Large Language Model Reasoning

A standard technique for scaling inference-time reasoning is Self-Consistency, whereby multiple candidate answers are sampled from an LLM and the most common answer is selected. More recently, it has been shown that weighted majority voting (e.g. Confidence-Informed Self Consistency (CISC)), which assigns a confidence value to each candidate answer and chooses the answer with the largest accumulated score, tends to be more accurate on a wide range of popular benchmarks. In practice, weighted majority voting necessitates calling a critic LLM on each candidate's reasoning trace to produce the answer's confidence score. This secondary series of LLM calls greatly increases the overhead and cost of weighted majority voting, despite its potential performance benefits. To reduce this expense, we propose VecCISC, a lightweight, adaptive framework that uses a measure of semantic similarity to filter reasoning traces that are semantically equivalent to others, degenerate, or hallucinated, thus decreasing the number of candidate answers that must be evaluated by the critic. To ensure adequate experimental thoroughness, we evaluate VecCISC on five challenging, widely-adopted datasets spanning the domains of mathematics, chemistry, biology, commonsense reasoning, and the humanities. Our results demonstrate that VecCISC reduces the total token usage by 47%, while maintaining or exceeding the accuracy of CISC.

We argue that decomposing reward into weighted, verifiable criteria and using an LLM judge to score them provides a partial-credit optimization signal: instead of a binary outcome or a single holistic score, each response is graded along multiple task-specific criteria. We formalize \emph{rubric-grounded reinforcement learning (RL)}: a framework in which the policy is optimized against a structured, multi-criterion reward produced by a frozen LLM judge that conditions on auxiliary grounding the policy never sees. We instantiate the framework by deriving rubrics from an Office of Scientific and Technical Information (OSTI)-derived corpus of roughly 100,000 scientific and technical documents and training Llama-3.1-8B-Instruct with Group Relative Policy Optimization (GRPO). With GRPO-based training, the model achieves $71.7\%$ normalized reward on held-out rubric evaluation. The GRPO-tuned policy also improves over the base model on four reasoning benchmarks not derived from the training corpus -- GSM8K, MATH, GPQA Main, and GPQA Diamond. These results provide evidence that structured, document-grounded rewards can improve held-out rubric performance and induce transferable reasoning behaviors beyond the corpus used to construct the training environment.

While recent advancements in inference-time learning have improved LLM reasoning on Text-to-SQL tasks, current solutions still struggle to perform well on the most challenging tasks in the Bird-Bench (BIRD) benchmark. This is due to inadequate solution space exploration, which is necessary to uncover promising candidate queries that can be further refined to produce the correct output. To address this challenge, we introduce CA-SQL, a novel Text-to-SQL pipeline that utilizes the estimated difficulty of a task to dynamically scale the breadth of the exploration for generating solution candidates. In addition, we use a custom prompt seeding method, based on principles of evolutionary search, to further elicit exploratory behavior from the base LLM and a novel voting method to select the best candidate solution at the end of the search. Experiments demonstrate that our solution achieves a state-of-the-art score of 51.72% on the "challenging" tier of BIRD development set problems, using only GPT-4o-mini, out-performing other in-context learning approaches, even those that leverage larger models. Overall, our method attains a competitive 61.06% execution accuracy and 68.77% Soft F1 score on the BIRD development dataset.

Humans rapidly learn abstract knowledge when encountering novel environments and flexibly deploy this knowledge to guide efficient and intelligent action. Can modern AI systems learn and plan in a similar way? We study this question using a dataset of complex human gameplay with concurrent fMRI recordings, in which participants learn novel video games that require rule discovery, hypothesis revision, and multi-step planning. We jointly evaluate models by their ability to play the games, match human learning behavior, and predict brain activity during the same task, comparing a suite of frontier Large Reasoning Models (LRMs) against model-free and model-based deep reinforcement learning agents and a Bayesian theory-based agent. We find that frontier LRMs most closely match human behavioral patterns during game discovery and predict brain activity an order of magnitude better than both reinforcement learning alternatives across cortical and subcortical regions, with effects robust to permutation controls. Through targeted manipulations, we further show that brain alignment reflects the model's in-context representation of the game state rather than its downstream planning or reasoning. Our results establish LRMs as compelling computational accounts of human learning and decision making in complex, naturalistic environments. Project page with interactive replays: https://botcs.github.io/reason-to-play/

Recent efforts to improve the reasoning abilities of Large Language Models (LLMs) have focused on integrating formal logic solvers within neurosymbolic frameworks. A key challenge is that formal solvers lack commonsense world knowledge, preventing them from making reasoning steps that humans find obvious. Prior methods address this by using LLMs to supply missing commonsense assumptions, but these approaches implicitly assume universal agreement on such commonsense facts. In reality, commonsense beliefs vary across individuals. We propose a probabilistic framework for abductive commonsense reasoning that explicitly models this variation, aiming to determine whether most people would judge a statement as true or false. We introduce Probabilistic Abductive CommonSense (PACS), a novel algorithm that uses an LLM and a formal solver to sample proofs as observations of individuals' distinct commonsense beliefs, and aggregates conclusions across these samples. Empirically, PACS outperforms chain-of-thought reasoning, prior neurosymbolic methods, and search-based approaches across multiple benchmarks.

Despite the rapid development of AI reviewers, evaluating such systems remains challenging: metrics favor overlap with human reviews over correctness. However, since human reviews often cover only a subset of salient issues and sometimes contain mistakes, they are unreliable as gold references. To address this, we build category-specific benchmark subsets and skip evaluation when the corresponding human reviews are missing to strengthen Completeness. We also leverage reviewer--author--meta-review discussions as expert annotations and filter unreliable reviews accordingly to strengthen Correctness. Finally, we introduce CoCoReviewBench, which curates 3,900 papers from ICLR and NeurIPS to enable reliable and fine-grained evaluation of AI reviewers. Analysis shows that AI reviewers remain limited in correctness and are prone to hallucinations, and highlights reasoning models as more effective reviewers, motivating further directions for improving AI reviewers. Benchmarks and models are available at https://github.com/hexuandeng/CoCoReviewBench.

Robot swarms promise scalable assistance in complex and hazardous environments. Task planning lies at the core of human-swarm collaboration, translating the operator's intent into coordinated swarm actions and helping determine when validation or intervention is required during execution. In long-horizon missions under dynamic scenarios, however, reliable task planning becomes difficult to maintain: emerging events and changing conditions demand continual adaptation, and sustained operator oversight imposes substantial cognitive burden. Existing LLM-based planning tools can support plan generation, yet they remain susceptible to invalid task orderings and infeasible robot actions, resulting in frequent manual adjustment. Here we introduce a neuro-symbolic framework for long-horizon human-swarm collaboration that tightly melds verifiable task planning with context-grounded LLM reasoning. We formalize mission goals and operational rules as temporal logic formulas and admissible task orderings as task automata. Conditioned on these formal constraints and live perceptual context, LLMs generate executable subtask sequences that satisfy mission rules and remain grounded in the current scene. An uncertainty-aware scheduler then assigns subtasks across the heterogeneous swarm to maximize parallelisms while remaining resilient to disruptions. An event-triggered interaction protocol further limits operator involvement to sparse, high-level confirmation and guidance. Deployment on a heterogeneous robotic fleet yields similar results while remaining robust to hardware-specific actuation and communication uncertainties. Together, these results support a formal and scalable paradigm for reliable and low-overhead human-swarm collaboration in dynamic environments

Relational learning is a challenging problem that has motivated a wide range of approaches, including graph-based models (e.g., graph neural networks, graph transformers), tabular methods (e.g., tabular foundation models), and sequence-based approaches (e.g., large language models), each with its own advantages and limitations. We propose RelAgent, an LLM-based autonomous data scientist for relational learning, which operates in two phases. In the search phase, an LLM agent uses database, validation, and evaluation workspace tools to construct SQL feature programs and select a predictive model. In the inference phase, the resulting program is executed without further LLM calls. The final predictor consists of SQL queries and a classical model, enabling fast, deterministic, and intrinsically interpretable predictions: features are human-readable queries, and predictions depend only on the resulting query-defined feature map, enabling scalable deployment using standard database systems.

Language model (LM) "reasoning", commonly described as Chain-of-Thought or test-time scaling, often improves benchmark performance, but the dynamics underlying this process remain poorly understood. We study these dynamics through the lens of uncertainty quantification by treating the "reasoning" traces, the intermediate token sequences generated by LMs, as evolving model states. We summarize each trace by an uncertainty trace profile: a small set of features describing the shape of the uncertainty signal over its trace, such as its slope and linearity. We find that across five LMs evaluated on GSM8K and ProntoQA, these profiles predict whether a trace yields a correct final answer with AUROC up to 0.807, improving markedly on recent related work. We reach AUROC 0.801 using only the first few hundred tokens of full traces, suggesting that errors can be detected early in the generation. A detailed comparison of correct and incorrect traces further reveals qualitatively distinct uncertainty profiles, with correct traces showing a steeper and less linear decline in uncertainty. Together, the results suggest that our method, grounded in decision-making under uncertainty, provides a principled lens for studying the generative process underlying LM "reasoning".

Tool-integrated reasoning (TIR) is difficult to scale to small language models due to instability in long-horizon tool interactions and limited model capacity. While reinforcement learning methods like group relative policy optimization provide only sparse outcome-level rewards. Recently, on-policy distillation (OPD) has gained popularity by supplying dense token-level supervision from a teacher on student-generated trajectories. However, our experiments indicate that applying OPD to TIR leads to a critical failure mode: erroneous tool calls tend to cascade across subsequent reasoning steps, progressively amplifying student-teacher divergence and rendering the teacher's token-level supervision increasingly unreliable. To address this, we propose SOD, a step-wise on-policy distillation framework for small language model agents, which adaptively reweights distillation strength at each step based on step-level divergence. Therefore, SOD can attenuate potentially misleading teacher signals in high-divergence regions while preserving dense guidance in well-aligned states. Experiments on challenging math, science, and code benchmarks show that SOD achieves up to 20.86% improvement over the second-best baseline. Notably, our 0.6B student achieves 26.13% on AIME 2025, demonstrating effective transfer of agentic reasoning to lightweight models. Our code is available at https://github.com/YoungZ365/SOD.

Chain-of-thought reasoning is often treated as a monotone way to improve language-model accuracy by letting a model think longer. We identify a countervailing effect, the coupling tax: when reasoning traces and final answers share one output-token budget, long traces can crowd out the answer they are meant to support. Across GSM8K, MATH-500, and five BIG-Bench Hard tasks with Qwen3 models at three scales, non-thinking mode matches or outperforms thinking mode on GSM8K and MATH-500 at every budget up to 2048 tokens, while harder tasks shift the crossover to larger budgets. We derive a truncation-waste decomposition, $\mathrm{Acc}_{\mathrm{think}}(b)=α_c F_L(b)+α_t(1-F_L(b))$, that predicts this crossover from chain-length and accuracy statistics and explains inverse scaling within the Qwen family. A DeepSeek-R1-Distill-Llama-8B replication shows the same pattern under a different thinking interface. As a mitigation, split-budget generation decouples reasoning and answer budgets; on full MATH-500, IRIS reaches 74.0% accuracy, a strengthened extraction variant reaches 78.8%, and a fixed non-oracle SC+IRIS gate reaches 83.6%. The results show that test-time reasoning should be evaluated as a budget-allocation problem, not only as a question of whether longer traces are available.

Large reasoning models (LRMs) achieve strong performance via extended chain-of-thought (CoT) reasoning, yet suffer from excessive token consumption and high inference latency. Existing reinforcement learning (RL) approaches for CoT compression rely on uniform, static length penalties that neglect model capability dynamics and problem-level difficulty variation. We propose \textbf{ExpThink}\xspace, an RL framework that addresses both dimensions through two complementary mechanisms. First, \emph{experience-guided reward shaping} tracks the shortest correct solution found so far for each problem and applies a three-tier reward: full credit for concise correct responses, discounted credit for verbose correct ones, and zero for incorrect ones. The threshold tightens automatically with model improvement, forming a self-evolving curriculum that requires no manual scheduling. Second, \emph{difficulty-adaptive advantage} replaces standard deviation normalization with correct-count normalization, yielding monotonically difficulty-scaled gradients that amplify learning on hard problems to preserve accuracy while suppressing gradients on easy ones to encourage brevity. Together, these mechanisms enforce an accuracy-first, compression-second training objective. Experiments on multiple mathematical reasoning benchmarks demonstrate that \textbf{ExpThink}\xspace reduces average response length by up to 77% while simultaneously improving accuracy, achieving up to $3\times$ higher accuracy-efficiency ratio (accuracy divided by average token count) than the vanilla baseline and outperforming existing RL-based compression methods on both metrics.

Rubrics have been extensively utilized for evaluating unverifiable, open-ended tasks, with recent research incorporating them into reward systems for reinforcement learning. However, existing frameworks typically treat rubrics only as external evaluator disjointed from the policy's primary reasoning trace. Such design confines rubrics to post-hoc measurement, leaving them unable to actively guide the model's generation process. In this work, we introduce Think-with-Rubrics, a novel paradigm for instruction following tasks. Think-with-Rubrics integrates rubric generation into the reasoning context, transforming the rubric from an independent artifact into an internal guidance of LLM's generation. During training, LLM sequentially generates a rubric followed by a response, while a trained rubric verifier provides joint supervision by evaluating the consistency between the answer and the self-generated / golden rubrics. Experiments across multiple benchmarks demonstrate that Think-with-Rubrics consistently outperforms the Rubric-as-Reward baseline supervised by golden rubrics by an average of 3.87 points. We have also discussed the mechanism by which Think-with-Rubrics enhances model performance. Experimental results demonstrate that supervision from golden rubrics and self-generated rubrics enhances the performance of Think-with-Rubrics by improving the quality of self-generated rubrics and increasing the internal consistency of responses respectively.

Reinforcement Learning with Verifiable Rewards (RLVR) has emerged as a pivotal technique for enhancing the reasoning capabilities of Large Language Models (LLMs). However, the de facto practice of mainstream RL algorithms is to treat all tokens of one response equally and assign the same optimization objective to each token, failing to provide granular guidance for the reasoning process. While in Chain-of-Thought (CoT) reasoning, different tokens usually play distinct roles. Therefore, the current RL algorithms lack an effective mechanism to dynamically balance the exploration-exploitation trade-off during learning. To this end, we propose Hierarchical Token-level Objective Control Policy Optimization (HTPO), a novel RL algorithm that takes the divide-and-conquer idea to hierarchically partition the response tokens into specific functional groups from three aspects (i.e., prompt difficulty, answer correctness, and token entropy). Within each group, according to the contributions to exploration or exploitation, we design specialized optimization objectives to facilitate the effective execution of each token's expected functionality. In this way, HTPO can achieve a more balanced exploration-exploitation trade-off. Extensive experiments on challenging reasoning benchmarks validate the superiority of our HTPO algorithm, which significantly outperforms the strong DAPO baseline (e.g., +8.6% and +6.7% on AIME'24 and AIME'25, respectively). When scaling test-time compute, the HTPO-trained model maintains a consistent performance advantage over the DAPO baseline, and the gap widens as the sampling budget increases, validating that our adaptive token-level control method fosters effective exploration without sacrificing exploitation performance. Code will be at https://github.com/xcyao00/HTPO.

Large reasoning models often reach correct answers through flawed intermediate steps, creating a gap between final accuracy and reasoning reliability. Existing alignment strategies address this with external verifiers or massive sampling, limiting scalability. In this work, we introduce CASPO (Confidence-Aware Step-wise Preference Optimization), a framework that aligns token-level confidence with step-wise logical correctness through iterative Direct Preference Optimization, without training a separate reward model. During inference, we propose Confidence-aware Thought (CaT), which leverages this calibrated confidence to dynamically prune uncertain reasoning branches with negligible O(V) latency. Experiments across ten benchmarks and multiple model families show that CASPO consistently improves reasoning reliability and inference efficiency. CASPO scales to Qwen3-8B-Base and surpasses tree-search baselines on AIME'24 and AIME'25 without using reward-model data. We also release a step-wise dataset with confidence annotations to support fine-grained analysis of reasoning reliability. Code is available at https://github.com/Thecommonirin/CASPO.

Video Reasoning Segmentation (VRS) aims to segment target objects in videos based on implicit instructions that convey human intent and temporal logic. Existing MLLM-based methods predict masks with a [SEG] token after selecting frames via simple sampling or an auxiliary MLLM, where limited supervision and frame-language similarity rules often yield narrow-scope keyframe choices that weaken holistic temporal understanding and lead to brittle localization in complex multi-object scenes. To address these issues, we introduce RCoT-Seg, a video-of-thought framework that factorizes VRS into temporal video reasoning (TVR) and keyframe target perception (KTP), explicitly separating temporal reasoning from spatial perception. Specifically, in the TVR stage, an agentic keyframe selection module, initialized with a curated CoT-start corpus and refined by GRPO under task-aligned rewards, is proposed to generate and reselect the keyframe through self-evaluation, strengthening moment localization and temporal reasoning. In the KTP stage, RCoT-Seg performs high-resolution segmentation on the selected frame and propagates masks with SAM2-based methods across the sequence, replacing heuristic sampling and external selectors while improving spatial precision and inter-frame consistency. Extensive experimental results demonstrate that the proposed RCoT-Seg achieves favorable performance against the state-of-the-art methods. The code and models will be publicly released at https://github.com/Victor-wjw/RCoT-Seg.

Deploying massive large language models (LLMs) as continuous cognitive engines for robotics is bottlenecked by the time-to-first-token (TTFT) latency required to process extensive state histories. Existing solutions like RAG or sliding windows compromise global context or incur prohibitive re-computation costs. We formalize the optimal task structure for minimizing latency and theoretically prove that prefix stability, incremental extensibility, and asynchronous state reconciliation are necessary conditions for real-time performance. Building on these proofs, we introduce the Cached State Representation (CSR) framework as the practical instantiation of these properties, ensuring optimal KV-cache reuse. To sustain these properties over infinite horizons, we further propose an Asynchronous State Reconciliation (ASR) algorithm that offloads state memory eviction to a parallel computational resource to eliminate latency spikes. On a physical robot wirelessly connected to an on-premise GPU server, CSR achieves a 26-fold latency reduction (14.67s to 0.56s) for 120K token contexts with a 235B parameter model compared to a standard baseline. On an embodied AI benchmark, we achieve SOTA recall (0.836 vs. 0.459) while maintaining RAG-level latency. ASR is validated to sustain bounded, spike-free TTFT over 10 eviction cycles in continuous real-world operation. Together, CSR and ASR enable massive LLMs to function as continuously operating, high-frequency (> 2 Hz) embodied policies.

Reinforcement learning with verifiable rewards improves LLM reasoning but often induces overthinking, where models generate unnecessarily long reasoning traces. Existing methods mainly rely on length penalties or early-exit strategies; however, the former may degrade accuracy and induce underthinking, whereas the latter assumes that substantial portions of reasoning traces can be safely truncated. To obtain a compression signal without these limitations, we revisit the training dynamics of existing compression methods. We observe that the length--accuracy correlation is initially negative but continually increases during compression, indicating that shorter responses are initially more likely to be correct but gradually lose this property as the policy moves toward underthinking. Based on this observation, we formalize overthinking: a negative correlation indicates an overthinking regime, while a positive one indicates underthinking. When overthinking, the shortest correct responses are shorter than the group-average response length in expectation, making them natural compression targets already present in on-policy rollouts. We therefore propose \emph{Implicit Compression Regularization} (ICR), an on-policy regularization method whose compression signal comes from a virtual shorter distribution induced by the shortest correct responses in rollout groups, guiding the policy toward concise yet correct trajectories. Training dynamics show that ICR maintains a better length--accuracy correlation during compression, indicating that short responses remain better aligned with correctness instead of drifting toward underthinking. Experiments on three reasoning backbones and multiple mathematical and knowledge-intensive benchmarks show that ICR consistently shortens responses while preserving or improving accuracy, achieving a stronger accuracy--length Pareto frontier.

Chain-of-thought (CoT) reasoning improves large language models (LLMs) on difficult tasks, but it also makes inference expensive because every intermediate step must be generated as a discrete token. Latent reasoning reduces visible token generation by propagating continuous states, yet replacing explicit derivations with latent computation can hurt tasks that require symbolic checking. We propose Latent-Then-Explicit Reasoning (LaTER), a two-stage paradigm that first performs bounded exploration in a continuous latent space and then switches to explicit CoT for verification and answer generation. In a training-free instantiation, LaTER projects final-layer hidden states back to the input embedding space, preserves the latent KV cache, and uses entropy and model-native stop-token probes to decide when to switch. We find that strong reasoning models already exhibit structured latent trajectories under this interface. On Qwen3-14B, training-free LaTER reduces total token usage by 16%-32% on several benchmarks while matching or improving accuracy on most of them; for example, it improves AIME 2025 from 70.0% to 73.3% while reducing tokens from 15,730 to 10,661. We further construct Latent-Switch-69K, a supervised corpus that pairs condensed solution intuitions with shortened explicit derivations. Fine-tuning with latent rollout and halting supervision yields additional gains: trained LaTER reaches 80.0% accuracy on AIME 2025, 10.0 points above the standard CoT baseline, while using 33% fewer tokens. Our code, data, and model are available at https://github.com/TioeAre/LaTER.

Modern reasoning language models generate dense, sequential chain-of-thought traces implicitly assuming that every token contributes and that steps must be consumed in order. We challenge both assumptions through a systematic intervention pipeline--removal, masking, shuffling, and noise injection--applied to model-generated reasoning chains across three models and three benchmarks. Our findings are counterintuitive on three dimensions. Order: Does the sequential order of a reasoning chain matter for answer extraction? No--line-level shuffling reduces accuracy by less than 0.5 pp; word-level shuffling retains 62%-89% accuracy; only token-level shuffling collapses to near zero. Pretrained-only and instruction-tuned variants exhibit near-identical tolerance (78.67% vs. 78.00% under line shuffling), indicating order-independence originates from pretraining rather than reasoning-specific fine-tuning. Dense: Is all the information in a reasoning chain important for answer extraction? No--masking numeric digits collapses accuracy to exactly 0%, while masking alphabetic prose improves accuracy by 4.7 pp. Robustness: Is a reasoning chain that is both order-shuffling and non-dense still robust? Yes--the most aggressively reduced representation (all natural language removed, lines arbitrarily shuffled) still achieves 83% accuracy, and injecting false answers at 3x true-answer frequency leaves accuracy unchanged (83.3%->83.3%), falsifying a frequency-based extraction account. These results establish that answer extraction operates on a sparse, order-insensitive, and structurally robust informational substrate, opening paths toward parallelized and token-efficient reasoning generation.

Multiple-choice reasoning benchmarks face dual challenges: rapid saturation from advancing models and data contamination that undermines static evaluations. Ad-hoc hardening methods (paraphrasing, perturbation) attempt to increase difficulty but sacrifice logical validity for surface complexity, falling short to challenge advanced reasoning models. We present LogiHard, a formal framework that deterministically transforms 0-order selection into 2-order logical judgment, which significantly increases the thinking overhead and reasoning steps. The framework integrates Item Response Theory (IRT) for computerized adaptive testing (CAT), enabling precise difficulty control with fewer questions than static benchmarks. We instantiate LogiHard-2k, a logical reasoning dataset constructed by cognitively ranking high-stakes examination questions via 9-dimensional analysis of model thinking traces, followed by combinatorial transformation of high-difficulty items. Evaluation across twelve state-of-the-art models reveals an accuracy degradation ranging from 31% to 56% on combinatorially hardened questions. LLMs suffer from the multi-select failure and early exit bias, which are not shared by human testees. Zero-shot transfer to MMLU demonstrates 47% accuracy degradation (89.84% to 42.86%), confirming applicability across domains with provable validity preservation. The consistent aggregate degeneration is domain-agnostic and stems not from knowledge deficits but from a combinatorial reasoning gap, reflecting a training-induced completeness-verification deficit.

Training a family of large language models (LLMs), either from scratch or via iterative compression, is prohibitively expensive and inefficient, requiring separate training runs for each model in the family. In this paper, we introduce Star Elastic, a novel LLM post-training method that adds N nested submodels to a given parent reasoning model using the compute of one run (N-fold savings) via a single post-training job. Beyond reducing training costs, Star Elastic also addresses a fundamental limitation of efficient reasoning: the rigidity of static architectures, which forces the allocation of constant resources regardless of token difficulty. By unlocking elastic budget control, Star Elastic enables a novel inference scheme that uses different submodels for each reasoning phase (thinking and answering). Star Elastic supports (1) nesting along the SSM, embedding channel, MoE, and FFN axes, (2) learning nested submodels via an end-to-end trainable router, and (3) curriculum-based knowledge distillation. Building on the Nemotron Elastic framework, we apply Star Elastic to the NVIDIA Nemotron Nano models, with a particular focus on hybrid Mixture-of-Experts (MoE) architectures: from Nemotron Nano v3 (30B/3.6A), we generate 23B (2.8A) and 12B (2.0A) variants with 160B training tokens. All nested models match or outperform independently trained baselines of comparable size and achieve a 360x reduction versus pretraining from scratch and a 7x reduction over state-of-the-art compression. Crucially, elastic budget control advances the accuracy-latency Pareto frontier, achieving up to 16% higher accuracy and 1.9x lower latency via dynamic per-phase model selection. We further extend Star Elastic to quantized regimes via Quantization-Aware Distillation (QAD), producing nested NVFP4 and FP8 elastic checkpoints that preserve zero-shot slicing while delivering smaller deployment footprints.

Reinforcement learning (RL) has achieved remarkable success in LLM reasoning, but whether it can also improve direct recall of parametric knowledge remains an open question. We study this question in a controlled zero-shot, one-hop, closed-book QA setting with no chain-of-thought, training only on binary correctness rewards and applying fact-level train-test deduplication to ensure gains reflect improved recall rather than reasoning or memorization. Across three model families and multiple factual QA benchmarks, RL yields ~27% average relative gains, surpassing both training- and inference-time baselines alike. Mechanistically, RL primarily redistributes probability mass over existing knowledge rather than acquiring new facts, moving correct answers from the low-probability tail into reliable greedy generations. Our data-attribution study reveals that the hardest examples are the most informative: those whose answers never appear in 128 pre-RL samples (only ~18% of training data) drive ~83% of the gain, since rare correct rollouts still emerge during training and get reinforced. Together, these findings broaden the role of RL beyond reasoning, repositioning it as a tool for unlocking rather than acquiring latent parametric knowledge.

When distilling reasoning from large language models (LLMs) into smaller ones, teacher rationales for similar problems often vary wildly in structure and strategy. Like a chef who makes the same dish differently each time, this inconsistency burdens the student with noisy supervision that is hard to internalize. We propose Distillation through Reasoning Path Compression (D-RPC), which constrains the teacher to follow a compact, dynamically maintained bank of reusable high-level reasoning paths. For each training question, D-RPC retrieves the most relevant path and conditions the teacher to follow it, producing rationales that are consistent across similar problems yet diverse enough to cover different problem types. A PAC-Bayes analysis formalizes the resulting trade-off between bank size and coverage: smaller banks reduce supervision entropy but risk coverage gaps, and the generalization bound identifies an optimal intermediate size confirmed by our ablations. Across five math and commonsense reasoning benchmarks with two student models, D-RPC consistently outperforms chain-of-thought distillation, freeform rationale generation, direct distillation, and structured-supervision baselines, while using fewer tokens than template-heavy alternatives.

Reinforcement learning with verifiable rewards (RLVR) has become a highly effective method for improving the reasoning abilities of Large Language Models (LLMs). Recent research shows that Negative Sample Reinforcement (NSR) -- which focuses on penalizing incorrect steps rather than simply rewarding correct ones -- can match or even exceed the performance of more complex frameworks like PPO and GRPO across the entire Pass@k spectrum. However, current NSR techniques usually apply a fixed penalty throughout the training process and treat every incorrect response with the same weight. To address these limitations, we propose two extensions to the NSR framework: Adaptive Negative Sample Reinforcement. Rather than using a fixed update rule, A-NSR uses time-dependent scheduling functions. In the initial training phases, the system focuses heavily on correcting errors to stabilize the model. As training continues, it shifts toward more subtle and controlled updates. We also introduce Confidence-Weighted Negative Reinforcement, which operates on the principle that different mistakes carry different levels of importance. CW-NSR assigns specific penalty weights based on the model's normalized sequence likelihood. If the model is highly confident in a wrong path, it receives a larger penalty and for uncertain errors -- where the model is effectively exploring -- are penalized less strictly. Our formal analysis shows how these mechanisms govern token-level updates, allowing the model to leverage prior-guided probability redistribution while providing a natural defense against overfitting. We evaluated these methods on difficult reasoning datasets, including MATH, AIME 2025, and AMC23, using the Qwen2.5-Math-1.5B architecture.

In-context reinforcement learning (ICRL) refers to the ability of RL agents to adapt to new tasks at inference time without parameter updates by conditioning on additional context. Recent empirical studies further demonstrate that Chain-of-Thought (CoT) generation can amplify this ICRL capability. This paper is the first to provide a theoretical understanding on how CoT interacts with ICRL. We conduct our analysis in a policy evaluation setup with linear Transformer. We prove that with specific Transformer parameters, the CoT generation process is equivalent to repeatedly executing temporal difference learning updates. Additionally, we provide finite sample convergence analysis showing that the policy evaluation error decreases geometrically with CoT length and eventually saturates at a statistical floor determined by the context length. We also prove that the desired Transformer parameters are a global minimizer of the pretraining loss, providing a theoretical understanding on the empirical emergence of those parameters.

Benchmarks like GSM8K are popular measures of mathematical reasoning, but leaderboard gains can overstate true capability due to memorization of fixed test sets. Most robustness variants apply surface-level perturbations (paraphrases, renamings, number swaps, distractors) that largely preserve the underlying facts, and static releases can themselves become memorization targets over time. We introduce GSM-SEM, a reusable and stochastic framework for generating semantically diverse benchmark variants with substantially higher semantic variance than prior approaches. GSM-SEM perturbs problem statements by modifying entities, attributes, and/or relationships, frequently altering underlying facts and requiring models to recompute solutions under new conditions, while constraining generation to preserve the original calculations/answer and approximate problem difficulty. GSM-SEM generates fresh variants on each run without requiring re-annotation, reducing reliance on static public benchmarks for evaluation and thereby lowering the bias of memorization. We apply GSM-SEM on GSM8K and two existing variation suites (GSM-Symbolic and GSM-Plus), producing GSM8K-SEM, GSM-Symbolic-SEM, and GSM-Plus-SEM. Evaluating 14 SOTA LLMs, we observe consistent performance drops with larger decline when semantic perturbations are coupled with symbolic/plus variations (average drop rate 28% in maximum strictness configuration of GSM-SEM). We publicly release the three SEM variants as fully human-validated datasets. Finally, to demonstrate applicability beyond GSM-style math problems, we apply GSM-SEM to additional benchmarks including BigBenchHard, LogicBench, and NLR-BIRD.

Large Language Models (LLMs) have shown good performance on various science educational benchmarks, demonstrating their potential for use in science and mathematics education. Yet, LLMs tend to be evaluated on science and mathematical educational datasets from the Western world, with an underrepresentation of datasets from the Global South. Furthermore, they tend to have multiple-choice answer options that are trivial to evaluate. In this work, we present NSMQ Riddles, a novel benchmark of Scientific and Mathematical Riddles from Ghana's National Science and Maths Quiz (NSMQ) competition to evaluate LLMs. The NSMQ is an annual live TV competition for senior secondary school students in Ghana that brings together the smartest high school students in Ghana who compete in teams of 2 by answering questions in biology, chemistry, physics, and math over five rounds and five stages until a winning team is crowned for that year. NSMQ Riddles consists of 11 years of riddle questions (n=1.8K) from the 5th round, with each riddle containing a minimum of 3 clues. Students compete to be the first to guess the answer on any of the clues, with earlier clues being vague and also fetching more points. The answers are usually a number, word, or short phrase, allowing for automatic evaluation. We evaluated state-of-the-art models: closed (GPT-5.4, Gemini 3.1 Pro, Claude Opus 4.6) and open models (Kimi-K2.5, DeepSeek-V3.1, GPT-OSS-120B) with high and low reasoning settings. Our evaluation shows that the dataset is challenging even for state-of-the-art LLMs, which performed worse than the best student contestants. This work contributes a novel and challenging benchmark for scientific and mathematical reasoning from the Global South towards enabling a true global benchmarking of LLMs' capabilities for science and mathematics education.

Large Language Models (LLMs) have achieved great improvements in recent years. Nevertheless, it still remains unclear how good LLMs are for reasoning tasks, especially for long-chain ones. In this paper, we evaluate LLMs' performance on the simplest yet long-chain reasoning task, namely the Equivalence Class Problem (ECP), i.e., determining whether two variables are equal given a set of randomly generated equivalence relations. We consider both reasoning and non-reasoning representative LLMs over a large variety of problem instances, ranging over different numbers of variables, connectivity probabilities, prompts, and other factors. The experimental results show that non-reasoning LLMs fail ECP, while reasoning models are significantly better but still struggle to completely solve this problem. Interestingly, considering various connectivity probabilities with a fixed number of variables, we observe that, for non-reasoning models, the hardest problem instances coincide with the phase transition point of ln n/(n-1), suggesting the chaos of the problem; in contrast, for reasoning models, the hardest ones coincide with the biggest diameter, suggesting the reasoning difficulty of the problem.

Large language models (LLMs), especially reasoning models, generate extended chain-of-thought (CoT) reasoning that often contains explicit deliberation over future outcomes. Yet whether this deliberation constitutes genuine planning, how it is structured, and what aspects of it drive performance remain poorly understood. In this work, we introduce a new method to characterize LLM planning by extracting and quantifying search trees from reasoning traces in the four-in-a-row board game. By fitting computational models on the extracted search trees, we characterize how plans are structured and how they influence move decisions. We find that LLMs' search is shallower than humans', and that performance is predicted by search breadth rather than depth. Most strikingly, although LLMs expand deep nodes in their traces, their move choices are best explained by a myopic model that ignores those nodes entirely. A causal intervention study where we selectively prune CoT paragraphs further suggests that move selection is driven predominantly by shallow rather than deep nodes. These patterns contrast with human planning, where performance is driven primarily by deep search. Together, our findings reveal a key difference between LLM and human planning: while human expertise is driven by deeper search, LLMs do not act on deep lookahead. This dissociation offers targeted guidance for aligning LLM and human planning. More broadly, our framework provides a generalizable approach for interpreting the structure of LLM planning across strategic domains.

Autoregressive generation lies at the heart of the mechanism of large language models. It can be viewed as the repeated application of a next-token generator: starting from an input string (prompt), the generator is applied for $M$ steps, and the last generated token is taken as the final output. [Joshi et al., 2025] proposed a PAC model for studying the learnability of the input-output maps arising from this process. We develop an online analogue of this framework, focusing on the mistake bound of learning the final output induced by an unknown next-token generator. We distinguish between two forms of feedback. In the End-to-End model, after each round the learner observes only the final token produced after $M$ autoregressive steps. In the Chain-of-Thought model, the learner is additionally shown the entire $M$-step trajectory. Our goal is to understand how the optimal mistake bound depends on the generation horizon $M$, and to what extent observing intermediate tokens can reduce this dependence. Our main results show that the online theory of autoregressive learning exhibits a qualitative picture analogous to the statistical one found by [Hanneke et al., 2026], but with a different scale of dependence on the generation horizon. In the End-to-End model, we prove a taxonomy of possible mistake-bound growth rates in the generation horizon $M$: essentially any rate between constant and logarithmic can arise. We further show that this logarithmic ceiling is unavoidable. In the Chain-of-Thought model, we show that access to the full generated trajectory eliminates the dependence on $M$ altogether. We also analyze autoregressive linear threshold classes, and prove optimal mistake bounds, as well as a new lower bound for the statistical setting. Along the way, our results resolve several questions left open by [Joshi et al., 2025].

Large Language Models (LLMs) demonstrate strong capabilities for solving scientific and mathematical problems, yet they struggle to produce valid, challenging, and novel problems - an essential component for advancing LLM training and enabling autonomous scientific research. Existing problem generation approaches either depend on expensive human expert involvement or adopt naive self-play paradigms, which frequently yield invalid problems due to reward hacking. This work introduces VHG, a verifier-enhanced hard problem generation framework built upon three-party self-play. By integrating an independent verifier into the conventional setter-solver duality, our design constrains the setter's reward to be jointly determined by problem validity (evaluated by the verifier) and difficulty (assessed by the solver). We instantiate two verifier variants: a Hard symbolic verifier and a Soft LLM-based verifier, with evaluations conducted on indefinite integral tasks and general mathematical reasoning tasks. Experimental results show that VHG substantially outperforms all baseline methods by a clear margin.

Reinforcement learning (RL) has been applied to improve large language model (LLM) reasoning, yet the systematic study of how training scales with task difficulty has been hampered by the lack of controlled, scalable environments. Observed LLM shortcomings in long-horizon reasoning have raised the prospect that they are fundamental to the autoregressive transformer architecture. To address this, we introduce ScaleLogic, a synthetic logical reasoning framework that offers independent control over two axes of difficulty: the depth of the required proof planning (i.e., the horizon) and the expressiveness of the underlying logic. Our proposed framework supports a wide range of logics: from simple implication-only logic ("if-then") towards more expressive first-order reasoning with conjunction ("and"), disjunction ("or"), negation ("not"), and universal quantification ("for all"). Using this framework, we show that the RL training compute $T$ follows a power law with respect to reasoning depth $D$ ($T \propto D^γ$, $R^{2} > 0.99$), and that the scaling exponent $γ$ increases monotonically with logical expressiveness, from $1.04$ to $2.60$. On downstream mathematics and general reasoning benchmarks, more expressive training settings yield both larger performance gains (up to $+10.66$ points) and more compute-efficient transfer compared to less expressive settings, demonstrating that what a model is trained on, not just how much it is trained, shapes downstream transfer. We further show that the power-law relationship holds across multiple RL methods, and curriculum-based training substantially improves scaling efficiency. More broadly, our results demonstrate that LLM shortcomings in long-horizon reasoning are not fundamental to the underlying architecture, and can be addressed by improved training methodology and data.

Reliable confidence estimation enables safe deployment of chain-of-thought (CoT) reasoning through text-only APIs. Yet the dominant black-box baseline, self-consistency over K samples, is linearly expensive and ignores the geometry of the trace. We propose a black-box trajectory-confidence score: we embed a CoT as a sliding-window trajectory and measure its convergence to external answer anchors with a one-parameter softmax. The method needs no logits, hidden states, or supervised calibrators. Across six (benchmark, reasoner) settings on MedQA-USMLE, GPQA Diamond, and MMLU-Pro with Gemini 3.1 Pro and Claude Sonnet 4.6, fusing this score with coverage and verbalized-confidence channels at K=4 yields Pareto improvements over self-consistency at K=8 in 6/6 settings (median AUC 0.78 vs 0.71, deltaAUC=+0.075). A fixed-pick control (+0.060) and E5 cross-embedder replication rule out answer switching and single-vendor artifacts. Geometry peaks in the penultimate window across benchmarks and reasoners, and inverts at the terminal window on GPQA Diamond. Three unscaffolded regimes separate black-box confidence into a judge-mediated Coverage prior (C), within-trace Geometry (G), and a conditional Verbalization channel (V). Across 18 benchmark x reasoner x proposer settings, C and G provide independent signal in 18/18 and 16/18, while V contributes residual signal in 6/18. Swapping the judge from GPT-5-mini to Claude Sonnet 4.6 leaves G-only AUC unchanged (|delta|<=0.013) and shifts C-only AUC by at most +/-0.02 (kappa=0.82). Fusion beats the best single channel in 17/18 settings (median AUC 0.78, max 0.92).

Single-step retrieval-augmented generation (RAG) provides an efficient way to incorporate external information for simple question answering tasks but struggles with complex questions. Agentic RAG extends this paradigm by replacing single-step retrieval with a multi-step process, in which the large language model (LLM) acts as a search agent that generates intermediate thoughts and subqueries to iteratively interact with the retrieval system. This iterative process incurs substantial latency due to the autoregressive generation of lengthy thoughts and subqueries. To address this limitation, we propose LatentRAG, a novel framework that shifts both reasoning and retrieval from discrete language space to continuous latent space. Unlike existing explicit methods that generate natural language thoughts or subqueries token-by-token, LatentRAG produces latent tokens for thoughts and subqueries directly from the hidden states in a single forward pass. We align LLMs with dense retrieval models in the latent space, enabling retrieval over latent subquery tokens and supporting end-to-end joint optimization. To improve transparency and encourage semantically meaningful latent representations, we incorporate a parallel latent decoding mechanism that translates latent tokens back into natural language. Extensive experiments on seven benchmark datasets show that LatentRAG achieves performance comparable to explicit agentic RAG methods while reducing inference latency by approximately 90%, substantially narrowing the latency gap with traditional single-step RAG.

Reinforcement learning has become the standard for improving reasoning in large language models, yet evidence increasingly suggests that RL does not teach new strategies; it redistributes probability mass over solutions the base model already contains. In this work, we ask: if RL merely steers the model toward paths it already knows, is the RL optimization loop itself necessary? Through token-level analysis across multiple model families and RL algorithms, we find that RL's beneficial footprint is a sparse, predictable correction concentrated at high-entropy decision points where the model is uncertain which branch to take. Only 1--3% of token positions are affected, the promoted token always lies within the base model's top-5 alternatives, and targeted corrections at those few positions causally recover a large fraction of RL's accuracy gain, while random corrections fail. The base model's own entropy identifies these positions without any RL-trained model, and the entire correction is low-dimensional, representable in a tiny fraction of model parameters. These findings reframe reasoning improvement as sparse policy selection, not capability acquisition. We translate this insight into ReasonMaxxer, a minimal RL-free method that applies contrastive loss only at entropy-gated decision points, using a few hundred base-model rollouts and no online generation. Across three model families, six scales, and six math reasoning benchmarks, ReasonMaxxer matches or exceeds full RL performance while requiring only tens of problems and minutes of single-GPU training, a reduction in training cost of roughly three orders of magnitude.

This paper studies test-time aggregation, an approach that generates multiple reasoning traces and aggregates them into a final answer. Most existing methods rely on evaluation signals collected from candidate traces in isolation or answer frequencies, while ignoring comparative interactions among candidates. We propose Joint Consistency (JC), formulated as a constrained Ising-type energy minimization problem, where independent evaluation signals act as external fields and pairwise comparisons act as interactions. JC provides a unified framework for test-time aggregation that subsumes existing voting and weighted aggregation methods as special cases. Our construction of the interaction matrix leverages LLM-as-a-judge comparisons, and admits a theoretical interpretation under answer-level homogeneity assumptions. Moreover, we develop an efficient approximation strategy that makes interaction modeling practical for large-scale test-time aggregation. Experiments on math and code reasoning benchmarks show that JC consistently outperforms existing baselines across tasks, judge models, trace budgets, and trace-generation settings.

On-Policy Self-Distillation (OPSD) has recently emerged as an alternative to Reinforcement Learning with Verifiable Rewards (RLVR), promising higher accuracy and shorter responses through token-level credit assignment from a self-teacher conditioned on privileged context. However, this promise does not carry over to thinking-enabled mathematical reasoning, where reported accuracy gains shrink and sometimes turn negative. We hypothesize that hindsight supervision can specify better token-level alternatives in short thinking-disabled outputs, but in long thinking-enabled traces it more readily identifies redundancy than supplies better replacements. To test this, we applied OPSD separately to correct and incorrect rollout groups, so that compression and correction can be observed in isolation. Our results show that in thinking-enabled mathematical reasoning, OPSD behaves most reliably as a compression mechanism rather than a correction mechanism: training only on correct rollouts preserves accuracy while substantially shortening responses, whereas training only on incorrect rollouts damages accuracy. In light of these findings, we propose a revised post-training pipeline for thinking-enabled mathematical reasoning: SFT then RLVR then OPSD.

Pest-induced crop losses pose a major threat to global food security and sustainable agricultural development. While recent advances in Multimodal Large Language Models (MLLMs) have shown strong potential for visual understanding and smart agriculture, their direct application to pest recognition remains limited due to the domain's unique challenges such as high inter-species complexity, intra-species variability, and the scarcity of expert-annotated data. In this work, we introduce Pest-Thinker, a knowledge-driven reinforcement learning (RL) framework that enables MLLMs to reason over fine-grained pest morphology. We first construct two high-definition pest benchmarks, QFSD and AgriInsect, comprising diverse species and expert-annotated morphological traits. Leveraging these datasets, we synthesize Chain-of-Thought (CoT) reasoning trajectories to facilitate structured learning of pest-specific visual cues through Supervised Fine-Tuning (SFT). Subsequently, we employ Group Relative Policy Optimization (GRPO) with a novel feature reward that guides the model to focus on observable morphological evidence, assessed by an LLM-as-a-Judge strategy. Extensive experiments demonstrate that Pest-Thinker substantially improves both in-domain and out-of-domain morphological understanding, marking a step toward expert-level visual reasoning for intelligent agricultural pest analysis. The datasets and source code are available upon acceptance.

Inference-time computation has greatly enhanced the performance of large language models (LLMs) on challenging reasoning tasks, but this strategy can incur high inference costs. One solution is to route intermediate chain-of-thought (CoT) states to language models of different sizes; however, existing approaches rely on handcrafted routing strategies that limit performance, or on training large process reward models that may be infeasible in many applications. We formulate stepwise model routing as a constrained decision-making problem, which we solve by training a small control policy using reinforcement learning in conjunction with threshold calibration to tune the performance-efficiency tradeoff. We validate our method on three math benchmarks (GSM8K, MATH500, and OmniMath) on both open and closed models. Our method consistently improves the accuracy-cost tradeoff compared to handcrafted approaches, while achieving a comparable tradeoff to methods that require training large process reward models.

Although advances such as chain-of-thought, tree-of-thought or reinforcement learning have improved the performance of LLMs in reasoning and planning tasks, they are still brittle and have not achieved human-level performance in many domains, and often suffer from high time and token costs. Inspired by the success of width-based search in planning, we explore how the concept of novelty can be transferred to language domains and how it can improve tree-of-thought reasoning. A tree of thoughts relies on building possible "paths" of consecutive ideas or thoughts. These are generated by repeatedly prompting an LLM. In our paper, a measurable concept of novelty is proposed that describes the uniqueness of a new node (thought) in comparison to nodes previously seen in the search tree. Novelty is estimated by prompting an LLM and making use of embedded general knowledge from pre-training. This metric can then be used to prune branches and reduce the scope of the search. Although this method introduces more prompts per state, the overall token cost can be reduced by pruning and reducing the overall tree size. This procedure is tested and compared using several benchmarks in language-based planning and general reasoning.

Large Language Models (LLMs) are evolving into autonomous trading agents, yet existing benchmarks often overlook the interplay between architectural reasoning and strategy consistency. We propose Strat-LLM, a framework grounded in Stratified Strategy Alignment. Operating in a live-forward setting throughout 2025, it integrates heterogeneous data including sequential prices, real-time news, and annual reports to eliminate look-ahead bias. Extensive stress tests on A-share and U.S. markets reveal: (1) reasoning-heavy models achieve peak utility in Free Mode via internal logic, whereas standard models require Strict Mode as a vital risk anchor; (2) alignment utility is regime-dependent, with Free and Guided modes capturing momentum in uptrending markets, while Strict Mode mitigates drawdowns in downtrends; (3) mid-scale models (35B) show optimal fidelity under strict constraints, whereas ultra-large models (122B) suffer an alignment tax under rigid rules but gain a performance premium in Guided Mode; (4) standard LLMs often fall into a high win-rate trap, optimizing for small gains at the expense of total returns, which can only be mitigated through deep reasoning or strict external guardrails. Project details are available at https://Strat-LLM.github.io.

Recent advances in generative video models are increasingly driven by post-training and test-time scaling, both of which critically depend on the quality of video reward models (RMs). An ideal reward model should predict accurate rewards that align with human preferences across diverse scenarios. However, existing paradigms face a fundamental dilemma: \textit{Discriminative RMs} regress rewards directly on features extracted by multimodal large language models (MLLMs) without explicit reasoning, making them prone to shortcut learning and heavily reliant on massive data scaling for generalization. In contrast, \textit{Generative RMs} with Chain-of-Thought (CoT) reasoning exhibit superior interpretability and generalization potential, as they leverage fine-grained semantic supervision to internalize the rationales behind human preferences. However, they suffer from inherent optimization bottlenecks due to the coupling of reasoning and scoring within a single autoregressive inference chain. To harness the generalization benefits of CoT reasoning while mitigating the training instability of coupled reasoning and scoring, we introduce DeScore, a training-efficient and generalizable video reward model. DeScore employs a decoupled ``think-then-score'' paradigm: an MLLM first generates an explicit CoT, followed by a dedicated discriminative scoring module consisting of a learnable query token and a regression head that predicts the final reward. DeScore is optimized via a two-stage framework: (1) a discriminative cold start incorporating a random mask mechanism to ensure robust scoring capabilities, and (2) a dual-objective reinforcement learning stage that independently refines CoT reasoning quality and calibrates the final reward, ensuring that higher-quality reasoning directly translates to superior model performance.

Verifiers are crucial components for enhancing modern LLMs' reasoning capability. Typicalverifiers require resource-intensive superviseddataset construction, which is costly and faceslimitations in data diversity. In this paper, wepropose LOVER, an unsupervised verifier regularized by logical rules. LOVER treats theverifier as a binary latent variable, utilizinginternal activations and enforcing three logical constraints on multiple reasoning paths:negation consistency, intra-group consistency,and inter-group consistency (grouped by thefinal answer). By incorporating logical rulesas priors, LOVER can leverage unlabeled examples and is directly compatible with any offthe-shelf LLMs. Experiments on 10 datasetsdemonstrate that LOVER significantly outperforms unsupervised baselines, achieving performance comparable to the supervised verifier(reaching its 95% level on average). The sourcecode is publicly available at https://github.com/wangxinyufighting/llm-lover.

Current reasoning paradigms for LLMs include chain-of-thought, ReAct, and post-hoc self-critique. These paradigms rely on two assumptions that fail on long-horizon, multi-stage tasks. As a result, errors accumulate silently across reasoning steps, leaving an open question: can a reasoning system effectively detect and recover from its own failures? We present ReFlect, a \emph{harness} system for LLM reasoning that creates standalone error detection and recovery logic as a deterministic wrapper around the model. Controlled experiments across 6 reasoning domains show that prompt-level self-critique produces formulaic templates that flag no issues in 90 of 100 audited reflection blocks, and the investigated LLMs wrongly accept a wrong answer in at least 76% of cases. Our ReFlect harness achieves task success rates ranging from 41% on gpt-4o-mini to 56% on Claude Sonnet 4.5 across six models spanning small and frontier scale, with per-model gains over Direct CoT ranging from +7 pp on Qwen2.5-72B to +29 pp on Claude Sonnet 4.5, and additionally raises SWE-bench patch-structural quality from 0% (Direct CoT) to between 82% (Qwen2.5-72B) and 87% (GPT-4o). Notably, the harness gain is inversely proportional to the model's Direct CoT task success rate (the fitted slope is -1.69 with r=-0.76): each pp lost in baseline success rate is mechanically recovered by 1.69 pp of harness gain. We spot that adding structured reasoning state and operators yields only 15.0--18.7% pair-mean on Llama-3.3-70B and Qwen2.5-72B because models at this scale cannot reliably populate the state its operators require. ReFlect is model-agnostic, training-free, and operates entirely at inference time.

Large reasoning models (LRMs) increasingly expose chain-of-thought-like reasoning for transparency, verification, and deliberate problem solving. This creates a safety blind spot: harmful or policy-violating content may appear in reasoning traces even when final answers appear safe. We test whether final-answer safety is a sufficient proxy for the full reasoning-answer trajectory by scoring both stages under a unified twenty-principle safety rubric. Using prompts from seven public harmfulness and jailbreak sources, plus four out-of-distribution (OOD) sources, we evaluate 15 open-weight and API-based LRMs across 41K prompts per model. Reasoning traces consistently reveal additional safety risks beyond final answers, especially in high-severity stage-wise failures: leak cases, where unsafe reasoning precedes a safe-looking answer, and escape cases, where benign-looking reasoning precedes an unsafe final response. Principle-level analysis shows that risk concentrates in misinformation, legal compliance, discrimination, physical harm, and psychological harm. We further propose adaptive multi-principle steering, a white-box test-time mitigation that learns one unsafe-to-safe activation direction per safety principle and activates only directions whose current hidden state is closer to the unsafe than safe centroid. On three steerable open reasoning models, adaptive steering reduces unsafe counts in both reasoning traces and final answers on held-out and OOD benchmarks. DeepSeek-R1-Qwen-7B achieves a 40.8% average unsafe-count reduction while retaining 97.7% macro-averaged accuracy on BBH, GSM8K, and MMLU. These results suggest that LRM safety should be evaluated and mitigated over the full exposed reasoning-answer trajectory, not only at the final-answer stage.

We introduce an axiomatic evaluation framework for latent thought representations in LLMs, comprising metrics that are independent of downstream benchmark scores and reveal representational failures that benchmark accuracy masks. Existing evaluations conflate representation quality with model capacity. Therefore, failures cannot be attributed to the representation rather than to the model that processes it. We formalize four functional axioms (Causality, Minimality, Separability, and Stability) and define a quantitative measure for each, computed directly on the representation independently of downstream accuracy. We audit open-weight LLMs across 23 reasoning tasks (e.g., Spatial Reasoning, Factual QA). We find that no candidate satisfies all four axioms simultaneously, that the representations distinguish task type reliably but cannot distinguish between two questions within the same task, and that the representations encode little information beyond what is already present in the input embedding. The failure is consistent across dense, reasoning-distilled, and RL-trained model families, indicating that the gap is structural rather than a property of model size or training procedure.

Retrieval-Augmented Generation (RAG) has become a core paradigm for enhancing factual grounding and multi-hop reasoning in Large Language Models (LLMs). Traditional text-based RAG often retrieves logically irrelevant pseudo-evidence, while graph-based RAG is frequently hindered by search-time pruning, which may discard potentially valid reasoning paths. Existing hybrid approaches primarily adopt simple evidence concatenation or unidirectional enhancement, which fails to address the fundamental "Information Island" problem caused by asymmetric reasoning flows between unstructured text and structured graphs. We propose \textbf{TGS-RAG}, a unified framework for \textbf{T}ext-\textbf{G}raph \textbf{S}ynergistic enhancement. TGS-RAG introduces a bidirectional mechanism: (i) a \textbf{Graph-to-Text} channel that employs a Global Voting strategy from visited graph nodes to re-rank and refine textual evidence, filtering out semantic noise; and (ii) a \textbf{Text-to-Graph} channel that utilizes the \textbf{Memory-based Orphan Entity Bridging} algorithm. This algorithm utilizes textual cues to proactively resurrect valid but previously pruned reasoning paths from the search history without additional database overhead. Experimental results on multiple multi-hop reasoning benchmarks demonstrate that TGS-RAG significantly outperforms state-of-the-art baselines, achieving a superior balance between retrieval precision and computational efficiency.

Reinforcement learning with verifiable rewards, particularly Group Relative Policy Optimization (GRPO), has significantly advanced the reasoning capabilities of Large Language Models (LLMs). However, in complex tasks, GRPO frequently suffers from the ``zero-advantage problem'': when all sampled rollouts for a query fail, the relative advantage collapses to zero. Consequently, the model loses effective training signals for these questions, wasting the training data and computational budget. While simply increasing the sampling budget for these questions is a common remedy, the static sampling policy inherently constrains reasoning exploration, limiting the success rate. In this paper, we propose Lorem Perturbation for Exploration (LoPE), a simple yet effective training framework to break this exploration bottleneck. We posit that task-irrelevant prompt-space perturbations can shift the model's output distribution enough to unlock orthogonal reasoning pathways for hard questions. Specifically, LoPE prepends sequences stochastically assembled from Lorem Ipsum vocabulary (a pseudo-Latin placeholder text) to the prompts before resampling. Experiments across 1.7B, 4B, and 7B models demonstrate that LoPE significantly outperforms resampling with the original prompts. Further analysis reveals that other Latin-based random sequences with low perplexity are also effective perturbations. Our results establish LoPE as a strong baseline for broadening exploration in LLM reinforcement learning.

Post-training quantization makes large reasoning models practical under tight memory and latency budgets, but it can distort the online signals that drive adaptive test-time compute allocation. Under a fixed cap on the number of newly generated tokens, miscalibrated confidence can lead to harmful early halting: the model may surface a plausible final line while the underlying reasoning is still wrong, or the controller may stop before the trace has stabilized. We study this interaction for greedy 4-bit inference and propose BitCal-TTS, a lightweight runtime controller that combines (i) inexpensive online proxies for token-level uncertainty and reasoning-trace stability, (ii) a bit-conditioned confidence rescaling that is conservative at low nominal precision, and (iii) a bit-aware post-marker confirmation horizon designed for GSM8K-style structured outputs. The method requires no fine-tuning of the base model and integrates with standard Hugging Face 4-bit inference using forward hooks for logits and last-layer hidden states. On small evaluation shards of GSM8K with Qwen2.5 Instruct models, BitCal-TTS improves exact-match accuracy over a non-bit-aware adaptive baseline at the 7B and 14B scales while preserving substantial token savings relative to fixed-budget decoding. At a token cap of B=512, on the evaluation shards we report (N=54 for 7B and N=35 for 14B; not the full GSM8K test set), accuracy gains are +3.7 points (7B) and +2.8 points (14B), with the premature-stop rate falling from 14.8% to 11.1% on 7B and from 17.1% to 11.4% on 14B. We report Wilson 95% confidence intervals throughout and explicitly discuss the limited statistical power of the partial-shard comparisons. We release code and figure-generation scripts to support full reproduction.

Natural language interfaces to databases have gained popularity, yet the theoretical foundations for evaluating and designing these systems remain underdeveloped. We present QUEST (Query Understanding Evaluation through Semantic Translation), a framework resting on two independently motivated components: the FAR structural invariant, which holds that every well-formed query reduces to Filter, Aggregate, and Return operations; and the W5H dimensional framework, which holds that all filtering criteria map to six semantic dimensions (Who, What, Where, When, Why, and How). Validated across five text-to-SQL datasets (n = 120,464), FAR conformance is universal across all domains and schema types, while W5H dimensional profiles vary substantially. Healthcare queries are strongly concentrated in temporal (WHEN: 80.4%) and person-centric (WHO: 73.0%) dimensions far exceeding general-domain benchmarks, and causal (WHY) and mechanistic (HOW) reasoning are near-zero everywhere, with apparent HOW exceptions reflecting quantitative aggregation rather than genuine procedural reasoning. These results identify a frontier that must be crossed for genuine machine reasoning over structured data.

LLMs can solve program synthesis tasks but remain inefficient and unreliable on hard instances requiring large combinatorial search. Given a small set of reasoning traces, we use coding agents to compile them into reusable symbolic program synthesizers over constrained DSLs. The resulting solvers require no LLM calls at test time and are strong standalone systems: symbolic solver ensembles reach 91.3% accuracy on PBEBench-Lite and 84.7% on PBEBench-Hard, outperforming LLMs with test-time scaling for the latter by +16.3 percentage points at zero LLM inference cost. They also complement LLM search, improving PBEBench-Hard accuracy from 68.4% to 85.8% while reducing reported token usage by 78%, and raising SLR-Bench hard-tier accuracy from 34.4% to 58.0% in a neuro-symbolic hybrid setting. Compared to directly using coding agents as per-instance solvers, induced solvers are substantially more Pareto-efficient, amortizing a small one-time construction cost over many zero-token executions. Finally, most solvers transfer zero-shot to a real historical linguistics task - predicting sound changes in natural language data - reaching 80.1% accuracy under ensembling and recovering some plausible linguistic rules. Together, these results show that reasoning traces can be compiled into reusable symbolic solvers that solve many tasks directly, complement LLM inference on hard cases, and provide a scalable route to domain-general solver induction. We release code and data for reproducibility.

Large language models increasingly operate in interactive settings where solving a task requires multiple rounds of information exchange with a user. However, most current systems treat dialogue reactively and lack a principled mechanism to reason about what information is missing and which question should be asked next. We propose BALAR (Bayesian Agentic Loop for Active Reasoning), a task-agnostic outer-loop algorithm that requires no fine-tuning and enables structured multi-turn interaction between an LLM agent and a user. BALAR maintains a structured belief over latent states, selects clarifying questions by maximizing expected mutual information, and dynamically expands its state representation when the current one proves insufficient. We evaluate BALAR on three diverse benchmarks: AR-Bench-DC (detective cases), AR-Bench-SP (thinking puzzles), and iCraft-MD (clinical diagnosis). BALAR significantly outperforms all baselines across all three benchmarks, with $14.6\%$ higher accuracy on AR-Bench-DC, $38.5\%$ on AR-Bench-SP, and $30.5\%$ on iCraft-MD.

Computational cognitive models discovered using large language models have so far relied solely on behavioral data. However, it is well-known that models produced from the behavioral trajectory alone are typically under-determined. In this work, we explore the use of Think Aloud traces as an additional form of data constraint during automated model discovery. When applied to the domain of risky decision-making, we find that the models discovered with think-aloud achieve significantly improved predictive performance on held-out data. Additionally, we find that the discovered models belong to different structural classes than those discovered from behavior alone for the majority of participants (69.4%), specifically, it shifts from Explicit comparator towards Integrated utility. These results suggest that process-level language data not only improve model fit, but also systematically reshape the structure of the discovered cognitive models, enabling the identification of mechanisms that are not recoverable from behavior alone.

This paper describes our system submitted to SemEval-2026 Task 11: Disentangling Content and Formal Reasoning in Large Language Models. We present an efficient modular neuro-symbolic approach, combining a symbolic prover with small reasoning LLMs (4B parameters). The system consists of an LLM-based parser that translates natural language syllogisms to a first-order logic (FOL) representation, an automated theorem prover, and two optional modules: machine translation for multilingual inputs and a symbolic retrieval component for the identification of relevant premises. The system achieves competitive accuracy and relatively low content effect on most subtasks. Our ablations show that this approach outperforms LLM-based zero-shot baselines in this parameter size range, but also reveal limited multilingual capabilities of small LLMs. Finally, we include a discussion of the task's main ranking metric and analyze its limitations.

This paper presents NoisyCoconut, a novel inference-time method that enhances large language model (LLM) reliability by manipulating internal representations. Unlike fine-tuning methods that require extensive retraining, NoisyCoconut operates directly on model representations during inference and requires no retraining. Rather than training models to reason in latent space, we inject controlled noise into latent trajectories to generate diverse reasoning paths. Agreement among these paths provides a confidence signal, enabling models to abstain when uncertain. We demonstrate that this approach achieves effective coverage-accuracy tradeoffs across multiple reasoning benchmarks without requiring access to training data or modification of model parameters. This approach provides a practical pathway to improving the reliability of LLM outputs while maintaining compatibility with existing models. Our experiments show that unanimous agreement among noise-perturbed paths reduces error rates from 40-70% to below 15%, enabling models to exceed 95% accuracy on mathematical reasoning tasks through selective abstention.

While Large Language Models (LLMs) excel in certain reasoning tasks, they struggle in multi-agent games where the final outcome depends on the joint strategies of all agents. In multi-agent games, the non-stationarity of other agents brings significant challenges on the evaluation of the reasoning process and the credit assignment over multiple reasoning steps. Existing single-agent reinforcement learning (RL) approaches and their multi-agent extensions fail to address these challenges as they do not incorporate other agents in the reasoning process. In this work, we propose Strat-Reasoner, a novel RL-based framework that improves LLMs' strategic reasoning ability in multi-agent games. We introduce a novel recursive reasoning paradigm where an agent's reasoning also integrates other agents' reasoning processes. To provide effective reward signals for the intermediate reasoning sequences, we employ a centralized Chain-of-Thought (CoT) comparison module to evaluate the reasoning quality. Finally, we compute an accurate hybrid advantage and develop a group-relative RL approach to optimize the LLM policy. Experimental results show that Strat-Reasoner substantially improves strategic abilities of underlying LLMs, achieving 22.1% average performance improvements across various multi-agent games. Code is publicly available at https://github.com/ydhe1012/Strat-Reasoner.

This paper presents the Personalized Thinking Model (PTM), a hierarchical and interpretable learner representation designed for AI supported education. PTM organizes evidence from learner journals into a five-layer structure covering behavioral instances, behavioral patterns, cognitive routines, metacognitive tendencies, and self-system values. PTM is grounded in Marzano's New Taxonomy of Educational Objectives and tries to clone learner's thinking model and build cognitive twin. It was constructed using a pipeline that combines large language model inference (Gemini 2.5 Pro), sentence embeddings, dimensionality reduction, and consensus clustering. This paper evaluates PTM fidelity through three methods applied to 40 participants in a seven-week study. First, automatic evaluation using atomic information point matching yielded an overall F1 score of 74.57% before human-in-the-loop (HITL) refinement and 75.48% after refinement. Second, user evaluation using a Likert scale produced mean ratings of 4.26 and 4.30 on a five-point scale for pre and post-HITL conditions respectively. Third, semantic alignment verification showed that topic coherence increased from 0.436 at the behavioral layer to 0.626 at the core value layer, while lexical overlap with journal vocabulary decreased from 0.114 to 0.007 across those same layers. These results suggest that the PTM produces outputs with acceptable fidelity, was generally perceived by users as reflecting their thinking, and showed a pattern consistent with semantic abstraction across layers.

Cyber threats are rapidly increasing, expanding their impact from large-scale enterprises to government services and individual users, making robust security systems increasingly essential. However, a significant shortage of skilled cybersecurity professionals exacerbates this challenge. While recent research has explored automating tasks such as penetration testing using LLM-based agents, existing frameworks often perform poorly due to limited capability in strategy formulation, domain-specific reasoning, and accurate action and tool selection. To overcome these limitations, we propose Pen-Strategist framework, consisting of a novel domain-specific reasoning model that derives pentesting strategies via logical reasoning and a classifier that converts the strategies into actionable steps. First, we construct a reasoning dataset containing logical explanations for both strategy derivation and step selection in pentesting scenarios. We then fine-tune a Qwen-3-14B model for strategy generation using reinforcement learning. Evaluation on the test split of the dataset demonstrates a 87% improvement in strategy derivation performance compared to the baseline. Furthermore, we integrate the fine-tuned Pen-Strategist model into existing automated pentesting frameworks, such as PentestGPT, and evaluate its performance on vulnerable machines, achieving a 47.5% improvement in subtask completion while surpassing the baseline GPT-5. Further experiments on the CTFKnow benchmark show an 18% performance gain over the base model. For step prediction, we train a semantic-based CNN classifier, which outperforms commercial LLMs by 28% and enhances execution stability. Finally, we conduct a user study to qualitatively assess the generated strategies, and Pen-Strategist demonstrates superior performance compared to the Claude-4.6-Sonnet.

Can LLMs simulate how humans form and change beliefs in social networks? We put this to the test by replicating an established study on belief dynamics, evaluating 12 LLMs across multiple model families and parameter sizes. The answer is a clear no, and in systematic ways. LLMs fail to capture initial human belief distributions and tend to be overall more conformist than humans, shifting their responses to align with those around them. They also take a nuanced approach to emulating human homophilic tendencies within networks. Our findings carry a double payoff: they highlight fundamental properties of LLM behavior, and they raise a sharp warning against deploying LLMs as human proxies in social simulations.