL objectives, where an implicit weighting by model accuracy naturally arises from the derivation and reveals a previously unnoticed bias toward easier questions. We empirically validate our method on the Qwen 2.5 and Qwen 3 model families across a wide range of reasoning tasks. Overall, our work provides a principled probabilistic perspective that unifies variational inference with RL-style methods and yields stable objectives for improving the reasoning ability of language models. Our code is available at https://github.com/sail-sg/variational-reasoning.

Motivated by the need to efficiently identify multiple candidates in high trial-and-error cost tasks such as drug discovery, we propose a near-optimal algorithm to identify all ε-best arms (i.e., those at most ε worse than the optimum). Specifically, we introduce LinFACT, an algorithm designed to optimize the identification of all ε-best arms in linear bandits. We establish a novel information-theoretic lower bound on the sample complexity of this problem and demonstrate that LinFACT achieves instance optimality by matching this lower bound up to a logarithmic factor. A key ingredient of our proof is to integrate the lower bound directly into the scaling process for upper bound derivation, determining the termination round and thus the sample complexity. We also extend our analysis to settings with model misspecification and generalized linear models. Numerical experiments, including synthetic and real drug discovery data, demonstrate that LinFACT identifies more promising candidates with reduced sample complexity, offering significant computational efficiency and accelerating early-stage exploratory experiments.

We study regret minimization for reinforcement learning (RL) in Latent Markov Decision Processes (LMDPs) with context in hindsight. We design a novel model-based algorithmic framework which can be instantiated with both a model-optimistic and a value-optimistic solver. We prove an O(mathsf{Var^star M Gamma S A K}) regret bound where O hides logarithm factors, M is the number of contexts, S is the number of states, A is the number of actions, K is the number of episodes, Gamma le S is the maximum transition degree of any state-action pair, and Var^star is a variance quantity describing the determinism of the LMDP. The regret bound only scales logarithmically with the planning horizon, thus yielding the first (nearly) horizon-free regret bound for LMDP. This is also the first problem-dependent regret bound for LMDP. Key in our proof is an analysis of the total variance of alpha vectors (a generalization of value functions), which is handled with a truncation method. We complement our positive result with a novel Omega(mathsf{Var^star M S A K}) regret lower bound with Gamma = 2, which shows our upper bound minimax optimal when Gamma is a constant for the class of variance-bounded LMDPs. Our lower bound relies on new constructions of hard instances and an argument inspired by the symmetrization technique from theoretical computer science, both of which are technically different from existing lower bound proof for MDPs, and thus can be of independent interest.

Evidence-grounded reasoning requires more than attaching retrieved text to a prediction: a model should make decisions that depend on whether the provided evidence supports the target claim. In practice, this often fails because supervision is weak, evidence is only loosely tied to the claim, and evaluation does not test evidence dependence directly. We introduce case-grounded evidence verification, a general framework in which a model receives a local case context, external evidence, and a structured claim, and must decide whether the evidence supports the claim for that case. Our key contribution is a supervision construction procedure that generates explicit support examples together with semantically controlled non-support examples, including counterfactual wrong-state and topic-related negatives, without manual evidence annotation. We instantiate the framework in radiology and train a standard verifier on the resulting support task. The learned verifier substantially outperforms both case-only and evidence-only baselines, remains strong under correct evidence, and collapses when evidence is removed or swapped, indicating genuine evidence dependence. This behavior transfers across unseen evidence articles and an external case distribution, though performance degrades under evidence-source shift and remains sensitive to backbone choice. Overall, the results suggest that a major bottleneck in evidence grounding is not only model capacity, but the lack of supervision that encodes the causal role of evidence.

We study the task of agnostically learning halfspaces under the Gaussian distribution. Specifically, given labeled examples (x,y) from an unknown distribution on R^n times { pm 1}, whose marginal distribution on x is the standard Gaussian and the labels y can be arbitrary, the goal is to output a hypothesis with 0-1 loss OPT+epsilon, where OPT is the 0-1 loss of the best-fitting halfspace. We prove a near-optimal computational hardness result for this task, under the widely believed sub-exponential time hardness of the Learning with Errors (LWE) problem. Prior hardness results are either qualitatively suboptimal or apply to restricted families of algorithms. Our techniques extend to yield near-optimal lower bounds for related problems, including ReLU regression.

We study linear contextual bandits in the misspecified setting, where the expected reward function can be approximated by a linear function class up to a bounded misspecification level zeta>0. We propose an algorithm based on a novel data selection scheme, which only selects the contextual vectors with large uncertainty for online regression. We show that, when the misspecification level zeta is dominated by tilde O (Delta / d) with Delta being the minimal sub-optimality gap and d being the dimension of the contextual vectors, our algorithm enjoys the same gap-dependent regret bound tilde O (d^2/Delta) as in the well-specified setting up to logarithmic factors. In addition, we show that an existing algorithm SupLinUCB (Chu et al., 2011) can also achieve a gap-dependent constant regret bound without the knowledge of sub-optimality gap Delta. Together with a lower bound adapted from Lattimore et al. (2020), our result suggests an interplay between misspecification level and the sub-optimality gap: (1) the linear contextual bandit model is efficiently learnable when zeta leq tilde O(Delta / d); and (2) it is not efficiently learnable when zeta geq tilde Omega({Delta} / {d}). Experiments on both synthetic and real-world datasets corroborate our theoretical results.

Recent methods for knowledge grounded dialogs generate responses by incorporating information from an external textual document. These methods do not require the exact document to be known during training and rely on the use of a retrieval system to fetch relevant documents from a large index. The documents used to generate the responses are modeled as latent variables whose prior probabilities need to be estimated. Models such as RAG and REALM, marginalize the document probabilities over the documents retrieved from the index to define the log likelihood loss function which is optimized end-to-end. In this paper, we develop a variational approach to the above technique wherein, we instead maximize the Evidence Lower bound (ELBO). Using a collection of three publicly available open-conversation datasets, we demonstrate how the posterior distribution, that has information from the ground-truth response, allows for a better approximation of the objective function during training. To overcome the challenges associated with sampling over a large knowledge collection, we develop an efficient approach to approximate the ELBO. To the best of our knowledge we are the first to apply variational training for open-scale unsupervised knowledge grounded dialog systems.

Recently, the study of linear misspecified bandits has generated intriguing implications of the hardness of learning in bandits and reinforcement learning (RL). In particular, Du et al. (2020) show that even if a learner is given linear features in R^d that approximate the rewards in a bandit or RL with a uniform error of varepsilon, searching for an O(varepsilon)-optimal action requires pulling at least Omega(exp(d)) queries. Furthermore, Lattimore et al. (2020) show that a degraded O(varepsilond)-optimal solution can be learned within poly(d/varepsilon) queries. Yet it is unknown whether a structural assumption on the ground-truth parameter, such as sparsity, could break the varepsilond barrier. In this paper, we address this question by showing that algorithms can obtain O(varepsilon)-optimal actions by querying O(varepsilon^{-s}d^s) actions, where s is the sparsity parameter, removing the exp(d)-dependence. We then establish information-theoretical lower bounds, i.e., Omega(exp(s)), to show that our upper bound on sample complexity is nearly tight if one demands an error O(s^{delta}varepsilon) for 0<delta<1. For deltageq 1, we further show that poly(s/varepsilon) queries are possible when the linear features are "good" and even in general settings. These results provide a nearly complete picture of how sparsity can help in misspecified bandit learning and provide a deeper understanding of when linear features are "useful" for bandit and reinforcement learning with misspecification.

The rapid propagation of misinformation poses substantial risks to public interest. To combat misinformation, large language models (LLMs) are adapted to automatically verify claim credibility. Nevertheless, existing methods heavily rely on the embedded knowledge within LLMs and / or black-box APIs for evidence collection, leading to subpar performance with smaller LLMs or upon unreliable context. In this paper, we propose retrieval augmented fact verification through the synthesis of contrasting arguments (RAFTS). Upon input claims, RAFTS starts with evidence retrieval, where we design a retrieval pipeline to collect and re-rank relevant documents from verifiable sources. Then, RAFTS forms contrastive arguments (i.e., supporting or refuting) conditioned on the retrieved evidence. In addition, RAFTS leverages an embedding model to identify informative demonstrations, followed by in-context prompting to generate the prediction and explanation. Our method effectively retrieves relevant documents as evidence and evaluates arguments from varying perspectives, incorporating nuanced information for fine-grained decision-making. Combined with informative in-context examples as prior, RAFTS achieves significant improvements to supervised and LLM baselines without complex prompts. We demonstrate the effectiveness of our method through extensive experiments, where RAFTS can outperform GPT-based methods with a significantly smaller 7B LLM.

We study the sample complexity of learning an ε-optimal policy in the Stochastic Shortest Path (SSP) problem. We first derive sample complexity bounds when the learner has access to a generative model. We show that there exists a worst-case SSP instance with S states, A actions, minimum cost c_{min}, and maximum expected cost of the optimal policy over all states B_{star}, where any algorithm requires at least Ω(SAB_{star}^3/(c_{min}ε^2)) samples to return an ε-optimal policy with high probability. Surprisingly, this implies that whenever c_{min} = 0 an SSP problem may not be learnable, thus revealing that learning in SSPs is strictly harder than in the finite-horizon and discounted settings. We complement this lower bound with an algorithm that matches it, up to logarithmic factors, in the general case, and an algorithm that matches it up to logarithmic factors even when c_{min} = 0, but only under the condition that the optimal policy has a bounded hitting time to the goal state.

We seek to understand fundamental tradeoffs between the accuracy of prior information that a learner has on a given problem and its learning performance. We introduce the notion of prioritized risk, which differs from traditional notions of minimax and Bayes risk by allowing us to study such fundamental tradeoffs in settings where reality does not necessarily conform to the learner's prior. We present a general reduction-based approach for extending classical minimax lower-bound techniques in order to lower bound the prioritized risk for statistical estimation problems. We also introduce a novel generalization of Fano's inequality (which may be of independent interest) for lower bounding the prioritized risk in more general settings involving unbounded losses. We illustrate the ability of our framework to provide insights into tradeoffs between prior information and learning performance for problems in estimation, regression, and reinforcement learning.

We propose a new localized inference algorithm for answering marginalization queries in large graphical models with the correlation decay property. Given a query variable and a large graphical model, we define a much smaller model in a local region around the query variable in the target model so that the marginal distribution of the query variable can be accurately approximated. We introduce two approximation error bounds based on the Dobrushin's comparison theorem and apply our bounds to derive a greedy expansion algorithm that efficiently guides the selection of neighbor nodes for localized inference. We verify our theoretical bounds on various datasets and demonstrate that our localized inference algorithm can provide fast and accurate approximation for large graphical models.

LLM inference often generates a batch of candidates for a prompt and selects one via strategies like majority voting or Best-of- N (BoN). For difficult tasks, this single-shot selection often underperforms. Consequently, evaluations commonly report Pass@k: the agent may submit up to k responses, and only the best of them is used when computing regret. Motivated by this, we study inference scaling in the more general Pass@k inference setting, and prove that neither majority voting nor BoN exhibits the desirable scaling with k and the sampling budget N. Combining the advantages of majority voting and BoN, we propose a new inference strategy called Best-of-Majority (BoM), with a pivotal step that restricts the candidates to the responses with high frequency in the N samples before selecting the top-k rewards. We prove that when the sampling budget is N=tildeOmega(C^*), the regret of BoM is O(epsilon_{opt}+epsilon_{mathrm{RM}^2C^*/k}), where C^* is the coverage coefficient, epsilon_{RM} is the estimation error of the reward model, and epsilon_{opt} is the estimation error of reward at the optimal response. We further establish a matching lower bound, certifying that our algorithm is minimax optimal. Beyond optimality, BoM has a key advantage: unlike majority voting and BoN, its performance does not degrade when increasing N. Experimental results of inference on math problems show BoM outperforming both majority voting and BoN.

Chain-of-thought (CoT) improves reasoning reliability but increases token cost, motivating post-training compression of explicit reasoning traces. However, the shortest sufficient reasoning is not universal: it depends on difficulty, model capacity, and training state, making fixed length targets brittle. In practice, naive RL-based compression can also undesirably shorten the user-facing answer, because a single completion-level learning signal leaks across the think/answer boundary. We propose Difficulty-Scaled Segment-Wise GRPO (DSS-GRPO), which decomposes returns into think and answer components, computes group-relative advantages per segment, and routes them with hard token masks so compression updates act only on think while answer alignment acts only on answer. DSS-GRPO uses prompt-wise within-group shaping and difficulty-aware scaling to encourage concise reasoning without collapsing answer behavior.

We improve the efficiency of algorithms for stochastic combinatorial semi-bandits. In most interesting problems, state-of-the-art algorithms take advantage of structural properties of rewards, such as independence. However, while being optimal in terms of asymptotic regret, these algorithms are inefficient. In our paper, we first reduce their implementation to a specific submodular maximization. Then, in case of matroid constraints, we design adapted approximation routines, thereby providing the first efficient algorithms that rely on reward structure to improve regret bound. In particular, we improve the state-of-the-art efficient gap-free regret bound by a factor m/log m, where m is the maximum action size. Finally, we show how our improvement translates to more general budgeted combinatorial semi-bandits.

We investigate the online bandit learning of the monotone multi-linear DR-submodular functions, designing the algorithm BanditMLSM that attains O(T^{2/3}log T) of (1-1/e)-regret. Then we reduce submodular bandit with partition matroid constraint and bandit sequential monotone maximization to the online bandit learning of the monotone multi-linear DR-submodular functions, attaining O(T^{2/3}log T) of (1-1/e)-regret in both problems, which improve the existing results. To the best of our knowledge, we are the first to give a sublinear regret algorithm for the submodular bandit with partition matroid constraint. A special case of this problem is studied by Streeter et al.(2009). They prove a O(T^{4/5}) (1-1/e)-regret upper bound. For the bandit sequential submodular maximization, the existing work proves an O(T^{2/3}) regret with a suboptimal 1/2 approximation ratio (Niazadeh et al. 2021).

We study the non-stationary dueling bandits problem with K arms, where the time horizon T consists of M stationary segments, each of which is associated with its own preference matrix. The learner repeatedly selects a pair of arms and observes a binary preference between them as feedback. To minimize the accumulated regret, the learner needs to pick the Condorcet winner of each stationary segment as often as possible, despite preference matrices and segment lengths being unknown. We propose the Beat, the, Winner, Reset algorithm and prove a bound on its expected binary weak regret in the stationary case, which tightens the bound of current state-of-art algorithms. We also show a regret bound for the non-stationary case, without requiring knowledge of M or T. We further propose and analyze two meta-algorithms, DETECT for weak regret and Monitored, Dueling, Bandits for strong regret, both based on a detection-window approach that can incorporate any dueling bandit algorithm as a black-box algorithm. Finally, we prove a worst-case lower bound for expected weak regret in the non-stationary case.

In the stochastic multi-armed bandit problem, a randomized probability matching policy called Thompson sampling (TS) has shown excellent performance in various reward models. In addition to the empirical performance, TS has been shown to achieve asymptotic problem-dependent lower bounds in several models. However, its optimality has been mainly addressed under light-tailed or one-parameter models that belong to exponential families. In this paper, we consider the optimality of TS for the Pareto model that has a heavy tail and is parameterized by two unknown parameters. Specifically, we discuss the optimality of TS with probability matching priors that include the Jeffreys prior and the reference priors. We first prove that TS with certain probability matching priors can achieve the optimal regret bound. Then, we show the suboptimality of TS with other priors, including the Jeffreys and the reference priors. Nevertheless, we find that TS with the Jeffreys and reference priors can achieve the asymptotic lower bound if one uses a truncation procedure. These results suggest carefully choosing noninformative priors to avoid suboptimality and show the effectiveness of truncation procedures in TS-based policies.

Learning complex functions that involve multi-step reasoning poses a significant challenge for standard supervised learning from input-output examples. Chain-of-thought (CoT) supervision, which provides intermediate reasoning steps together with the final output, has emerged as a powerful empirical technique, underpinning much of the recent progress in the reasoning capabilities of large language models. This paper develops a statistical theory of learning under CoT supervision. A key characteristic of the CoT setting, in contrast to standard supervision, is the mismatch between the training objective (CoT risk) and the test objective (end-to-end risk). A central part of our analysis, distinguished from prior work, is explicitly linking those two types of risk to achieve sharper sample complexity bounds. This is achieved via the *CoT information measure* I_{D, h_star}^{CoT}(epsilon; calH), which quantifies the additional discriminative power gained from observing the reasoning process. The main theoretical results demonstrate how CoT supervision can yield significantly faster learning rates compared to standard E2E supervision. Specifically, it is shown that the sample complexity required to achieve a target E2E error epsilon scales as d/I_{D, h_star}^{CoT}(epsilon; calH), where d is a measure of hypothesis class complexity, which can be much faster than standard d/epsilon rates. Information-theoretic lower bounds in terms of the CoT information are also obtained. Together, these results suggest that CoT information is a fundamental measure of statistical complexity for learning under chain-of-thought supervision.

Given the intractably large size of the space of proofs, any model that is capable of general deductive reasoning must generalize to proofs of greater complexity. Recent studies have shown that large language models (LLMs) possess some abstract deductive reasoning ability given chain-of-thought prompts. However, they have primarily been tested on proofs using modus ponens or of a specific size, and from the same distribution as the in-context examples. To measure the general deductive reasoning ability of LLMs, we test on a broad set of deduction rules and measure their ability to generalize to more complex proofs from simpler demonstrations from multiple angles: depth-, width-, and compositional generalization. To facilitate systematic exploration, we construct a new synthetic and programmable reasoning dataset that enables control over deduction rules and proof complexity. Our experiments on four LLMs of various sizes and training objectives show that they are able to generalize to longer and compositional proofs. However, they require explicit demonstrations to produce hypothetical subproofs, specifically in proof by cases and proof by contradiction.

Sequential learning with feedback graphs is a natural extension of the multi-armed bandit problem where the problem is equipped with an underlying graph structure that provides additional information - playing an action reveals the losses of all the neighbors of the action. This problem was introduced by mannor2011 and received considerable attention in recent years. It is generally stated in the literature that the minimax regret rate for this problem is of order alpha T, where alpha is the independence number of the graph, and T is the time horizon. However, this is proven only when the number of rounds T is larger than alpha^3, which poses a significant restriction for the usability of this result in large graphs. In this paper, we define a new quantity R^*, called the problem complexity, and prove that the minimax regret is proportional to R^* for any graph and time horizon T. Introducing an intricate exploration strategy, we define the \mainAlgorithm algorithm that achieves the minimax optimal regret bound and becomes the first provably optimal algorithm for this setting, even if T is smaller than alpha^3.

Existing offline hierarchical reinforcement learning methods rely on high-level policy learning to generate subgoal sequences. However, their efficiency degrades as task horizons increase, and they lack effective strategies for stitching useful state transitions across different trajectories. We propose Graph-Assisted Stitching (GAS), a novel framework that formulates subgoal selection as a graph search problem rather than learning an explicit high-level policy. By embedding states into a Temporal Distance Representation (TDR) space, GAS clusters semantically similar states from different trajectories into unified graph nodes, enabling efficient transition stitching. A shortest-path algorithm is then applied to select subgoal sequences within the graph, while a low-level policy learns to reach the subgoals. To improve graph quality, we introduce the Temporal Efficiency (TE) metric, which filters out noisy or inefficient transition states, significantly enhancing task performance. GAS outperforms prior offline HRL methods across locomotion, navigation, and manipulation tasks. Notably, in the most stitching-critical task, it achieves a score of 88.3, dramatically surpassing the previous state-of-the-art score of 1.0. Our source code is available at: https://github.com/qortmdgh4141/GAS.

Experts advising decision-makers are likely to display expertise which varies as a function of the problem instance. In practice, this may lead to sub-optimal or discriminatory decisions against minority cases. In this work we model such changes in depth and breadth of knowledge as a partitioning of the problem space into regions of differing expertise. We provide here new algorithms that explicitly consider and adapt to the relationship between problem instances and experts' knowledge. We first propose and highlight the drawbacks of a naive approach based on nearest neighbor queries. To address these drawbacks we then introduce a novel algorithm - expertise trees - that constructs decision trees enabling the learner to select appropriate models. We provide theoretical insights and empirically validate the improved performance of our novel approach on a range of problems for which existing methods proved to be inadequate.

We investigate stochastic combinatorial semi-bandits, where the entire joint distribution of outcomes impacts the complexity of the problem instance (unlike in the standard bandits). Typical distributions considered depend on specific parameter values, whose prior knowledge is required in theory but quite difficult to estimate in practice; an example is the commonly assumed sub-Gaussian family. We alleviate this issue by instead considering a new general family of sub-exponential distributions, which contains bounded and Gaussian ones. We prove a new lower bound on the expected regret on this family, that is parameterized by the unknown covariance matrix of outcomes, a tighter quantity than the sub-Gaussian matrix. We then construct an algorithm that uses covariance estimates, and provide a tight asymptotic analysis of the regret. Finally, we apply and extend our results to the family of sparse outcomes, which has applications in many recommender systems.

Inequality proving, crucial across diverse scientific and mathematical fields, tests advanced reasoning skills such as discovering tight bounds and strategic theorem application. This makes it a distinct, demanding frontier for large language models (LLMs), offering insights beyond general mathematical problem-solving. Progress in this area is hampered by existing datasets that are often scarce, synthetic, or rigidly formal. We address this by proposing an informal yet verifiable task formulation, recasting inequality proving into two automatically checkable subtasks: bound estimation and relation prediction. Building on this, we release IneqMath, an expert-curated dataset of Olympiad-level inequalities, including a test set and training corpus enriched with step-wise solutions and theorem annotations. We also develop a novel LLM-as-judge evaluation framework, combining a final-answer judge with four step-wise judges designed to detect common reasoning flaws. A systematic evaluation of 29 leading LLMs on IneqMath reveals a surprising reality: even top models like o1 achieve less than 10% overall accuracy under step-wise scrutiny; this is a drop of up to 65.5% from their accuracy considering only final answer equivalence. This discrepancy exposes fragile deductive chains and a critical gap for current LLMs between merely finding an answer and constructing a rigorous proof. Scaling model size and increasing test-time computation yield limited gains in overall proof correctness. Instead, our findings highlight promising research directions such as theorem-guided reasoning and self-refinement. Code and data are available at https://ineqmath.github.io/.

Understanding causality should be a core requirement of any attempt to build real impact through AI. Due to the inherent unobservability of counterfactuals, large randomised trials (RCTs) are the standard for causal inference. But large experiments are generically expensive, and randomisation carries its own costs, e.g. when suboptimal decisions are trialed. Recent work has proposed more sample-efficient alternatives to RCTs, but these are not adaptable to the downstream application for which the causal effect is sought. In this work, we develop a task-specific approach to experimental design and derive sampling strategies customised to particular downstream applications. Across a range of important tasks, real-world datasets, and sample sizes, our method outperforms other benchmarks, e.g. requiring an order-of-magnitude less data to match RCT performance on targeted marketing tasks.

Current medical retrieval benchmarks primarily emphasize lexical or shallow semantic similarity, overlooking the reasoning-intensive demands that are central to clinical decision-making. In practice, physicians often retrieve authoritative medical evidence to support diagnostic hypotheses. Such evidence typically aligns with an inferred diagnosis rather than the surface form of a patient's symptoms, leading to low lexical or semantic overlap between queries and relevant documents. To address this gap, we introduce R2MED, the first benchmark explicitly designed for reasoning-driven medical retrieval. It comprises 876 queries spanning three tasks: Q&A reference retrieval, clinical evidence retrieval, and clinical case retrieval. These tasks are drawn from five representative medical scenarios and twelve body systems, capturing the complexity and diversity of real-world medical information needs. We evaluate 15 widely-used retrieval systems on R2MED and find that even the best model achieves only 31.4 nDCG@10, demonstrating the benchmark's difficulty. Classical re-ranking and generation-augmented retrieval methods offer only modest improvements. Although large reasoning models improve performance via intermediate inference generation, the best results still peak at 41.4 nDCG@10. These findings underscore a substantial gap between current retrieval techniques and the reasoning demands of real clinical tasks. We release R2MED as a challenging benchmark to foster the development of next-generation medical retrieval systems with enhanced reasoning capabilities. Data and code are available at https://github.com/R2MED/R2MED

We provide theoretical and empirical evidence that using tighter evidence lower bounds (ELBOs) can be detrimental to the process of learning an inference network by reducing the signal-to-noise ratio of the gradient estimator. Our results call into question common implicit assumptions that tighter ELBOs are better variational objectives for simultaneous model learning and inference amortization schemes. Based on our insights, we introduce three new algorithms: the partially importance weighted auto-encoder (PIWAE), the multiply importance weighted auto-encoder (MIWAE), and the combination importance weighted auto-encoder (CIWAE), each of which includes the standard importance weighted auto-encoder (IWAE) as a special case. We show that each can deliver improvements over IWAE, even when performance is measured by the IWAE target itself. Furthermore, our results suggest that PIWAE may be able to deliver simultaneous improvements in the training of both the inference and generative networks.

We consider reinforcement learning in an environment modeled by an episodic, finite, stage-dependent Markov decision process of horizon H with S states, and A actions. The performance of an agent is measured by the regret after interacting with the environment for T episodes. We propose an optimistic posterior sampling algorithm for reinforcement learning (OPSRL), a simple variant of posterior sampling that only needs a number of posterior samples logarithmic in H, S, A, and T per state-action pair. For OPSRL we guarantee a high-probability regret bound of order at most mathcal{O}(H^3SAT) ignoring polylog(HSAT) terms. The key novel technical ingredient is a new sharp anti-concentration inequality for linear forms which may be of independent interest. Specifically, we extend the normal approximation-based lower bound for Beta distributions by Alfers and Dinges [1984] to Dirichlet distributions. Our bound matches the lower bound of order Ω(H^3SAT), thereby answering the open problems raised by Agrawal and Jia [2017b] for the episodic setting.

We study the problem of online generalized linear regression in the stochastic setting, where the label is generated from a generalized linear model with possibly unbounded additive noise. We provide a sharp analysis of the classical follow-the-regularized-leader (FTRL) algorithm to cope with the label noise. More specifically, for sigma-sub-Gaussian label noise, our analysis provides a regret upper bound of O(sigma^2 d log T) + o(log T), where d is the dimension of the input vector, T is the total number of rounds. We also prove a Omega(sigma^2dlog(T/d)) lower bound for stochastic online linear regression, which indicates that our upper bound is nearly optimal. In addition, we extend our analysis to a more refined Bernstein noise condition. As an application, we study generalized linear bandits with heteroscedastic noise and propose an algorithm based on FTRL to achieve the first variance-aware regret bound.

Large Language Models (LLMs) often struggle with inherent knowledge boundaries and hallucinations, limiting their reliability in knowledge-intensive tasks. While Retrieval-Augmented Generation (RAG) mitigates these issues, it frequently overlooks structural interdependencies essential for multi-hop reasoning. Graph-based RAG approaches attempt to bridge this gap, yet they typically face trade-offs between accuracy and efficiency due to challenges such as costly graph traversals and semantic noise in LLM-generated summaries. In this paper, we propose HyperNode Expansion and Logical Path-Guided Evidence Localization strategies for GraphRAG (HELP), a novel framework designed to balance accuracy with practical efficiency through two core strategies: 1) HyperNode Expansion, which iteratively chains knowledge triplets into coherent reasoning paths abstracted as HyperNodes to capture complex structural dependencies and ensure retrieval accuracy; and 2) Logical Path-Guided Evidence Localization, which leverages precomputed graph-text correlations to map these paths directly to the corpus for superior efficiency. HELP avoids expensive random walks and semantic distortion, preserving knowledge integrity while drastically reducing retrieval latency. Extensive experiments demonstrate that HELP achieves competitive performance across multiple simple and multi-hop QA benchmarks and up to a 28.8times speedup over leading Graph-based RAG baselines.

We introduce DeepSeek-Prover-V2, an open-source large language model designed for formal theorem proving in Lean 4, with initialization data collected through a recursive theorem proving pipeline powered by DeepSeek-V3. The cold-start training procedure begins by prompting DeepSeek-V3 to decompose complex problems into a series of subgoals. The proofs of resolved subgoals are synthesized into a chain-of-thought process, combined with DeepSeek-V3's step-by-step reasoning, to create an initial cold start for reinforcement learning. This process enables us to integrate both informal and formal mathematical reasoning into a unified model. The resulting model, DeepSeek-Prover-V2-671B, achieves state-of-the-art performance in neural theorem proving, reaching 88.9% pass ratio on the MiniF2F-test and solving 49 out of 658 problems from PutnamBench. In addition to standard benchmarks, we introduce ProverBench, a collection of 325 formalized problems, to enrich our evaluation, including 15 selected problems from the recent AIME competitions (years 24-25). Further evaluation on these 15 AIME problems shows that the model successfully solves 6 of them. In comparison, DeepSeek-V3 solves 8 of these problems using majority voting, highlighting that the gap between formal and informal mathematical reasoning in large language models is substantially narrowing.

Large Language Models (LLMs) are fluent but prone to hallucinations, producing answers that appear plausible yet are unsupported by available evidence. This failure is especially problematic in high-stakes domains where decisions must be justified by verifiable information. We introduce EvidenceRL, a reinforcement learning framework that enforces evidence adherence during training. EvidenceRL scores candidate responses for grounding (entailment with retrieved evidence and context) and correctness (agreement with reference answers) and optimizes the generator using Group Relative Policy Optimization (GRPO). We evaluate across two high-stakes domains, cardiac diagnosis and legal reasoning, where EvidenceRL consistently improves evidence grounding and faithfulness without sacrificing task accuracy. On cardiac diagnosis, F1@3 increases from 37.0 to 54.5 on Llama-3.2-3B while grounding (G_{max}@3) rises from 47.6 to 78.2; hallucinations drop nearly 5times and evidence-supported diagnoses increase from 31.8\% to 61.6\%. On legal reasoning, EvidenceRL raises Faithfulness from 32.8\% to 67.6\% on Llama-3.1-8B, demonstrating consistent behavioral change across domains. Our code is open-sourced at https://github.com/Wizaaard/EvidenceRL.git.

We consider the task of identifying the Copeland winner(s) in a dueling bandits problem with ternary feedback. This is an underexplored but practically relevant variant of the conventional dueling bandits problem, in which, in addition to strict preference between two arms, one may observe feedback in the form of an indifference. We provide a lower bound on the sample complexity for any learning algorithm finding the Copeland winner(s) with a fixed error probability. Moreover, we propose POCOWISTA, an algorithm with a sample complexity that almost matches this lower bound, and which shows excellent empirical performance, even for the conventional dueling bandits problem. For the case where the preference probabilities satisfy a specific type of stochastic transitivity, we provide a refined version with an improved worst case sample complexity.

We present a complete theoretical characterization of Latent Posterior Factors (LPF), a principled framework for aggregating multiple heterogeneous evidence items in probabilistic prediction tasks. Multi-evidence reasoning arises pervasively in high-stakes domains including healthcare diagnosis, financial risk assessment, legal case analysis, and regulatory compliance, yet existing approaches either lack formal guarantees or fail to handle multi-evidence scenarios architecturally. LPF encodes each evidence item into a Gaussian latent posterior via a variational autoencoder, converting posteriors to soft factors through Monte Carlo marginalization, and aggregating factors via exact Sum-Product Network inference (LPF-SPN) or a learned neural aggregator (LPF-Learned). We prove seven formal guarantees spanning the key desiderata for trustworthy AI: Calibration Preservation (ECE <= epsilon + C/sqrt(K_eff)); Monte Carlo Error decaying as O(1/sqrt(M)); a non-vacuous PAC-Bayes bound with train-test gap of 0.0085 at N=4200; operation within 1.12x of the information-theoretic lower bound; graceful degradation as O(epsilon*delta*sqrt(K)) under corruption, maintaining 88% performance with half of evidence adversarially replaced; O(1/sqrt(K)) calibration decay with R^2=0.849; and exact epistemic-aleatoric uncertainty decomposition with error below 0.002%. All theorems are empirically validated on controlled datasets spanning up to 4,200 training examples. Our theoretical framework establishes LPF as a foundation for trustworthy multi-evidence AI in safety-critical applications.

Machine learning models often perform poorly on subgroups that are underrepresented in the training data. Yet, little is understood on the variation in mechanisms that cause subpopulation shifts, and how algorithms generalize across such diverse shifts at scale. In this work, we provide a fine-grained analysis of subpopulation shift. We first propose a unified framework that dissects and explains common shifts in subgroups. We then establish a comprehensive benchmark of 20 state-of-the-art algorithms evaluated on 12 real-world datasets in vision, language, and healthcare domains. With results obtained from training over 10,000 models, we reveal intriguing observations for future progress in this space. First, existing algorithms only improve subgroup robustness over certain types of shifts but not others. Moreover, while current algorithms rely on group-annotated validation data for model selection, we find that a simple selection criterion based on worst-class accuracy is surprisingly effective even without any group information. Finally, unlike existing works that solely aim to improve worst-group accuracy (WGA), we demonstrate the fundamental tradeoff between WGA and other important metrics, highlighting the need to carefully choose testing metrics. Code and data are available at: https://github.com/YyzHarry/SubpopBench.

Multilingual Retrieval-Augmented Generation (mRAG) leverages cross-lingual evidence to ground Large Language Models (LLMs) in global knowledge. However, we show that current mRAG systems suffer from a language bias during reranking, systematically favoring English and the query's native language. By introducing an estimated oracle evidence analysis, we quantify a substantial performance gap between existing rerankers and the achievable upper bound. Further analysis reveals a critical distributional mismatch: while optimal predictions require evidence scattered across multiple languages, current systems systematically suppress such ``answer-critical'' documents, thereby limiting downstream generation performance. To bridge this gap, we propose \textbf{Language-Agnostic Utility-driven Reranker Alignment (LAURA)}, which aligns multilingual evidence ranking with downstream generative utility. Experiments across diverse languages and generation models show that LAURA effectively mitigates language bias and consistently improves mRAG performance.

Recent years have witnessed meteoric progress in reasoning models: neural networks that generate intermediate reasoning traces (RTs) before producing a final output. Despite the rapid advancement, our understanding of how RTs support reasoning, and the limits of this paradigm, remain incomplete. To promote greater clarity, we introduce PITA: a novel large-scale dataset of over 23 million statements in propositional logic and their corresponding proofs. As a benchmark for robust reasoning, we focus on length generalization: if a model is trained to determine truth or falsity on statements with proofs up to fixed length, how well does it generalize to statements requiring longer proofs? We propose notions of (1) task depth and (2) task breadth, which measure respectively (1) the number of steps required to solve an example from a task and (2) the number of unique examples across a task. We vary these quantities across subsets of PITA, and find that RT models generalize well on broad and shallow subsets, while deteriorating on narrow and deep subsets relative to non-RT baselines. To determine whether our results are idiosyncratic to PITA or indicative of general phenomena, we compare our results to a simple synthetic task based on syllogisms. Our resulting theory suggests fundamental scalings that limit how well RT models perform on deep tasks, and highlights their generalization strengths on broad tasks. Our findings overall identify fundamental benefits and limitations inherent in using reasoning traces.

Large Language Models (LLMs) leverage step-by-step reasoning to solve complex problems. Standard evaluation practice involves generating a complete reasoning trace and assessing the correctness of the final answer presented at its conclusion. In this paper, we challenge the reliance on the final answer by posing the following two questions: Does the final answer reliably represent the model's optimal conclusion? Can alternative reasoning paths yield different results? To answer these questions, we analyze intermediate reasoning steps, termed subthoughts, and propose a method based on our findings. Our approach involves segmenting a reasoning trace into sequential subthoughts based on linguistic cues. We start by prompting the model to generate continuations from the end-point of each intermediate subthought. We extract a potential answer from every completed continuation originating from different subthoughts. We find that aggregating these answers by selecting the most frequent one (the mode) often yields significantly higher accuracy compared to relying solely on the answer derived from the original complete trace. Analyzing the consistency among the answers derived from different subthoughts reveals characteristics that correlate with the model's confidence and correctness, suggesting potential for identifying less reliable answers. Our experiments across various LLMs and challenging mathematical reasoning datasets (AIME2024 and AIME2025) show consistent accuracy improvements, with gains reaching up to 13\% and 10\% respectively. Implementation is available at: https://github.com/hammoudhasan/SubthoughtReasoner.

In this paper, we revisit the problem of sparse linear regression in the local differential privacy (LDP) model. Existing research in the non-interactive and sequentially local models has focused on obtaining the lower bounds for the case where the underlying parameter is 1-sparse, and extending such bounds to the more general k-sparse case has proven to be challenging. Moreover, it is unclear whether efficient non-interactive LDP (NLDP) algorithms exist. To address these issues, we first consider the problem in the epsilon non-interactive LDP model and provide a lower bound of Omega(sqrt{dklog d}{nepsilon}) on the ell_2-norm estimation error for sub-Gaussian data, where n is the sample size and d is the dimension of the space. We propose an innovative NLDP algorithm, the very first of its kind for the problem. As a remarkable outcome, this algorithm also yields a novel and highly efficient estimator as a valuable by-product. Our algorithm achieves an upper bound of O({dsqrt{k}{nepsilon}}) for the estimation error when the data is sub-Gaussian, which can be further improved by a factor of O(d) if the server has additional public but unlabeled data. For the sequentially interactive LDP model, we show a similar lower bound of Omega({sqrt{dk}{nepsilon}}). As for the upper bound, we rectify a previous method and show that it is possible to achieve a bound of O(ksqrt{d}{nepsilon}). Our findings reveal fundamental differences between the non-private case, central DP model, and local DP model in the sparse linear regression problem.

We study a distributed stochastic multi-armed bandit where a client supplies the learner with communication-constrained feedback based on the rewards for the corresponding arm pulls. In our setup, the client must encode the rewards such that the second moment of the encoded rewards is no more than P, and this encoded reward is further corrupted by additive Gaussian noise of variance sigma^2; the learner only has access to this corrupted reward. For this setting, we derive an information-theoretic lower bound of Omegaleft(frac{KT{SNR wedge1}} right) on the minimax regret of any scheme, where SNR := P{sigma^2}, and K and T are the number of arms and time horizon, respectively. Furthermore, we propose a multi-phase bandit algorithm, UEtext{-UCB++}, which matches this lower bound to a minor additive factor. UEtext{-UCB++} performs uniform exploration in its initial phases and then utilizes the {\em upper confidence bound }(UCB) bandit algorithm in its final phase. An interesting feature of UEtext{-UCB++} is that the coarser estimates of the mean rewards formed during a uniform exploration phase help to refine the encoding protocol in the next phase, leading to more accurate mean estimates of the rewards in the subsequent phase. This positive reinforcement cycle is critical to reducing the number of uniform exploration rounds and closely matching our lower bound.

Remarkable progress has been made on automated reasoning with natural text, by using Language Models (LMs) and methods such as Chain-of-Thought and Selection-Inference. These techniques search for proofs in the forward direction from axioms to the conclusion, which suffers from a combinatorial explosion of the search space, and thus high failure rates for problems requiring longer chains of reasoning. The classical automated reasoning literature has shown that reasoning in the backward direction (i.e. from the intended conclusion to supporting axioms) is significantly more efficient at proof-finding. Importing this intuition into the LM setting, we develop a Backward Chaining algorithm, called LAMBADA, that decomposes reasoning into four sub-modules. These sub-modules are simply implemented by few-shot prompted LM inference. We show that LAMBADA achieves sizable accuracy boosts over state-of-the-art forward reasoning methods on challenging logical reasoning datasets, particularly when deep and accurate proof chains are required.

Large Language Models (LLMs) are powerful candidates for complex decision-making, leveraging vast encoded knowledge and remarkable zero-shot abilities. However, their adoption in high-stakes environments is hindered by their opacity; their outputs lack faithful explanations and cannot be effectively contested to correct errors, undermining trustworthiness. In this paper, we propose ART (Adaptive Reasoning Trees), a hierarchical method for claim verification. The process begins with a root claim, which branches into supporting and attacking child arguments. An argument's strength is determined bottom-up via a pairwise tournament of its children, adjudicated by a judge LLM, allowing a final, transparent and contestable verdict to be systematically derived which is missing in methods like Chain-of-Thought (CoT). We empirically validate ART on multiple datasets, analyzing different argument generators and comparison strategies. Our findings show that ART's structured reasoning outperforms strong baselines, establishing a new benchmark for explainable claim verification which is more reliable and ensures clarity in the overall decision making step.

Shadow tomography for quantum states provides a sample efficient approach for predicting the properties of quantum systems when the properties are restricted to expectation values of 2-outcome POVMs. However, these shadow tomography procedures yield poor bounds if there are more than 2 outcomes per measurement. In this paper, we consider a general problem of learning properties from unknown quantum states: given an unknown d-dimensional quantum state rho and M unknown quantum measurements M_1,...,M_M with Kgeq 2 outcomes, estimating the probability distribution for applying M_i on rho to within total variation distance epsilon. Compared to the special case when K=2, we need to learn unknown distributions instead of values. We develop an online shadow tomography procedure that solves this problem with high success probability requiring O(Klog^2Mlog d/epsilon^4) copies of rho. We further prove an information-theoretic lower bound that at least Omega(min{d^2,K+log M}/epsilon^2) copies of rho are required to solve this problem with high success probability. Our shadow tomography procedure requires sample complexity with only logarithmic dependence on M and d and is sample-optimal for the dependence on K.

We study the problem of designing minimax procedures in linear regression under the quantile risk. We start by considering the realizable setting with independent Gaussian noise, where for any given noise level and distribution of inputs, we obtain the exact minimax quantile risk for a rich family of error functions and establish the minimaxity of OLS. This improves on the known lower bounds for the special case of square error, and provides us with a lower bound on the minimax quantile risk over larger sets of distributions. Under the square error and a fourth moment assumption on the distribution of inputs, we show that this lower bound is tight over a larger class of problems. Specifically, we prove a matching upper bound on the worst-case quantile risk of a variant of the recently proposed min-max regression procedure, thereby establishing its minimaxity, up to absolute constants. We illustrate the usefulness of our approach by extending this result to all p-th power error functions for p in (2, infty). Along the way, we develop a generic analogue to the classical Bayesian method for lower bounding the minimax risk when working with the quantile risk, as well as a tight characterization of the quantiles of the smallest eigenvalue of the sample covariance matrix.

Many important optimization problems, such as the minimum spanning tree and minimum-cost flow, can be solved optimally by a greedy method. In this work, we study a learning variant of these problems, where the model of the problem is unknown and has to be learned by interacting repeatedly with the environment in the bandit setting. We formalize our learning problem quite generally, as learning how to maximize an unknown modular function on a known polymatroid. We propose a computationally efficient algorithm for solving our problem and bound its expected cumulative regret. Our gap-dependent upper bound is tight up to a constant and our gap-free upper bound is tight up to polylogarithmic factors. Finally, we evaluate our method on three problems and demonstrate that it is practical.

Reinforcement learning with verifiable rewards (RLVR) has emerged as a promising paradigm for post-training large language models (LLMs) on complex reasoning tasks. Yet, the conditions under which RLVR yields robust generalization remain poorly understood. This paper provides an empirical study of RLVR generalization in the setting of probabilistic inference over causal graphical models. This setting offers two natural axes along which to examine generalization: (i) the level of the probabilistic query -- associational, interventional, or counterfactual -- and (ii) the structural complexity of the query, measured by the size of its relevant subgraph. We construct datasets of causal graphs and queries spanning these difficulty axes and fine-tune Qwen-2.5-Instruct models using RLVR or supervised fine-tuning (SFT). We vary both the model scale (3B-32B) and the query level included in training. We find that RLVR yields stronger within-level and across-level generalization than SFT, but only for specific combinations of model size and training query level. Further analysis shows that RLVR's effectiveness depends on the model's initial reasoning competence. With sufficient initial competence, RLVR improves an LLM's marginalization strategy and reduces errors in intermediate probability calculations, producing substantial accuracy gains, particularly on more complex queries. These findings show that RLVR can improve specific causal reasoning subskills, with its benefits emerging only when the model has sufficient initial competence.

We study the computational complexity of approximating general constrained Markov decision processes. Our primary contribution is the design of a polynomial time (0,ε)-additive bicriteria approximation algorithm for finding optimal constrained policies across a broad class of recursively computable constraints, including almost-sure, chance, expectation, and their anytime variants. Matching lower bounds imply our approximation guarantees are optimal so long as P neq NP. The generality of our approach results in answers to several long-standing open complexity questions in the constrained reinforcement learning literature. Specifically, we are the first to prove polynomial-time approximability for the following settings: policies under chance constraints, deterministic policies under multiple expectation constraints, policies under non-homogeneous constraints (i.e., constraints of different types), and policies under constraints for continuous-state processes.

As the mathematical capabilities of large language models (LLMs) improve, it becomes increasingly important to evaluate their performance on research-level tasks at the frontier of mathematical knowledge. However, existing benchmarks are limited, as they focus solely on final-answer questions or high-school competition problems. To address this gap, we introduce IMProofBench, a private benchmark consisting of 39 peer-reviewed problems developed by expert mathematicians. Each problem requires a detailed proof and is paired with subproblems that have final answers, supporting both an evaluation of mathematical reasoning capabilities by human experts and a large-scale quantitative analysis through automated grading. Furthermore, unlike prior benchmarks, the evaluation setup simulates a realistic research environment: models operate in an agentic framework with tools like web search for literature review and mathematical software such as SageMath. Our results show that current LLMs can succeed at the more accessible research-level questions, but still encounter significant difficulties on more challenging problems. Quantitatively, Grok-4 achieves the highest accuracy of 52% on final-answer subproblems, while GPT-5 obtains the best performance for proof generation, achieving a fully correct solution for 22% of problems. IMProofBench will continue to evolve as a dynamic benchmark in collaboration with the mathematical community, ensuring its relevance for evaluating the next generation of LLMs.

Evaluating whether multimodal large language models truly understand long-form scientific papers remains challenging: answer-only metrics and synthetic "Needle-In-A-Haystack" tests often reward answer matching without requiring a causal, evidence-linked reasoning trace in the document. We propose the "Fish-in-the-Ocean" (FITO) paradigm, which requires models to construct explicit cross-modal evidence chains within native scientific documents. To operationalize FITO, we build SIN-Data, a scientific interleaved corpus that preserves the native interleaving of text and figures. On top of it, we construct SIN-Bench with four progressive tasks covering evidence discovery (SIN-Find), hypothesis verification (SIN-Verify), grounded QA (SIN-QA), and evidence-anchored synthesis (SIN-Summary). We further introduce "No Evidence, No Score", scoring predictions when grounded to verifiable anchors and diagnosing evidence quality via matching, relevance, and logic. Experiments on eight MLLMs show that grounding is the primary bottleneck: Gemini-3-pro achieves the best average overall score (0.573), while GPT-5 attains the highest SIN-QA answer accuracy (0.767) but underperforms on evidence-aligned overall scores, exposing a gap between correctness and traceable support.

Graph-based retrieval-augmented generation (Graph-based RAG) has demonstrated significant potential in enhancing Large Language Models (LLMs) with structured knowledge. However, existing methods face three critical challenges: Inaccurate Graph Construction, caused by LLM hallucination; Poor Reasoning Ability, caused by failing to generate explicit reasons telling LLM why certain chunks were selected; and Inadequate Answering, which only partially answers the query due to the inadequate LLM reasoning, making their performance lag behind NaiveRAG on certain tasks. To address these issues, we propose AGRAG, an advanced graph-based retrieval-augmented generation framework. When constructing the graph, AGRAG substitutes the widely used LLM entity extraction method with a statistics-based method, avoiding hallucination and error propagation. When retrieval, AGRAG formulates the graph reasoning procedure as the Minimum Cost Maximum Influence (MCMI) subgraph generation problem, where we try to include more nodes with high influence score, but with less involving edge cost, to make the generated reasoning paths more comprehensive. We prove this problem to be NP-hard, and propose a greedy algorithm to solve it. The MCMI subgraph generated can serve as explicit reasoning paths to tell LLM why certain chunks were retrieved, thereby making the LLM better focus on the query-related part contents of the chunks, reducing the impact of noise, and improving AGRAG's reasoning ability. Furthermore, compared with the simple tree-structured reasoning paths, our MCMI subgraph can allow more complex graph structures, such as cycles, and improve the comprehensiveness of the generated reasoning paths.

In this work, we derive sharp non-asymptotic deviation bounds for weighted sums of Dirichlet random variables. These bounds are based on a novel integral representation of the density of a weighted Dirichlet sum. This representation allows us to obtain a Gaussian-like approximation for the sum distribution using geometry and complex analysis methods. Our results generalize similar bounds for the Beta distribution obtained in the seminal paper Alfers and Dinges [1984]. Additionally, our results can be considered a sharp non-asymptotic version of the inverse of Sanov's theorem studied by Ganesh and O'Connell [1999] in the Bayesian setting. Based on these results, we derive new deviation bounds for the Dirichlet process posterior means with application to Bayesian bootstrap. Finally, we apply our estimates to the analysis of the Multinomial Thompson Sampling (TS) algorithm in multi-armed bandits and significantly sharpen the existing regret bounds by making them independent of the size of the arms distribution support.

LLM agents excel when environments are mostly static and the needed information fits in a model's context window, but they often fail in open-ended investigations where explanations must be constructed by iteratively mining evidence from massive, heterogeneous operational data. These investigations exhibit hidden dependency structure: entities interact, signals co-vary, and the importance of a fact may only become clear after other evidence is discovered. Because the context window is bounded, agents must summarize intermediate findings before their significance is known, increasing the risk of discarding key evidence. ReAct-style agents are especially brittle in this regime. Their retrieve-summarize-reason loop makes conclusions sensitive to exploration order and introduces run-to-run non-determinism, producing a reliability gap where Pass-at-k may be high but Majority-at-k remains low. Simply sampling more rollouts or generating longer reasoning traces does not reliably stabilize results, since hypotheses cannot be autonomously checked as new evidence arrives and there is no explicit mechanism for belief bookkeeping and revision. In addition, ReAct entangles semantic reasoning with controller duties such as tool orchestration and state tracking, so execution errors and plan drift degrade reasoning while consuming scarce context. We address these issues by formulating investigation as abductive reasoning over a dependency graph and proposing EoG (Explanations over Graphs), a disaggregated framework in which an LLM performs bounded local evidence mining and labeling (cause vs symptom) while a deterministic controller manages traversal, state, and belief propagation to compute a minimal explanatory frontier. On a representative ITBench diagnostics task, EoG improves both accuracy and run-to-run consistency over ReAct baselines, including a 7x average gain in Majority-at-k entity F1.

We introduce the problem of active causal structure learning with advice. In the typical well-studied setting, the learning algorithm is given the essential graph for the observational distribution and is asked to recover the underlying causal directed acyclic graph (DAG) G^* while minimizing the number of interventions made. In our setting, we are additionally given side information about G^* as advice, e.g. a DAG G purported to be G^*. We ask whether the learning algorithm can benefit from the advice when it is close to being correct, while still having worst-case guarantees even when the advice is arbitrarily bad. Our work is in the same space as the growing body of research on algorithms with predictions. When the advice is a DAG G, we design an adaptive search algorithm to recover G^* whose intervention cost is at most O(max{1, log psi}) times the cost for verifying G^*; here, psi is a distance measure between G and G^* that is upper bounded by the number of variables n, and is exactly 0 when G=G^*. Our approximation factor matches the state-of-the-art for the advice-less setting.

We study the problem of adaptively identifying patient subpopulations that benefit from a given treatment during a confirmatory clinical trial. This type of adaptive clinical trial has been thoroughly studied in biostatistics, but has been allowed only limited adaptivity so far. Here, we aim to relax classical restrictions on such designs and investigate how to incorporate ideas from the recent machine learning literature on adaptive and online experimentation to make trials more flexible and efficient. We find that the unique characteristics of the subpopulation selection problem -- most importantly that (i) one is usually interested in finding subpopulations with any treatment benefit (and not necessarily the single subgroup with largest effect) given a limited budget and that (ii) effectiveness only has to be demonstrated across the subpopulation on average -- give rise to interesting challenges and new desiderata when designing algorithmic solutions. Building on these findings, we propose AdaGGI and AdaGCPI, two meta-algorithms for subpopulation construction. We empirically investigate their performance across a range of simulation scenarios and derive insights into their (dis)advantages across different settings.

Reinforcement learning has recently shown promise in improving retrieval-augmented generation (RAG). Despite these advances, its effectiveness in multi-hop question answering (QA) remains limited by two fundamental limitations: (i) global planning absence to structure multi-step reasoning, and (ii) unfaithful execution, which hinders effective query formulation and consistent use of retrieved evidence. We propose GlobalRAG, a reinforcement learning framework designed to enhance global reasoning in multi-hop QA. GlobalRAG decomposes questions into subgoals, coordinates retrieval with reasoning, and refines evidence iteratively. To guide this process, we introduce Planning Quality Reward and SubGoal Completion Reward, which encourage coherent planning and reliable subgoal execution. In addition, a progressive weight annealing strategy balances process-oriented and outcome-based objectives. Extensive experiments on both in-domain and out-of-domain benchmarks demonstrate that GlobalRAG significantly outperforms strong baselines while using only 8k training data (42% of the training data used by strong baselines), achieving average improvements of 14.2% in both EM and F1.

In causal inference, estimating heterogeneous treatment effects (HTE) is critical for identifying how different subgroups respond to interventions, with broad applications in fields such as precision medicine and personalized advertising. Although HTE estimation methods aim to improve accuracy, how to provide explicit subgroup descriptions remains unclear, hindering data interpretation and strategic intervention management. In this paper, we propose CURLS, a novel rule learning method leveraging HTE, which can effectively describe subgroups with significant treatment effects. Specifically, we frame causal rule learning as a discrete optimization problem, finely balancing treatment effect with variance and considering the rule interpretability. We design an iterative procedure based on the minorize-maximization algorithm and solve a submodular lower bound as an approximation for the original. Quantitative experiments and qualitative case studies verify that compared with state-of-the-art methods, CURLS can find subgroups where the estimated and true effects are 16.1% and 13.8% higher and the variance is 12.0% smaller, while maintaining similar or better estimation accuracy and rule interpretability. Code is available at https://osf.io/zwp2k/.

In location estimation, we are given n samples from a known distribution f shifted by an unknown translation lambda, and want to estimate lambda as precisely as possible. Asymptotically, the maximum likelihood estimate achieves the Cram\'er-Rao bound of error mathcal N(0, 1{nmathcal I}), where mathcal I is the Fisher information of f. However, the n required for convergence depends on f, and may be arbitrarily large. We build on the theory using smoothed estimators to bound the error for finite n in terms of mathcal I_r, the Fisher information of the r-smoothed distribution. As n to infty, r to 0 at an explicit rate and this converges to the Cram\'er-Rao bound. We (1) improve the prior work for 1-dimensional f to converge for constant failure probability in addition to high probability, and (2) extend the theory to high-dimensional distributions. In the process, we prove a new bound on the norm of a high-dimensional random variable whose 1-dimensional projections are subgamma, which may be of independent interest.

Recovering causal relationships from data is an important problem. Using observational data, one can typically only recover causal graphs up to a Markov equivalence class and additional assumptions or interventional data are needed for complete recovery. In this work, under some standard assumptions, we study causal graph discovery via adaptive interventions with node-dependent interventional costs. For this setting, we show that no algorithm can achieve an approximation guarantee that is asymptotically better than linear in the number of vertices with respect to the verification number; a well-established benchmark for adaptive search algorithms. Motivated by this negative result, we define a new benchmark that captures the worst-case interventional cost for any search algorithm. Furthermore, with respect to this new benchmark, we provide adaptive search algorithms that achieve logarithmic approximations under various settings: atomic, bounded size interventions and generalized cost objectives.

Building upon our previous investigations of O1 replication (Part 1: Journey Learning [Qin et al., 2024] and Part 2: Distillation [Huang et al., 2024]), this work explores the potential of inference-time scaling in large language models (LLMs) for medical reasoning tasks, ranging from diagnostic decision-making to treatment planning. Through extensive experiments on medical benchmarks of varying complexity (MedQA, Medbullets, and JAMA Clinical Challenges), our investigation reveals several key insights: (1) Increasing inference time does lead to improved performance. With a modest training set of 500 samples, our model yields substantial performance improvements of 6%-11%. (2) Task complexity directly correlates with the required length of reasoning chains, confirming the necessity of extended thought processes for challenging problems. (3) The differential diagnoses generated by our model adhere to the principles of the hypothetico-deductive method, producing a list of potential conditions that may explain a patient's symptoms and systematically narrowing these possibilities by evaluating the evidence. These findings demonstrate the promising synergy between inference-time scaling and journey learning in advancing LLMs' real-world clinical reasoning capabilities.

Scoring systems are linear classification models that only require users to add, subtract and multiply a few small numbers in order to make a prediction. These models are in widespread use by the medical community, but are difficult to learn from data because they need to be accurate and sparse, have coprime integer coefficients, and satisfy multiple operational constraints. We present a new method for creating data-driven scoring systems called a Supersparse Linear Integer Model (SLIM). SLIM scoring systems are built by solving an integer program that directly encodes measures of accuracy (the 0-1 loss) and sparsity (the ell_0-seminorm) while restricting coefficients to coprime integers. SLIM can seamlessly incorporate a wide range of operational constraints related to accuracy and sparsity, and can produce highly tailored models without parameter tuning. We provide bounds on the testing and training accuracy of SLIM scoring systems, and present a new data reduction technique that can improve scalability by eliminating a portion of the training data beforehand. Our paper includes results from a collaboration with the Massachusetts General Hospital Sleep Laboratory, where SLIM was used to create a highly tailored scoring system for sleep apnea screening

For observational studies, we study the sensitivity of causal inference when treatment assignments may depend on unobserved confounders. We develop a loss minimization approach for estimating bounds on the conditional average treatment effect (CATE) when unobserved confounders have a bounded effect on the odds ratio of treatment selection. Our approach is scalable and allows flexible use of model classes in estimation, including nonparametric and black-box machine learning methods. Based on these bounds for the CATE, we propose a sensitivity analysis for the average treatment effect (ATE). Our semi-parametric estimator extends/bounds the augmented inverse propensity weighted (AIPW) estimator for the ATE under bounded unobserved confounding. By constructing a Neyman orthogonal score, our estimator of the bound for the ATE is a regular root-n estimator so long as the nuisance parameters are estimated at the o_p(n^{-1/4}) rate. We complement our methodology with optimality results showing that our proposed bounds are tight in certain cases. We demonstrate our method on simulated and real data examples, and show accurate coverage of our confidence intervals in practical finite sample regimes with rich covariate information.

In this paper, the causal bandit problem is investigated, in which the objective is to select an optimal sequence of interventions on nodes in a causal graph. It is assumed that the graph is governed by linear structural equations; it is further assumed that both the causal topology and the distribution of interventions are unknown. By exploiting the causal relationships between the nodes whose signals contribute to the reward, interventions are optimized. First, based on the difference between the two types of graph identification errors (false positives and negatives), a causal graph learning method is proposed, which strongly reduces sample complexity relative to the prior art by learning sub-graphs. Under the assumption of Gaussian exogenous inputs and minimum-mean squared error weight estimation, a new uncertainty bound tailored to the causal bandit problem is derived. This uncertainty bound drives an upper confidence bound based intervention selection to optimize the reward. To cope with non-stationary bandits, a sub-graph change detection mechanism is proposed, with high sample efficiency. Numerical results compare the new methodology to existing schemes and show a substantial performance improvement in both stationary and non-stationary settings. Compared to existing approaches, the proposed scheme takes 67% fewer samples to learn the causal structure and achieves an average reward gain of 85%.

When provided with sufficient explanatory context, smaller Language Models have been shown to exhibit strong reasoning ability on challenging short-answer question-answering tasks where the questions are unseen in training. We evaluate two methods for further improvement in this setting. Both methods focus on combining rationales generated by a larger Language Model with longer contexts created from a multi-hop dense retrieval system. The first method (RR) involves training a Rationale Ranking model to score both generated rationales and retrieved contexts with respect to relevance and truthfulness. We then use the scores to derive combined contexts from both knowledge sources using a number of combinatory strategies. For the second method (RATD) we utilise retrieval-augmented training datasets developed by Hartill et al. 2023 to train a smaller Reasoning model such that it becomes proficient at utilising relevant information from longer text sequences that may be only partially evidential and frequently contain many irrelevant sentences. We find that both methods significantly improve results. Our single best Reasoning model materially improves upon strong comparable prior baselines for unseen evaluation datasets (StrategyQA 58.9 rightarrow 61.7 acc., CommonsenseQA 63.6 rightarrow 72.7 acc., ARC-DA 31.6 rightarrow 52.1 F1, IIRC 25.5 rightarrow 27.3 F1) and a version utilising our prior knowledge of each type of question in selecting a context combination strategy does even better. Our proposed models also generally outperform direct prompts against much larger models (BLOOM 175B and StableVicuna 13B) in both few-shot chain-of-thought and standard few-shot settings.

A major technique in learning-augmented online algorithms is combining multiple algorithms or predictors. Since the performance of each predictor may vary over time, it is desirable to use not the single best predictor as a benchmark, but rather a dynamic combination which follows different predictors at different times. We design algorithms that combine predictions and are competitive against such dynamic combinations for a wide class of online problems, namely, metrical task systems. Against the best (in hindsight) unconstrained combination of ell predictors, we obtain a competitive ratio of O(ell^2), and show that this is best possible. However, for a benchmark with slightly constrained number of switches between different predictors, we can get a (1+epsilon)-competitive algorithm. Moreover, our algorithms can be adapted to access predictors in a bandit-like fashion, querying only one predictor at a time. An unexpected implication of one of our lower bounds is a new structural insight about covering formulations for the k-server problem.

Despite achieving high accuracy on medical benchmarks, LLMs exhibit the Einstellung Effect in clinical diagnosis--relying on statistical shortcuts rather than patient-specific evidence, causing misdiagnosis in atypical cases. Existing benchmarks fail to detect this critical failure mode. We introduce MedEinst, a counterfactual benchmark with 5,383 paired clinical cases across 49 diseases. Each pair contains a control case and a "trap" case with altered discriminative evidence that flips the diagnosis. We measure susceptibility via Bias Trap Rate--probability of misdiagnosing traps despite correctly diagnosing controls. Extensive Evaluation of 17 LLMs shows frontier models achieve high baseline accuracy but severe bias trap rates. Thus, we propose ECR-Agent, aligning LLM reasoning with Evidence-Based Medicine standard via two components: (1) Dynamic Causal Inference (DCI) performs structured reasoning through dual-pathway perception, dynamic causal graph reasoning across three levels (association, intervention, counterfactual), and evidence audit for final diagnosis; (2) Critic-Driven Graph and Memory Evolution (CGME) iteratively refines the system by storing validated reasoning paths in an exemplar base and consolidating disease-specific knowledge into evolving illness graphs. Source code is to be released.

Recent large language models often answer factual questions correctly. But users can't trust any given claim a model makes without fact-checking, because language models can hallucinate convincing nonsense. In this work we use reinforcement learning from human preferences (RLHP) to train "open-book" QA models that generate answers whilst also citing specific evidence for their claims, which aids in the appraisal of correctness. Supporting evidence is drawn from multiple documents found via a search engine, or from a single user-provided document. Our 280 billion parameter model, GopherCite, is able to produce answers with high quality supporting evidence and abstain from answering when unsure. We measure the performance of GopherCite by conducting human evaluation of answers to questions in a subset of the NaturalQuestions and ELI5 datasets. The model's response is found to be high-quality 80\% of the time on this Natural Questions subset, and 67\% of the time on the ELI5 subset. Abstaining from the third of questions for which it is most unsure improves performance to 90\% and 80\% respectively, approaching human baselines. However, analysis on the adversarial TruthfulQA dataset shows why citation is only one part of an overall strategy for safety and trustworthiness: not all claims supported by evidence are true.

Mixture of experts (MoE) are a popular class of statistical and machine learning models that have gained attention over the years due to their flexibility and efficiency. In this work, we consider Gaussian-gated localized MoE (GLoME) and block-diagonal covariance localized MoE (BLoME) regression models to present nonlinear relationships in heterogeneous data with potential hidden graph-structured interactions between high-dimensional predictors. These models pose difficult statistical estimation and model selection questions, both from a computational and theoretical perspective. This paper is devoted to the study of the problem of model selection among a collection of GLoME or BLoME models characterized by the number of mixture components, the complexity of Gaussian mean experts, and the hidden block-diagonal structures of the covariance matrices, in a penalized maximum likelihood estimation framework. In particular, we establish non-asymptotic risk bounds that take the form of weak oracle inequalities, provided that lower bounds for the penalties hold. The good empirical behavior of our models is then demonstrated on synthetic and real datasets.

A key challenge in applying reinforcement learning (RL) to diffusion large language models (dLLMs) lies in the intractability of their likelihood functions, which are essential for the RL objective, necessitating corresponding approximation in each training step. While existing methods approximate the log-likelihoods by their evidence lower bounds (ELBOs) via customized Monte Carlo (MC) sampling, the forward computational graphs of all MC samples need to be retained for the gradient computation of non-linear terms in the RL objective, resulting in significant memory overhead. This constraint restricts feasible sample sizes, leading to imprecise likelihood approximations and ultimately distorting the RL objective. To overcome this limitation, we propose Boundary-Guided Policy Optimization (BGPO), a memory-efficient RL algorithm that maximizes a specially constructed lower bound of the ELBO-based objective. This lower bound is carefully designed to satisfy two key properties: (1) Linearity: it is formulated in a linear sum where each term depends only on a single MC sample, thereby enabling gradient accumulation across samples and ensuring constant memory usage; (2) Equivalence: Both the value and gradient of this lower bound are equal to those of the ELBO-based objective in on-policy training, making it also an effective approximation for the original RL objective. These properties allow BGPO to adopt a large MC sample size, resulting in more accurate likelihood approximations and improved RL objective estimation, which in turn leads to enhanced performance. Experiments show that BGPO significantly outperforms previous RL algorithms for dLLMs in math problem solving, code generation, and planning tasks.

Logical reasoning remains a challenge for natural language processing, but it can be improved by training language models to mimic theorem provers on procedurally generated problems. Previous work used domain-specific proof generation algorithms, which biases reasoning toward specific proof traces and limits auditability and extensibility. We present a simpler and more general declarative framework with flexible context-sensitive rules binding multiple languages (specifically, simplified English and the TPTP theorem-proving language). We construct first-order logic problems by selecting up to 32 premises and one hypothesis. We demonstrate that using semantic constraints during generation and careful English verbalization of predicates enhances logical reasoning without hurting natural English tasks. We use relatively small DeBERTa-v3 models to achieve state-of-the-art accuracy on the FOLIO human-authored logic dataset, surpassing GPT-4 in accuracy with or without an external solver by 12%.

While Reinforcement Learning (RL) has advanced LLM reasoning, applying it to long-context scenarios is hindered by sparsity of outcome rewards. This limitation fails to penalize ungrounded "lucky guesses," leaving the critical process of needle-in-a-haystack evidence retrieval largely unsupervised. To address this, we propose EAPO (Evidence-Augmented Policy Optimization). We first establish the Evidence-Augmented Reasoning paradigm, validating via Tree-Structured Evidence Sampling that precise evidence extraction is the decisive bottleneck for long-context reasoning. Guided by this insight, EAPO introduces a specialized RL algorithm where a reward model computes a Group-Relative Evidence Reward, providing dense process supervision to explicitly improve evidence quality. To sustain accurate supervision throughout training, we further incorporate an Adaptive Reward-Policy Co-Evolution mechanism. This mechanism iteratively refines the reward model using outcome-consistent rollouts, sharpening its discriminative capability to ensure precise process guidance. Comprehensive evaluations across eight benchmarks demonstrate that EAPO significantly enhances long-context reasoning performance compared to SOTA baselines.

Bayesian persuasion studies how an informed sender should influence beliefs of rational receivers who take decisions through Bayesian updating of a common prior. We focus on the online Bayesian persuasion framework, in which the sender repeatedly faces one or more receivers with unknown and adversarially selected types. First, we show how to obtain a tight tilde O(T^{1/2}) regret bound in the case in which the sender faces a single receiver and has partial feedback, improving over the best previously known bound of tilde O(T^{4/5}). Then, we provide the first no-regret guarantees for the multi-receiver setting under partial feedback. Finally, we show how to design no-regret algorithms with polynomial per-iteration running time by exploiting type reporting, thereby circumventing known intractability results on online Bayesian persuasion. We provide efficient algorithms guaranteeing a O(T^{1/2}) regret upper bound both in the single- and multi-receiver scenario when type reporting is allowed.

We use automated theorem provers to significantly shorten a formal development in higher order set theory. The development includes many standard theorems such as the fundamental theorem of arithmetic and irrationality of square root of two. Higher order automated theorem provers are particularly useful here, since the underlying framework of higher order set theory coincides with the classical extensional higher order logic of (most) higher order automated theorem provers, so no significant translation or encoding is required. Additionally, many subgoals are first order and so first order automated provers often suffice. We compare the performance of different provers on the subgoals generated from the development. We also discuss possibilities for proof reconstruction, i.e., obtaining formal proof terms when an automated theorem prover claims to have proven the subgoal.

The {K_{1,1}, K_{1,2},C_m: mgeq3}-factor of a graph is a spanning subgraph whose each component is an element of {K_{1,1}, K_{1,2},C_m: mgeq3}. In this paper, through the graph spectral methods, we establish the lower bound of the signless Laplacian spectral radius and the upper bound of the distance spectral radius to determine whether a graph admits a {K_2}-factor. We get a lower bound on the size (resp. the spectral radius) of G to guarantee that G contains a {K_{1,1}, K_{1,2},C_m: mgeq3}-factor. Then we determine an upper bound on the distance spectral radius of G to ensure that G has a {K_{1,1}, K_{1,2},C_m: mgeq3}-factor. Furthermore, by constructing extremal graphs, we show that the above all bounds are best possible.

In reinforcement learning (RL), rewards of states are typically considered additive, and following the Markov assumption, they are independent of states visited previously. In many important applications, such as coverage control, experiment design and informative path planning, rewards naturally have diminishing returns, i.e., their value decreases in light of similar states visited previously. To tackle this, we propose submodular RL (SubRL), a paradigm which seeks to optimize more general, non-additive (and history-dependent) rewards modelled via submodular set functions which capture diminishing returns. Unfortunately, in general, even in tabular settings, we show that the resulting optimization problem is hard to approximate. On the other hand, motivated by the success of greedy algorithms in classical submodular optimization, we propose SubPO, a simple policy gradient-based algorithm for SubRL that handles non-additive rewards by greedily maximizing marginal gains. Indeed, under some assumptions on the underlying Markov Decision Process (MDP), SubPO recovers optimal constant factor approximations of submodular bandits. Moreover, we derive a natural policy gradient approach for locally optimizing SubRL instances even in large state- and action- spaces. We showcase the versatility of our approach by applying SubPO to several applications, such as biodiversity monitoring, Bayesian experiment design, informative path planning, and coverage maximization. Our results demonstrate sample efficiency, as well as scalability to high-dimensional state-action spaces.

This paper studies the fundamental limits of reinforcement learning (RL) in the challenging partially observable setting. While it is well-established that learning in Partially Observable Markov Decision Processes (POMDPs) requires exponentially many samples in the worst case, a surge of recent work shows that polynomial sample complexities are achievable under the revealing condition -- A natural condition that requires the observables to reveal some information about the unobserved latent states. However, the fundamental limits for learning in revealing POMDPs are much less understood, with existing lower bounds being rather preliminary and having substantial gaps from the current best upper bounds. We establish strong PAC and regret lower bounds for learning in revealing POMDPs. Our lower bounds scale polynomially in all relevant problem parameters in a multiplicative fashion, and achieve significantly smaller gaps against the current best upper bounds, providing a solid starting point for future studies. In particular, for multi-step revealing POMDPs, we show that (1) the latent state-space dependence is at least Omega(S^{1.5}) in the PAC sample complexity, which is notably harder than the Theta(S) scaling for fully-observable MDPs; (2) Any polynomial sublinear regret is at least Omega(T^{2/3}), suggesting its fundamental difference from the single-step case where O(T) regret is achievable. Technically, our hard instance construction adapts techniques in distribution testing, which is new to the RL literature and may be of independent interest.

Integrating web search tools has significantly extended the capability of LLMs to address open-world, real-time, and long-tail problems. However, evaluating these Search Agents presents formidable challenges. First, constructing high-quality deep search benchmarks is prohibitively expensive, while unverified synthetic data often suffers from unreliable sources. Second, static benchmarks face dynamic obsolescence: as internet information evolves, complex queries requiring deep research often degrade into simple retrieval tasks due to increased popularity, and ground truths become outdated due to temporal shifts. Third, attribution ambiguity confounds evaluation, as an agent's performance is often dominated by its parametric memory rather than its actual search and reasoning capabilities. Finally, reliance on specific commercial search engines introduces variability that hampers reproducibility. To address these issues, we propose a novel framework, Mind-ParaWorld, for evaluating Search Agents in a Parallel World. Specifically, MPW samples real-world entity names to synthesize future scenarios and questions situated beyond the model's knowledge cutoff. A ParaWorld Law Model then constructs a set of indivisible Atomic Facts and a unique ground-truth for each question. During evaluation, instead of retrieving real-world results, the agent interacts with a ParaWorld Engine Model that dynamically generates SERPs grounded in these inviolable Atomic Facts. We release MPW-Bench, an interactive benchmark spanning 19 domains with 1,608 instances. Experiments across three evaluation settings show that, while search agents are strong at evidence synthesis given complete information, their performance is limited not only by evidence collection and coverage in unfamiliar search environments, but also by unreliable evidence sufficiency judgment and when-to-stop decisions-bottlenecks.

Learning with few samples is a major challenge for parameter-rich models like deep networks. In contrast, people learn complex new concepts even from very few examples, suggesting that the sample complexity of learning can often be reduced. Many approaches to few-shot learning build on transferring a representation from well-sampled classes, or using meta learning to favor architectures that can learn with few samples. Unfortunately, such approaches often struggle when learning in an online way or with non-stationary data streams. Here we describe a new approach to learn with fewer samples, by using additional information that is provided per sample. Specifically, we show how the sample complexity can be reduced by providing semantic information about the relevance of features per sample, like information about the presence of objects in a scene or confidence of detecting attributes in an image. We provide an improved generalization error bound for this case. We cast the problem of using per-sample feature relevance by using a new ellipsoid-margin loss, and develop an online algorithm that minimizes this loss effectively. Empirical evaluation on two machine vision benchmarks for scene classification and fine-grain bird classification demonstrate the benefits of this approach for few-shot learning.

Categorical distributions are ubiquitous in machine learning, e.g., in classification, language models, and recommendation systems. However, when the number of possible outcomes is very large, using categorical distributions becomes computationally expensive, as the complexity scales linearly with the number of outcomes. To address this problem, we propose augment and reduce (A&R), a method to alleviate the computational complexity. A&R uses two ideas: latent variable augmentation and stochastic variational inference. It maximizes a lower bound on the marginal likelihood of the data. Unlike existing methods which are specific to softmax, A&R is more general and is amenable to other categorical models, such as multinomial probit. On several large-scale classification problems, we show that A&R provides a tighter bound on the marginal likelihood and has better predictive performance than existing approaches.

This paper describes the results of SemEval 2023 task 7 -- Multi-Evidence Natural Language Inference for Clinical Trial Data (NLI4CT) -- consisting of 2 tasks, a Natural Language Inference (NLI) task, and an evidence selection task on clinical trial data. The proposed challenges require multi-hop biomedical and numerical reasoning, which are of significant importance to the development of systems capable of large-scale interpretation and retrieval of medical evidence, to provide personalized evidence-based care. Task 1, the entailment task, received 643 submissions from 40 participants, and Task 2, the evidence selection task, received 364 submissions from 23 participants. The tasks are challenging, with the majority of submitted systems failing to significantly outperform the majority class baseline on the entailment task, and we observe significantly better performance on the evidence selection task than on the entailment task. Increasing the number of model parameters leads to a direct increase in performance, far more significant than the effect of biomedical pre-training. Future works could explore the limitations of large models for generalization and numerical inference, and investigate methods to augment clinical datasets to allow for more rigorous testing and to facilitate fine-tuning. We envisage that the dataset, models, and results of this task will be useful to the biomedical NLI and evidence retrieval communities. The dataset, competition leaderboard, and website are publicly available.

Textual entailment models are increasingly applied in settings like fact-checking, presupposition verification in question answering, or summary evaluation. However, these represent a significant domain shift from existing entailment datasets, and models underperform as a result. We propose WiCE, a new fine-grained textual entailment dataset built on natural claim and evidence pairs extracted from Wikipedia. In addition to standard claim-level entailment, WiCE provides entailment judgments over sub-sentence units of the claim, and a minimal subset of evidence sentences that support each subclaim. To support this, we propose an automatic claim decomposition strategy using GPT-3.5 which we show is also effective at improving entailment models' performance on multiple datasets at test time. Finally, we show that real claims in our dataset involve challenging verification and retrieval problems that existing models fail to address.

In this work, we study first-order algorithms for solving Bilevel Optimization (BO) where the objective functions are smooth but possibly nonconvex in both levels and the variables are restricted to closed convex sets. As a first step, we study the landscape of BO through the lens of penalty methods, in which the upper- and lower-level objectives are combined in a weighted sum with penalty parameter sigma > 0. In particular, we establish a strong connection between the penalty function and the hyper-objective by explicitly characterizing the conditions under which the values and derivatives of the two must be O(sigma)-close. A by-product of our analysis is the explicit formula for the gradient of hyper-objective when the lower-level problem has multiple solutions under minimal conditions, which could be of independent interest. Next, viewing the penalty formulation as O(sigma)-approximation of the original BO, we propose first-order algorithms that find an epsilon-stationary solution by optimizing the penalty formulation with sigma = O(epsilon). When the perturbed lower-level problem uniformly satisfies the small-error proximal error-bound (EB) condition, we propose a first-order algorithm that converges to an epsilon-stationary point of the penalty function, using in total O(epsilon^{-3}) and O(epsilon^{-7}) accesses to first-order (stochastic) gradient oracles when the oracle is deterministic and oracles are noisy, respectively. Under an additional assumption on stochastic oracles, we show that the algorithm can be implemented in a fully {\it single-loop} manner, i.e., with O(1) samples per iteration, and achieves the improved oracle-complexity of O(epsilon^{-3}) and O(epsilon^{-5}), respectively.

Observational studies can yield clinically actionable evidence at scale, but executing them on real-world databases is open-ended and requires coherent decisions across cohort construction, analysis, and reporting. Prior evaluations of LLM agents emphasize isolated steps or single answers, missing the integrity and internal structure of the resulting evidence bundle. To address this gap, we introduce RWE-bench, a benchmark grounded in MIMIC-IV and derived from peer-reviewed observational studies. Each task provides the corresponding study protocol as the reference standard, requiring agents to execute experiments in a real database and iteratively generate tree-structured evidence bundles. We evaluate six LLMs (three open-source, three closed-source) under three agent scaffolds using both question-level correctness and end-to-end task metrics. Across 162 tasks, task success is low: the best agent reaches 39.9%, and the best open-source model reaches 30.4%. Agent scaffolds also matter substantially, causing over 30% variation in performance metrics. Furthermore, we implement an automated cohort evaluation method to rapidly localize errors and identify agent failure modes. Overall, the results highlight persistent limitations in agents' ability to produce end-to-end evidence bundles, and efficient validation remains an important direction for future work. Code and data are available at https://github.com/somewordstoolate/RWE-bench.

We study the problem of designing mechanisms for information acquisition scenarios. This setting models strategic interactions between an uniformed receiver and a set of informed senders. In our model the senders receive information about the underlying state of nature and communicate their observation (either truthfully or not) to the receiver, which, based on this information, selects an action. Our goal is to design mechanisms maximizing the receiver's utility while incentivizing the senders to report truthfully their information. First, we provide an algorithm that efficiently computes an optimal incentive compatible (IC) mechanism. Then, we focus on the online problem in which the receiver sequentially interacts in an unknown game, with the objective of minimizing the cumulative regret w.r.t. the optimal IC mechanism, and the cumulative violation of the incentive compatibility constraints. We investigate two different online scenarios, i.e., the full and bandit feedback settings. For the full feedback problem, we propose an algorithm that guarantees mathcal O(sqrt T) regret and violation, while for the bandit feedback setting we present an algorithm that attains mathcal O(T^{alpha}) regret and mathcal O(T^{1-alpha/2}) violation for any alphain[1/2, 1]. Finally, we complement our results providing a tight lower bound.

We develop a rigorous mathematical analysis of zero-shot learning with attributes. In this setting, the goal is to label novel classes with no training data, only detectors for attributes and a description of how those attributes are correlated with the target classes, called the class-attribute matrix. We develop the first non-trivial lower bound on the worst-case error of the best map from attributes to classes for this setting, even with perfect attribute detectors. The lower bound characterizes the theoretical intrinsic difficulty of the zero-shot problem based on the available information -- the class-attribute matrix -- and the bound is practically computable from it. Our lower bound is tight, as we show that we can always find a randomized map from attributes to classes whose expected error is upper bounded by the value of the lower bound. We show that our analysis can be predictive of how standard zero-shot methods behave in practice, including which classes will likely be confused with others.

We present Prover Agent, a novel AI agent for automated theorem proving that integrates large language models (LLMs) with a formal proof assistant, Lean. Prover Agent coordinates an informal reasoning LLM, a formal prover model, and feedback from Lean while also generating auxiliary lemmas. These auxiliary lemmas are not limited to subgoals in the formal proof but can also include special cases or potentially useful facts derived from the assumptions, which help in discovering a viable proof strategy. It achieves an 88.1% success rate on the MiniF2F benchmark, establishing a new state-of-the-art among methods using small language models (SLMs) with a much lower sample budget than previous approaches. We also present theoretical analyses and case studies that illustrate how these generated lemmas contribute to solving challenging problems. Our code is publicly available at: https://github.com/kAIto47802/Prover-Agent.

Maximizing a monotone submodular function under cardinality constraint k is a core problem in machine learning and database with many basic applications, including video and data summarization, recommendation systems, feature extraction, exemplar clustering, and coverage problems. We study this classic problem in the fully dynamic model where a stream of insertions and deletions of elements of an underlying ground set is given and the goal is to maintain an approximate solution using a fast update time. A recent paper at NeurIPS'20 by Lattanzi, Mitrovic, Norouzi{-}Fard, Tarnawski, Zadimoghaddam claims to obtain a dynamic algorithm for this problem with a 1{2} -epsilon approximation ratio and a query complexity bounded by poly(log(n),log(k),epsilon^{-1}). However, as we explain in this paper, the analysis has some important gaps. Having a dynamic algorithm for the problem with polylogarithmic update time is even more important in light of a recent result by Chen and Peng at STOC'22 who show a matching lower bound for the problem -- any randomized algorithm with a 1{2}+epsilon approximation ratio must have an amortized query complexity that is polynomial in n. In this paper, we develop a simpler algorithm for the problem that maintains a (1{2}-epsilon)-approximate solution for submodular maximization under cardinality constraint k using a polylogarithmic amortized update time.

The eternal vertex cover game is played between an attacker and a defender on an undirected graph G. The defender identifies k vertices to position guards on to begin with. The attacker, on their turn, attacks an edge e, and the defender must move a guard along e to defend the attack. The defender may move other guards as well, under the constraint that every guard moves at most once and to a neighboring vertex. The smallest number of guards required to defend attacks forever is called the eternal vertex cover number of G, denoted evc(G). For any graph G, evc(G) is at least the vertex cover number of G, denoted mvc(G). A graph is Spartan if evc(G) = mvc(G). It is known that a bipartite graph is Spartan if and only if every edge belongs to a perfect matching. We show that the only König graphs that are Spartan are the bipartite Spartan graphs. We also give new lower bounds for evc(G), generalizing a known lower bound based on cut vertices. We finally show a new matching-based characterization of all Spartan graphs.

Recent progress in reasoning models suggests that generating plausible attempts for research-level mathematics may be within reach, but verification remains a bottleneck, consuming scarce expert time. We hypothesize that a meaningful solution should contain enough method-level information that, when applied to a neighborhood of related questions, it should yield better downstream performance than incorrect solutions. Building on this idea, we propose Consequence-Based Utility, an oracle-free evaluator that scores each candidate by testing its value as an in-context exemplar in solving related yet verifiable questions. Our approach is evaluated on an original set of research-level math problems, each paired with one expert-written solution and nine LLM-generated solutions. Notably, Consequence-Based Utility consistently outperforms reward models, generative reward models, and LLM judges on ranking quality. Specifically, for GPT-OSS-120B, it improves Acc@1 from 67.2 to 76.3 and AUC from 71.4 to 79.6, with similarly large AUC gains on GPT-OSS-20B (69.0 to 79.2). Furthermore, compared to LLM-Judges, it also exhibits a larger solver-evaluator gap, maintaining a stronger correct-wrong separation even on instances where the underlying solver often fails to solve.

Retrieval-enhanced methods have become a primary approach in fact verification (FV); it requires reasoning over multiple retrieved pieces of evidence to verify the integrity of a claim. To retrieve evidence, existing work often employs off-the-shelf retrieval models whose design is based on the probability ranking principle. We argue that, rather than relevance, for FV we need to focus on the utility that a claim verifier derives from the retrieved evidence. We introduce the feedback-based evidence retriever(FER) that optimizes the evidence retrieval process by incorporating feedback from the claim verifier. As a feedback signal we use the divergence in utility between how effectively the verifier utilizes the retrieved evidence and the ground-truth evidence to produce the final claim label. Empirical studies demonstrate the superiority of FER over prevailing baselines.

In the experts problem, on each of T days, an agent needs to follow the advice of one of n ``experts''. After each day, the loss associated with each expert's advice is revealed. A fundamental result in learning theory says that the agent can achieve vanishing regret, i.e. their cumulative loss is within o(T) of the cumulative loss of the best-in-hindsight expert. Can the agent perform well without sufficient space to remember all the experts? We extend a nascent line of research on this question in two directions: bullet We give a new algorithm against the oblivious adversary, improving over the memory-regret tradeoff obtained by [PZ23], and nearly matching the lower bound of [SWXZ22]. bullet We also consider an adaptive adversary who can observe past experts chosen by the agent. In this setting we give both a new algorithm and a novel lower bound, proving that roughly n memory is both necessary and sufficient for obtaining o(T) regret.

Recent domain generalization (DG) approaches typically use the hypothesis learned on source domains for inference on the unseen target domain. However, such a hypothesis can be arbitrarily far from the optimal one for the target domain, induced by a gap termed ``adaptivity gap''. Without exploiting the domain information from the unseen test samples, adaptivity gap estimation and minimization are intractable, which hinders us to robustify a model to any unknown distribution. In this paper, we first establish a generalization bound that explicitly considers the adaptivity gap. Our bound motivates two strategies to reduce the gap: the first one is ensembling multiple classifiers to enrich the hypothesis space, then we propose effective gap estimation methods for guiding the selection of a better hypothesis for the target. The other method is minimizing the gap directly by adapting model parameters using online target samples. We thus propose Domain-specific Risk Minimization (DRM). During training, DRM models the distributions of different source domains separately; for inference, DRM performs online model steering using the source hypothesis for each arriving target sample. Extensive experiments demonstrate the effectiveness of the proposed DRM for domain generalization with the following advantages: 1) it significantly outperforms competitive baselines on different distributional shift settings; 2) it achieves either comparable or superior accuracies on all source domains compared to vanilla empirical risk minimization; 3) it remains simple and efficient during training, and 4) it is complementary to invariant learning approaches.

The complexity of learning a concept class under Gaussian marginals in the difficult agnostic model is closely related to its L_1-approximability by low-degree polynomials. For any concept class with Gaussian surface area at most Γ, Klivans et al. (2008) show that degree d = O(Γ^2 / varepsilon^4) suffices to achieve an varepsilon-approximation. This leads to the best-known bounds on the complexity of learning a variety of concept classes. In this note, we improve their analysis by showing that degree d = tilde O (Γ^2 / varepsilon^2) is enough. In light of lower bounds due to Diakonikolas et al. (2021), this yields (near) optimal bounds on the complexity of agnostically learning polynomial threshold functions in the statistical query model. Our proof relies on a direct analogue of a construction of Feldman et al. (2020), who considered L_1-approximation on the Boolean hypercube.

We propose the Bayes-UCBVI algorithm for reinforcement learning in tabular, stage-dependent, episodic Markov decision process: a natural extension of the Bayes-UCB algorithm by Kaufmann et al. (2012) for multi-armed bandits. Our method uses the quantile of a Q-value function posterior as upper confidence bound on the optimal Q-value function. For Bayes-UCBVI, we prove a regret bound of order O(H^3SAT) where H is the length of one episode, S is the number of states, A the number of actions, T the number of episodes, that matches the lower-bound of Ω(H^3SAT) up to poly-log terms in H,S,A,T for a large enough T. To the best of our knowledge, this is the first algorithm that obtains an optimal dependence on the horizon H (and S) without the need for an involved Bernstein-like bonus or noise. Crucial to our analysis is a new fine-grained anti-concentration bound for a weighted Dirichlet sum that can be of independent interest. We then explain how Bayes-UCBVI can be easily extended beyond the tabular setting, exhibiting a strong link between our algorithm and Bayesian bootstrap (Rubin, 1981).

Large language models (LLMs) are transforming the landscape of medicine, yet two fundamental challenges persist: keeping up with rapidly evolving medical knowledge and providing verifiable, evidence-grounded reasoning. Retrieval-augmented generation (RAG) has been widely adopted to address these limitations by supplementing model outputs with retrieved evidence. However, whether RAG reliably achieves these goals remains unclear. Here, we present the most comprehensive expert evaluation of RAG in medicine to date. Eighteen medical experts contributed a total of 80,502 annotations, assessing 800 model outputs generated by GPT-4o and Llama-3.1-8B across 200 real-world patient and USMLE-style queries. We systematically decomposed the RAG pipeline into three components: (i) evidence retrieval (relevance of retrieved passages), (ii) evidence selection (accuracy of evidence usage), and (iii) response generation (factuality and completeness of outputs). Contrary to expectation, standard RAG often degraded performance: only 22% of top-16 passages were relevant, evidence selection remained weak (precision 41-43%, recall 27-49%), and factuality and completeness dropped by up to 6% and 5%, respectively, compared with non-RAG variants. Retrieval and evidence selection remain key failure points for the model, contributing to the overall performance drop. We further show that simple yet effective strategies, including evidence filtering and query reformulation, substantially mitigate these issues, improving performance on MedMCQA and MedXpertQA by up to 12% and 8.2%, respectively. These findings call for re-examining RAG's role in medicine and highlight the importance of stage-aware evaluation and deliberate system design for reliable medical LLM applications.

Negation is poorly captured by current language models, although the extent of this problem is not widely understood. We introduce a natural language inference (NLI) test suite to enable probing the capabilities of NLP methods, with the aim of understanding sub-clausal negation. The test suite contains premise--hypothesis pairs where the premise contains sub-clausal negation and the hypothesis is constructed by making minimal modifications to the premise in order to reflect different possible interpretations. Aside from adopting standard NLI labels, our test suite is systematically constructed under a rigorous linguistic framework. It includes annotation of negation types and constructions grounded in linguistic theory, as well as the operations used to construct hypotheses. This facilitates fine-grained analysis of model performance. We conduct experiments using pre-trained language models to demonstrate that our test suite is more challenging than existing benchmarks focused on negation, and show how our annotation supports a deeper understanding of the current NLI capabilities in terms of negation and quantification.

Long-form video reasoning remains a major challenge for Video Large Language Models (Video LLMs), as static uniform frame sampling leads to information dilution and obscures critical evidence. Furthermore, existing pixel-space video reasoning agents, which are designed to actively interact with the video to acquire new visual information, remain suboptimal due to their lack of rigorous reward mechanisms to enforce evidence purity and their inability to perform temporal information supplementation beyond pre-sampled frames. To address this critical gap, we propose a novel evidence-prioritized adaptive framework built upon our core philosophy: "Select Less, Reason More." Our core contribution is the evidence-aware reinforcement learning (EARL) framework, which transforms the model into an active interrogator of evidence. EARL is precisely engineered to dynamically select the most relevant frames and, crucially, to perform localized re-sampling around the selected key frames to access fine-grained temporal detail. Extensive experiments on five demanding video reasoning benchmarks demonstrate that our EARL-trained model achieves new state-of-the-art among open-source Video LLMs, simultaneously learning an effective and high-purity visual evidence selection policy. Impressively, our 7B model achieves 59.8% on LongVideoBench, 69.0% on MVBench and 64.9% on VideoMME. These results highlight the importance of prioritizing evidence purity and the effectiveness of our framework.

Simple regret is a natural and parameter-free performance criterion for pure exploration in multi-armed bandits yet is less popular than the probability of missing the best arm or an epsilon-good arm, perhaps due to lack of easy ways to characterize it. In this paper, we make significant progress on minimizing simple regret in both data-rich (Tge n) and data-poor regime (T le n) where n is the number of arms, and T is the number of samples. At its heart is our improved instance-dependent analysis of the well-known Sequential Halving (SH) algorithm, where we bound the probability of returning an arm whose mean reward is not within epsilon from the best (i.e., not epsilon-good) for any choice of epsilon>0, although epsilon is not an input to SH. Our bound not only leads to an optimal worst-case simple regret bound of n/T up to logarithmic factors but also essentially matches the instance-dependent lower bound for returning an epsilon-good arm reported by Katz-Samuels and Jamieson (2020). For the more challenging data-poor regime, we propose Bracketing SH (BSH) that enjoys the same improvement even without sampling each arm at least once. Our empirical study shows that BSH outperforms existing methods on real-world tasks.

We consider the problem of constructing small coresets for k-Median in Euclidean spaces. Given a large set of data points Psubset R^d, a coreset is a much smaller set Ssubset R^d, so that the k-Median costs of any k centers w.r.t. P and S are close. Existing literature mainly focuses on the high-dimension case and there has been great success in obtaining dimension-independent bounds, whereas the case for small d is largely unexplored. Considering many applications of Euclidean clustering algorithms are in small dimensions and the lack of systematic studies in the current literature, this paper investigates coresets for k-Median in small dimensions. For small d, a natural question is whether existing near-optimal dimension-independent bounds can be significantly improved. We provide affirmative answers to this question for a range of parameters. Moreover, new lower bound results are also proved, which are the highest for small d. In particular, we completely settle the coreset size bound for 1-d k-Median (up to log factors). Interestingly, our results imply a strong separation between 1-d 1-Median and 1-d 2-Median. As far as we know, this is the first such separation between k=1 and k=2 in any dimension.

Reinforcement learning is emerging as a primary driver for improving language model reasoning capabilities. A fundamental question is whether current reinforcement learning algorithms -- such as Group Relative Policy Optimization (GRPO), the de facto standard algorithm used to improve language model reasoning -- merely sharpen the base model's distribution around problems it can already solve. We investigate this question in the context of formal theorem proving, which has access to a perfect verifier. We identify a degenerate rank bias in GRPO in which highly probable trajectories are reinforced and rare ones are neglected. This results in distribution sharpening: the model can solve some problems with fewer samples, but underperforms simply sampling more solutions from the original model. To overcome GRPO's rank bias we introduce unlikeliness reward, a simple method for explicitly up-weighting rare but correct solutions. We show that unlikeliness reward mitigates rank bias and improves pass@N across a large range of N in both synthetic and real theorem proving settings. We also uncover an unexpected link between rank bias and a seemingly mundane hyperparameter -- the number of updates per batch -- that leads to a second, complementary mitigation. We combine our insights into a revised GRPO training recipe for formal theorem proving, yielding an open pipeline that achieves competitive performance to DeepSeek-Prover-V1.5-RL on the miniF2F-test benchmark. We release our implementation at https://github.com/AndreHe02/rewarding-unlikely-release

Interference is ubiquitous when conducting causal experiments over networks. Except for certain network structures, causal inference on the network in the presence of interference is difficult due to the entanglement between the treatment assignments and the interference levels. In this article, we conduct causal inference under interference on an observed, sparse but connected network, and we propose a novel design of experiments based on an independent set. Compared to conventional designs, the independent-set design focuses on an independent subset of data and controls their interference exposures through the assignments to the rest (auxiliary set). We provide a lower bound on the size of the independent set from a greedy algorithm , and justify the theoretical performance of estimators under the proposed design. Our approach is capable of estimating both spillover effects and treatment effects. We justify its superiority over conventional methods and illustrate the empirical performance through simulations.

Evaluating Retrieval-Augmented Generation (RAG) in large language models (LLMs) is challenging because benchmarks can quickly become stale. Questions initially requiring retrieval may become answerable from pretraining knowledge as newer models incorporate more recent information during pretraining, making it difficult to distinguish evidence-based reasoning from recall. We introduce NeoQA (News Events for Out-of-training Question Answering), a benchmark designed to address this issue. To construct NeoQA, we generated timelines and knowledge bases of fictional news events and entities along with news articles and Q\&A pairs to prevent LLMs from leveraging pretraining knowledge, ensuring that no prior evidence exists in their training data. We propose our dataset as a new platform for evaluating evidence-based question answering, as it requires LLMs to generate responses exclusively from retrieved evidence and only when sufficient evidence is available. NeoQA enables controlled evaluation across various evidence scenarios, including cases with missing or misleading details. Our findings indicate that LLMs struggle to distinguish subtle mismatches between questions and evidence, and suffer from short-cut reasoning when key information required to answer a question is missing from the evidence, underscoring key limitations in evidence-based reasoning.

Large language models (LLMs) have demonstrated impressive performance on reasoning-intensive tasks, but enhancing their reasoning abilities typically relies on either reinforcement learning (RL) with verifiable signals or supervised fine-tuning (SFT) with high-quality long chain-of-thought (CoT) demonstrations, both of which are expensive. In this paper, we study a novel problem of incentivizing the reasoning capacity of LLMs without expensive high-quality demonstrations and reinforcement learning. We investigate whether the reasoning capabilities of LLMs can be effectively incentivized via supervision from significantly weaker models. We further analyze when and why such weak supervision succeeds in eliciting reasoning abilities in stronger models. Our findings show that supervision from significantly weaker reasoners can substantially improve student reasoning performance, recovering close to 94% of the gains of expensive RL at a fraction of the cost. Experiments across diverse benchmarks and model architectures demonstrate that weak reasoners can effectively incentivize reasoning in stronger student models, consistently improving performance across a wide range of reasoning tasks. Our results suggest that this simple weak-to-strong paradigm is a promising and generalizable alternative to costly methods for incentivizing strong reasoning capabilities at inference-time in LLMs. The code is publicly available at https://github.com/yuanyige/w2sr.

Automated Theorem Proving (ATP) in formal languages is a foundational challenge for AI. While Large Language Models (LLMs) have driven remarkable progress, a significant gap remains between their powerful informal reasoning capabilities and their weak formal proving performance. Recent studies show that the informal accuracy exceeds 80% while formal success remains below 8% on benchmarks like PutnamBench. We argue this gap persists because current state-of-the-art provers, by tightly coupling reasoning and proving, are trained with paradigms that inadvertently punish deep reasoning in favor of shallow, tactic-based strategies. To bridge this fundamental gap, we propose a novel framework that decouples high-level reasoning from low-level proof generation. Our approach utilizes two distinct, specialized models: a powerful, general-purpose Reasoner to generate diverse, strategic subgoal lemmas, and an efficient Prover to rigorously verify them. This modular design liberates the model's full reasoning potential and bypasses the pitfalls of end-to-end training. We evaluate our method on a challenging set of post-2000 IMO problems, a problem set on which no prior open-source prover has reported success. Our decoupled framework successfully solves 5 of these problems, demonstrating a significant step towards automated reasoning on exceptionally difficult mathematical challenges. To foster future research, we release our full dataset of generated and verified lemmas for a wide range of IMO problems, available at https://tencent-imo.github.io/ .

Existing theoretical studies on offline reinforcement learning (RL) mostly consider a dataset sampled directly from the target task. In practice, however, data often come from several heterogeneous but related sources. Motivated by this gap, this work aims at rigorously understanding offline RL with multiple datasets that are collected from randomly perturbed versions of the target task instead of from itself. An information-theoretic lower bound is derived, which reveals a necessary requirement on the number of involved sources in addition to that on the number of data samples. Then, a novel HetPEVI algorithm is proposed, which simultaneously considers the sample uncertainties from a finite number of data samples per data source and the source uncertainties due to a finite number of available data sources. Theoretical analyses demonstrate that HetPEVI can solve the target task as long as the data sources collectively provide a good data coverage. Moreover, HetPEVI is demonstrated to be optimal up to a polynomial factor of the horizon length. Finally, the study is extended to offline Markov games and offline robust RL, which demonstrates the generality of the proposed designs and theoretical analyses.

Large language models have achieved near-expert performance in structured reasoning domains like mathematics and programming, yet their ability to perform compositional multi-hop reasoning in specialized scientific fields remains limited. We propose a bottom-up learning paradigm in which models are grounded in axiomatic domain facts and compose them to solve complex, unseen tasks. To this end, we present a post-training pipeline, based on a combination of supervised fine-tuning and reinforcement learning (RL), in which knowledge graphs act as implicit reward models. By deriving novel reward signals from knowledge graph paths, we provide verifiable, scalable, and grounded supervision that encourages models to compose intermediate axioms rather than optimize only final answers during RL. We validate this approach in the medical domain, training a 14B model on short-hop reasoning paths (1-3 hops) and evaluating its zero-shot generalization to complex multi-hop queries (4-5 hops). Our experiments show that path-derived rewards act as a "compositional bridge", enabling our model to significantly outperform much larger models and frontier systems like GPT-5.2 and Gemini 3 Pro, on the most difficult reasoning tasks. Furthermore, we demonstrate the robustness of our approach to adversarial perturbations against option-shuffling stress tests. This work suggests that grounding the reasoning process in structured knowledge is a scalable and efficient path toward intelligent reasoning.

Retrieval-augmented generation (RAG) is typically optimized for topical relevance, yet its success ultimately depends on whether retrieved passages are useful for a large language model (LLM) to generate correct and complete answers. We argue that such utility is often LLM-specific rather than universal, due to differences in models' knowledge, reasoning, and ability to leverage evidence. We formalize LLM-specific utility as the performance improvement of a target LLM when a passage is provided, compared to answering without evidence. To systematically study LLM-specific utility, we construct a benchmark of LLM-specific gold utilitarian passages for four LLMs (Qwen3-8B/14B/32B and Llama3.1-8B) on three QA datasets (Natural Questions, TriviaQA, and MS MARCO-FQA). Our analysis shows that utilitarian passages are model-dependent and non-transferable: each LLM performs best with its own utilitarian evidence, while evidence optimized for other LLMs is consistently suboptimal. Human-annotated evidence remains a strong general baseline but does not fully match individual LLM utility needs. We further introduce the LLM-specific utility judgment task and find that existing utility-aware selection and scoring methods largely capture model-agnostic usefulness and struggle to reliably estimate LLM-specific utility. Overall, our findings highlight the limitations of current utility-aware retrieval and motivate generator-tailored evidence selection for improving RAG.

Patient recruitment is challenging for clinical trials. We introduce TrialGPT, an end-to-end framework for zero-shot patient-to-trial matching with large language models. TrialGPT comprises three modules: it first performs large-scale filtering to retrieve candidate trials (TrialGPT-Retrieval); then predicts criterion-level patient eligibility (TrialGPT-Matching); and finally generates trial-level scores (TrialGPT-Ranking). We evaluate TrialGPT on three cohorts of 183 synthetic patients with over 75,000 trial annotations. TrialGPT-Retrieval can recall over 90% of relevant trials using less than 6% of the initial collection. Manual evaluations on 1,015 patient-criterion pairs show that TrialGPT-Matching achieves an accuracy of 87.3% with faithful explanations, close to the expert performance. The TrialGPT-Ranking scores are highly correlated with human judgments and outperform the best-competing models by 43.8% in ranking and excluding trials. Furthermore, our user study reveals that TrialGPT can reduce the screening time by 42.6% in patient recruitment. Overall, these results have demonstrated promising opportunities for patient-to-trial matching with TrialGPT.

Group Relative Policy Optimization (GRPO) is widely used for reinforcement learning with verifiable rewards, but it often suffers from advantage collapse: when all rollouts in a group receive the same reward, the group yields zero relative advantage and thus no learning signal. For example, if a question is too hard for the reasoner, all sampled rollouts can be incorrect and receive zero reward. Recent work addresses this issue by adding hints or auxiliary scaffolds to such hard questions so that the reasoner produces mixed outcomes and recovers a non-zero update. However, existing hints are usually fixed rather than adapted to the current reasoner, and a hint that creates learning signal under the hinted input does not necessarily improve the no-hint policy used at test time. To this end, we propose Hint Learning for Reinforcement Learning (HiLL), a framework that jointly trains a hinter policy and a reasoner policy during RL. For each hard question, the hinter generates hints online conditioned on the current reasoner's incorrect rollout, allowing hint generation to adapt to the reasoner's evolving errors. We further introduce hint reliance, which measures how strongly correct hinted trajectories depend on the hint. We derive a transferability result showing that lower hint reliance implies stronger transfer from hinted success to no-hint success, and we use this result to define a transfer-weighted reward for training the hinter. Therefore, HiLL favors hints that not only recover informative GRPO groups, but also produce signals that are more likely to improve the original no-hint policy. Experiments across multiple benchmarks show that HiLL consistently outperforms GRPO and prior hint-based baselines, demonstrating the value of adaptive and transfer-aware hint learning for RL. The code is available at https://github.com/Andree-9/HiLL.

Inverse reinforcement learning (IRL) denotes a powerful family of algorithms for recovering a reward function justifying the behavior demonstrated by an expert agent. A well-known limitation of IRL is the ambiguity in the choice of the reward function, due to the existence of multiple rewards that explain the observed behavior. This limitation has been recently circumvented by formulating IRL as the problem of estimating the feasible reward set, i.e., the region of the rewards compatible with the expert's behavior. In this paper, we make a step towards closing the theory gap of IRL in the case of finite-horizon problems with a generative model. We start by formally introducing the problem of estimating the feasible reward set, the corresponding PAC requirement, and discussing the properties of particular classes of rewards. Then, we provide the first minimax lower bound on the sample complexity for the problem of estimating the feasible reward set of order {Omega}Bigl( H^3SA{epsilon^2} bigl( log bigl(1{delta}bigl) + S bigl)Bigl), being S and A the number of states and actions respectively, H the horizon, epsilon the desired accuracy, and delta the confidence. We analyze the sample complexity of a uniform sampling strategy (US-IRL), proving a matching upper bound up to logarithmic factors. Finally, we outline several open questions in IRL and propose future research directions.

We study convergence lower bounds of without-replacement stochastic gradient descent (SGD) for solving smooth (strongly-)convex finite-sum minimization problems. Unlike most existing results focusing on final iterate lower bounds in terms of the number of components n and the number of epochs K, we seek bounds for arbitrary weighted average iterates that are tight in all factors including the condition number kappa. For SGD with Random Reshuffling, we present lower bounds that have tighter kappa dependencies than existing bounds. Our results are the first to perfectly close the gap between lower and upper bounds for weighted average iterates in both strongly-convex and convex cases. We also prove weighted average iterate lower bounds for arbitrary permutation-based SGD, which apply to all variants that carefully choose the best permutation. Our bounds improve the existing bounds in factors of n and kappa and thereby match the upper bounds shown for a recently proposed algorithm called GraB.

Recent advances in large language models (LLMs) highlight the importance of post training techniques for improving reasoning and mathematical ability. Group Relative Policy Optimization (GRPO) has shown promise in this domain by combining group relative advantage estimation, PPO style clipping, and KL regularization. However, its complexity raises the question of whether all components are necessary for fostering reasoning behaviors. We conduct a systematic analysis of GRPO and identify two key findings: (1) incorporating negative feedback is essential training solely on actions above a baseline limits learning; and (2) PPO style constraints, such as policy ratio clipping, are not required to improve mathematical reasoning or performance. Building on these insights, we propose REINFORCE with Group Relative Advantage (RGRA), a simplified variant that retains group relative advantage estimation but removes PPO style clipping and policy ratio terms. Experiments across standard mathematical benchmarks indicate that RGRA has the potential to achieve stronger performance than GRPO. Our results suggest that simpler REINFORCE based approaches can effectively enhance reasoning in LLMs, offering a more transparent and efficient alternative to GRPO.

Graph-based Retrieval-Augmented Generation (GraphRAG) mitigates hallucinations in Large Language Models (LLMs) by grounding them in structured knowledge. However, current GraphRAG methods are constrained by a prevailing build-then-reason paradigm, which relies on a static, pre-constructed Knowledge Graph (KG). This paradigm faces two critical challenges. First, the KG's inherent incompleteness often breaks reasoning paths. Second, the graph's low signal-to-noise ratio introduces distractor facts, presenting query-relevant but misleading knowledge that disrupts the reasoning process. To address these challenges, we argue for a reason-and-construct paradigm and propose Relink, a framework that dynamically builds a query-specific evidence graph. To tackle incompleteness, Relink instantiates required facts from a latent relation pool derived from the original text corpus, repairing broken paths on the fly. To handle misleading or distractor facts, Relink employs a unified, query-aware evaluation strategy that jointly considers candidates from both the KG and latent relations, selecting those most useful for answering the query rather than relying on their pre-existence. This empowers Relink to actively discard distractor facts and construct the most faithful and precise evidence path for each query. Extensive experiments on five Open-Domain Question Answering benchmarks show that Relink achieves significant average improvements of 5.4\% in EM and 5.2\% in F1 over leading GraphRAG baselines, demonstrating the superiority of our proposed framework.