Large Language Model Reasoning

Natural-language explanations are often treated as a unified interface for understanding model behavior, but different explanation sources may support simulation in different ways. This paper compares two families of explanations for question answering models: verbalized feature attributions and self-generated rationales. We evaluate them under a shared counterfactual simulation setting, using an LLM judge as predictor and measuring whether it can better predict a model's answers to follow-up questions when given its explanation. Across multiple instruction-tuned models, we analyze how explanation source, verbalization strategy, and feature granularity affect the simulatability of explanations. Our results show that explanation format and granularity affect simulatability: attribution-based explanations and self-generated rationales differ in how much they improve counterfactual prediction, with effects that vary across models and formats.

While Reasoning Language Models (RLMs) are rapidly emerging as powerful tools for scientific research, their impact is primarily concentrated in "hard science" fields. The slow -- or lack of -- adoption of RLMs in other branches of science is causing a widening gap in research productivity. In this survey, we provide the first comprehensive analysis of RLM adoption across 28 scientific disciplines following the classification used by the European Research Council (ERC), spanning the Social Sciences and Humanities, Physical Sciences and Engineering, and Life Sciences. We examine how RLMs are developed, evaluated, and applied across disciplines. Furthermore, we introduce a maturity-oriented assessment framework based on available domain-specific development and evaluation resources, revealing substantial disparities in RLM maturity that become even more pronounced when only publicly available resources are considered. Finally, we highlight current implementation paradigms that are gaining popularity across disciplines, current challenges, and future directions in enabling RLM adoption across science.

Single-score translation metrics can conflate legitimate variation with error, a problem especially acute for classical languages where multiple defensible English renderings of the same passage coexist. We audit Pali-to-English output from four flagship large language models (LLMs): GPT-5.5, Claude Sonnet 4.6, Gemini 3.1 Pro, and Grok 4.3, on 1,700 passages from the Pali Canon, using three established human translations by Bhikkhu Sujato, Thanissaro Bhikkhu, and Bhikkhu Bodhi as a local reference envelope rather than a single gold standard. Each candidate's normalized embedding drift from the reference centroid serves as a triage signal, not an error label; the 1,203 candidates above a 1.5 drift threshold are then adjudicated by a blinded three-model LLM judge panel, calibrated against a 300-instance author-adjudicated validation set. Two results stand out. First, drift predicts severity rather than error per se: the major-error rate among adjudicated high-drift candidates rose monotonically from 7.9% in the 1.5-2.0 band to 51.6% above 3.0, while approximately 80% of 1.5-2.0 outliers were judged valid translation variations. Second, model differences were clearest in the high-drift tail: GPT-5.5 had the lowest adjudicated high-drift major-error rate, with confidence intervals overlapping those of Claude Sonnet 4.6 and Gemini 3.1 Pro; Grok 4.3 had both the largest outlier volume and the highest tail major-error rate (27.6% overall, 74.4% above drift 3.0). The dominant major-error categories (e.g. omission or truncation, doctrinal term errors) are precisely the failures most likely to mislead readers of doctrinal text. The contribution is a reusable audit design for classical-to-modern translation: define a local reference envelope from multiple human translators, use embedding drift to prioritize review, and adjudicate the flagged tail rather than treating outlier status as error.

Recent work suggests that large language models (LLMs) can improve through self-evolution (SE), using supervision signals generated by the model itself. In this work, we ask: under a strict closed-loop setup, where the self-evolution algorithm has access only to an unlabeled prompt set and a base model, how close can internally generated supervision come to oracle-supervised training? We analyze four representative strategies in a unified offline self-evolution framework: single-round verification, multi-turn revision with feedback, iterative training, and curriculum learning. Our primary experiments use Knights and Knaves (KK) logical reasoning tasks, which provide deterministic solutions, controlled difficulty levels, and a clean testbed for easy-to-hard generalization. We first show that self-evolution consistently improves over the base model, but plateaus after excessive training compute is invested, and eventually still leaves a non-trivial gap to oracle supervision. We find that multi-turn critic-revision with large models can reach strong self-evolution performance, with Gemma 12B nearly matching oracle-supervised training. Beyond Knights and Knaves, we also evaluate self-evolution on real-world reasoning benchmarks, where gains are also modest. Overall, our results characterize when closed-loop self-evolution can help and show how internally generated supervision remains insufficient under this minimal formulation.

Reinforcement learning with verifiable rewards (RLVR) has become central to LLM reasoning, but its outcome-level rewards can make models more willing to give confident answers when evidence or reasoning is unreliable. Existing SFT or RL methods mainly teach LLMs to refuse or express uncertainty at the response level, which can overfit abstention behavior rather than improve reasoning reliability. To address this limitation, we propose Cognitive Pairwise Training (CPT), a cognitive mid-training alignment stage that turns pairwise comparisons over reasoning traces into a reusable alignment signal. By learning to distinguish trustworthy from flawed reasoning, CPT encourages the model to internalize a reasoning-quality discrimination boundary rather than memorize surface refusal patterns. Across five model scales and three model families, CPT improves the reasoning--metacognition trade-off. At 14B, CPT+RL outperforms the standard SFT+RL pipeline by +2.2 math-average points and +5.2 abstention-F1 points. Further analyses show that CPT improves trace quality and exhibits strong robustness and scalability across evaluation and training settings. Code and models are released at https://github.com/Tsinghua-dhy/CPT.

Strong reasoning depends not only on model knowledge but also on how effectively cognitive behaviors are deployed during generation. Existing methods often rely on explicit behavior-level control, making them insufficiently adaptive when failures and required corrections vary across reasoning states, tasks, and models. To this end, we propose Latent Reward Steering (LRS), an adaptive inference-time framework that promotes cognitive behaviors by optimizing the sparse-autoencoder (SAE) latent states that implicitly carry them. Rather than relying on predefined cognitive behaviors or steering directions derived from them, LRS trains a latent reward model on reasoning traces by final answer correctness to estimate the quality of intermediate latent states. During inference, reward gradients provide state-specific correction directions for fragile latent states, while a reward and confidence gate restricts intervention to states the reward signal flags as fragile. Experiments on multiple reasoning LLM backbones and benchmarks show that \ours consistently improves performance over various baselines, and post-hoc analyses further indicate that \ours implicitly promotes good cognitive behaviors that fix the original reasoning errors. Code is available at: https://github.com/jiakanglee/Latent-Reward-Steering.

Recent progress in the development of language models has been defined by scale, with each generation absorbing more of the world's knowledge into its weights. However, many practical applications benefit more from robust reasoning than from extensive parametric knowledge. In this setting, task-specialized small language models (SLMs) offer a principled design choice. We introduce Optimal Cognitive Core (OCC), a family of SLMs built around this premise. As a variant of OCC, we present OCC-RAG, optimized for faithful question answering (QA) grounded in the provided context. This task directly aligns with the OCC design approach, requiring multi-hop reasoning over supplied passages while ignoring memorized knowledge. To train OCC-RAG, we implement a novel pipeline for synthesizing multi-context, multi-hop QA data at scale, producing a corpus of over three million examples targeting multi-hop reasoning, strict context faithfulness, and calibrated abstention. We release OCC-RAG-0.6B and OCC-RAG-1.7B, both mid-trained on this corpus. The models produce structured reasoning traces with source citations grounded in literal quotes from the context. Through OCC-RAG, we demonstrate that compact, task-specialized SLMs can match or exceed general-purpose models 2 -- 6x their size across multi-hop reasoning (HotpotQA, MuSiQue, TAT-QA), faithfulness (ConFiQA), and refusal (MuSiQue-Un) benchmarks.

Reasoning traces have become a valuable form of learning signals for improving and transferring the capabilities of large language models. In particular, detailed traces can help distill reasoning behavior from stronger teacher models into weaker student models. The value of capability transfer has motivated many deployed systems with reasoning models to hide raw internal traces and expose at most summaries and answers to users. As a result, we ask whether such interface-level trace hiding prevents users from obtaining useful reasoning supervision through prompting. We study this question with Reasoning Exposure Prompting (REP), a lightweight in-context elicitation method that uses shadow-model-generated demonstrations wrapped in auxiliary code-like formats to raise user-visible reasoning traces from a victim model. Across the common reasoning dataset, different victim models, and different student model distillation, REP substantially increases similarity between exposed and REP-conditioned internal traces while preserving useful reasoning signals.

Self-distillation improves learning efficiency by rewriting reference answers as training data that better matches the model's own distribution. However, reference answers also introduce strong stylistic biases, causing the generative model to imitate surface forms rather than learn useful reasoning patterns. We observe that the rewriting data contains a large number of high-perplexity (PPL) tokens, coming from two distinct sources: beneficial knowledge-enhancing logical corrections, and harmful stylistic drift induced by reference imitation. Treating all such tokens equally can disrupt the base model's original distribution and degrade performance, especially on difficult reasoning tasks. To address this, we propose Distribution-Aligned Self-Distillation (DASD), which uses an answer-aware reference model to generate candidate tokens and dynamically filters them according to the base model's confidence. DASD preserves tokens that encode useful logical knowledge while suppressing distributionally misaligned style noise. Experiments on math, code, and commonsense reasoning benchmarks show that DASD consistently outperforms competitive baselines, reduces high-PPL tokens, and improves robustness across tasks of varying difficulty.

Recent Vision-Language Models (VLMs) struggle with grounded reasoning, temporal consistency, and context aware planning in videos. We introduce pause-and-think-T, a reasoning-centric training dataset that encourages models to pause, reason over visual evidence, and produce concise, actionable responses. The dataset promotes structured reasoning prior to answer generation, guiding models toward human-like, scene-grounded assistance. We fine-tune a compact 4B-parameter model and evaluate it on our pause-and-think-B benchmark targeting contextual understanding and goal planning tasks. The model achieves 58.0% accuracy at 59x fewer parameters than Qwen3-VL-235B (58.9%), matching GPT-5.2 on scene understanding and surpassing GPT-4o. Beyond our benchmark, it also shows strong out-of-distribution performance on EgoThink and TempCompass, with substantial gains in affordance, assistance, attribution recognition, situated reasoning, and temporal order, without benchmark-specific training. Our results indicate that targeted reasoning supervision enables compact models to deliver actionable, visually grounded guidance while generalizing beyond training data, without requiring large-scale model expansion.

Agentic search systems iteratively interact with retrieval models to answer complex queries. Despite substantial progress, optimizing retrievers for agentic search remains challenging, often requiring heavy co-training or gold-standard annotations that limit real-world applicability. We propose Critic-R, a framework that explicitly closes the feedback loop between the reasoning agent and the retrieval model during both inference and training. Critic-R introduces a critic model that evaluates the agent's introspective reasoning trace after consuming retrieved evidence to determine whether the retrieved context sufficiently supports the next reasoning step. Critic-R has two complementary mechanisms: Critic-R-Zero, an inference-time query refinement loop that iteratively rewrites queries and retrieval instructions, and Critic-Embed, an optimization approach for retrieval models that leverages successful and failed refinement trajectories as automatic supervision without requiring manual relevance annotation. We evaluate Critic-R on HotpotQA, 2WikiMultihopQA, MuSiQue, and Bamboogle. Results show that Critic-R significantly improves both retrieval quality and downstream answer accuracy.

Network faults propagate layer by layer along topology and protocol dependencies, yet operations systems typically observe only symptomatic alerts at the tail end of propagation chains, where distinct root-cause faults may produce highly similar end-point symptoms. Existing approaches, whether rule-based, machine learning (ML)-based, or large language model (LLM)-based, fundamentally map the alert set to a diagnosis in a single pass and are structurally incapable of resolving this end-point ambiguity. This paper proposes PropLLM, which is the first to integrate the hop-by-hop scene reconstruction paradigm with the generative reasoning capabilities of LLMs. Starting from end-point alerts, PropLLM traces back hop-by-hop along the propagation path, retrieving verifiable factual evidence from a dual-layer knowledge graph (KG) at each hop, while the proposed Temporal Causal Propagation Attention (TCPA) mechanism encodes known topological causal priors directly into the attention computation to guide the model along the correct causal direction, ultimately localizing the root cause and determining the fault type through a fully evidenced causal chain. On a real-world Wi-Fi multimodal fault dataset, PropLLM improves fault type diagnosis accuracy by 3.9% and root cause localization accuracy by 4.7% over the strongest baseline, while reducing the hallucination rate by 50.8%. Supplementary experiments on the TeleLogs 5G dataset further demonstrate the effectiveness of the proposed method across different network scenarios.

Speech recognition in specialized domains requires leveraging contextual or topical information to improve the recognition of domain-specific entities. Speech Large Language Models (Speech LLMs) have substantially advanced speech understanding and reasoning capabilities, making context-aware speech recognition possible without predefined bias lists. In this paper, we propose LaSR (Latent Speech Reasoning), a novel training paradigm featuring a context-aware reasoning trajectory that leverages the latent reasoning process. Instead of generating explicit intermediate tokens, LaSR aligns chain-of-thought (CoT) supervision around the acoustic feature region of the target word, and introduces latent reasoning periods for context information grounding and transcriptional transition. Furthermore, to effectively benchmark context-aware speech recognition, we propose Spoken Darwin-Science, a large-scale corpus focusing on academic terminologies. Preliminary experiments on Fun-Audio-Chat demonstrate that LaSR significantly improves terminology recognition without introducing additional latency and consistently outperforms standard supervised fine-tuning baselines. Our findings highlight the potential of latent reasoning in building efficient, context-aware speech assistants.

Extended chain-of-thought reasoning can degrade performance on deterministic state-tracking tasks, not due to preference biases, but limits rooted in the information-theoretic capacity of decoder-only attention. We establish: (1) an Attention Bottleneck Theorem with a complementary achievability construction, bounding state-tracking capacity as $O(H \cdot \log(L/H) \cdot \sqrt{d_h})$; (2) a context-dependent error model yielding super-exponential accuracy decay; (3) the State-Space Jaccard metric distinguishing capability from preference failures; (4) a Deterministic Horizon $d^* \in [19, 31]$ beyond which tool delegation becomes necessary. Across 12 models and 8 task domains (including SWE-Bench, WebArena, and SQL-Multi), tool-integrated reasoning consistently outperforms neural chain-of-thought; on the primary model suite it reaches 86-94% accuracy versus 24-42% for neural chain-of-thought. Fine-tuning on optimal-length traces yields $<$5% improvement, confirming an architectural ceiling, and high cross-model correlation ($r = 0.81$-$0.91$) indicates these failures are architectural rather than training-specific. Our results provide principled guidance for when pure neural reasoning should yield to hybrid approaches in agentic systems.

On-Policy Distillation (OPD) improves large language model reasoning by training a student model on trajectories sampled from its own policy under teacher supervision. Although OPD operates on trajectories, its learning signal remains token-level: it identifies deviations through high-loss tokens and repairs them through local reverse-KL correction. We show that this "trajectory-sampled but token-learned" mechanism cannot reliably bridge student trajectories toward teacher trajectories. About 30% of high-loss tokens fall into the low-divergence regime, indicating that many are surface-form mismatches rather than real reasoning forks. Moreover, even truly divergent tokens are difficult to repair with isolated token-level supervision, since reasoning failures often unfold as short-horizon distributional drift. We propose Trajectory-aware OPD (TOPD), which uses near-future trajectory information to identify real divergent states and distribute guidance across multiple future tokens. Experiments show that suppressing non-divergent high-loss tokens improves standard OPD from 47.8% to 48.2% average accuracy, while TOPD further improves performance to 52.2%, with gains on AIME24 from 60.0% to 63.3% and AIME25 from 46.7% to 53.3%.

We study fact-level repair for multimodal generation, where a fluent output may contain specific facts that are not supported by the input. Existing inference-time repair methods often generate feedback by jointly conditioning on the input and the current output. This design has two limitations: hallucinated claims in the output can bias the model's interpretation of the input, and free-form feedback cannot be ranked or scheduled at the fact level. We present TIGER, an inference-time framework that redesigns feedback for localized repair. TIGER independently extracts an observation graph from the input and a claim graph from the current output, then assigns each claim a graph-conditioned risk score based on support and conflict. The model repairs selected high-risk claims while keeping the backbone frozen. We provide a convergence analysis showing that the expected total risk decreases geometrically to an explicit asymptotic bound under mild assumptions. Experiments across four cross-modal paths, including image-to-text, image+text-to-text, audio-to-text, and video-to-text, show that TIGER reduces unsupported content while preserving task quality. The gains hold across multiple backbones, and a CrisisFACTS case study suggests that the same repair mechanism can improve grounding in multi-source settings.

Post-training quantization (PTQ) is widely used to deploy large language models efficiently, but its effect on reasoning models is not well understood. Across math, coding, and science QA, we find that aggressive PTQ reduces accuracy while increasing chain-of-thought (CoT) length. Surprisingly, we show that in up to 52% of the quantized models' failures, models reach the right answer in intermediate reasoning steps but do not output it as a final answer. To understand why quantization leads to this increase in overthinking errors, we measure the token-level KL divergence between quantized and full-precision output distributions. Positions with high KL divergence correlate strongly with high next-token entropy, and at these positions quantized models disproportionately sample overthinking markers such as "wait", "but", and "alternatively". We show that simply introducing a training-free logit penalty on a curated set of overthinking markers can reduce CoT length by 12--23% while preserving or improving accuracy across 5 models (1.5B-32B parameters), 3 quantization methods, and 5 benchmarks, yielding a favorable Pareto frontier of accuracy against reasoning cost compared to penalizing other token sets. Overthinking errors produced by quantized models are particularly reduced by up to 58%.

Long-context reasoning remains a central challenge for large language models, which often fail to locate and integrate key information in extensive distracting content. Reinforcement learning with verifiable rewards (RLVR) has shown promise for this task, yet existing methods are limited by low-confusability distractors and sparse, outcome-only reward signals that cannot supervise intermediate reasoning steps. To address these issues, we introduce \textsc{LongTraceRL}. For data construction, we generate multi-hop questions via knowledge graph random walks and leverage search agent trajectories to build \emph{tiered distractors}: documents the agent read but did not cite (high confusability) and documents that appeared in search results but were never opened (low confusability), producing training contexts that are far more challenging than those built by random sampling or one-shot search. For reward design, we propose a \emph{rubric reward} that uses the gold entities along each reasoning chain as fine-grained, entity-level process supervision. This rubric reward is applied only to responses with correct final answers (positive-only strategy), distinguishing the reasoning quality among correct responses and preventing reward hacking. Experiments on three reasoning LLMs (4B--30B) across five long-context benchmarks demonstrate that \textsc{LongTraceRL} consistently outperforms strong baselines and encourages comprehensive, evidence-grounded reasoning. Codes, datasets and models are available at \href{https://github.com/THU-KEG/LongTraceRL}{https://github.com/THU-KEG/LongTraceRL}.

Reasoning is essential for autonomous driving (AD) in long-tail scenarios, where vehicles must apply commonsense knowledge, understand spatial relations, infer agent interactions, and make safe decisions. However, existing AD datasets and benchmarks mainly target perception, prediction, or planning, and provide limited supervision for reasoning over realistic long-tail driving scenes. We introduce nuReasoning, a large-scale real-world dataset and benchmark for reasoning-centric AD. Following the lineage of nuScenes and nuPlan, nuReasoning advances real-world AD datasets and benchmarks toward reasoning in long-tail driving scenarios. The dataset contains 20,000 clips, each 20 seconds long, collected across multiple cities, with synchronized multi-camera images, LiDAR data, HD maps, object annotations, and human-verified reasoning annotations spanning Spatial Reasoning, Decision Reasoning, and Counterfactual Reasoning. Unlike prior datasets that focus primarily on visual question answering, nuReasoning supports both reasoning evaluation and planning evaluation, enabling a direct study of how reasoning supervision affects driving performance. Experiments show that fine-tuning VLMs on nuReasoning substantially improves driving-specific question answering, while incorporating reasoning supervision into VLA training improves planning performance even when textual reasoning outputs are disabled at inference time. These results establish nuReasoning as a foundation for evaluating and improving robust, interpretable, reasoning-driven AD systems in realistic long-tail settings.

Test-time reasoning has become a significant field of study since the introduction of chain-of-thought reasoning in large language models (LLMs). However, the mechanisms of this reasoning process are still under-explored -- from the same input prompt, and even the same partial solution, LLMs can produce varied answers if sampled multiple times. We propose to leverage question-asking as an inference-time intervention that articulates information about the model's hidden state. To achieve that, we present a student-teacher setting where a student asks questions to a teacher. We train a probe on the student's hidden state before and after asking a question and find it is predictive of the trajectory's final correctness, even before generating the teacher's answer. This suggests there is a meaningful signal from the self-diagnosis that occurs during question generation rather than information transfer from the teacher. We then frame question-asking as a sequential decision problem, using this probe as a quality score, and define a gating policy to ask questions that maximize likelihood of correctness. We find that the success of question-asking as an intervention is largely dependent on the model's self-consistency. Our empirical results show a gap between detection and recovery; while our gating policy captures model correctness and uncertainty, interventions are equally likely to harm correct trajectories as they are to recover incorrect ones. This gap between diagnosis and correction has broader implications on language models' capacity for self-refinement under uncertainty.

Table question answering requires models to recover semantic relations encoded implicitly by two-dimensional layout, merged cells, and hierarchical headers. Current pipelines typically use HTML or Markdown as intermediate table representations, but these layout-oriented serializations introduce markup overhead and require large language models to infer header-cell alignments from row and column spans. We propose Semantic Triplet Restoration (STR), a protocol that rewrites each cell as an atomic fact <item path, feature path, value>, where the item path specifies the row-wise entity, the feature path specifies the hierarchical attribute, and the value contains the cell content. We also present TripletQL, a lightweight query-aware router that uses STR to select an appropriate rendering or filtered subset of triplets for each question. Across four Chinese and English table-QA benchmarks, STR matches or improves upon HTML-based baselines while reducing input tokens. The relative benefit grows for smaller language models and longer table contexts, suggesting that explicit semantic representations are especially useful under constrained inference budgets. Code and data are available at https://github.com/Phoenix-ni/STR.git .

Large language models (LLMs) often solve reasoning problems by generating intermediate traces that explore and revise partial solutions. From a search perspective, these traces can be viewed as linearized search trees, where the model extends a partial solution, abandons it when it fails, and backtracks to try alternatives. Compared with traditional heuristic-guided search, such a policy has a potential advantage: it conditions on the whole search trace rather than only on the current local state. We first test whether LLMs utilize this advantage by comparing trace-conditioned reasoning policies against best-first search equipped with an LLM heuristic that only observes the current local state. Across three controlled reasoning environments, Blocks World, grid Navigation, and Sokoban, we find that raw access to search history alone is not enough to reliably outperform heuristic search. We then study one possible reason: in LLM reasoning traces, the underlying search tree is only implicitly represented, and when the model backtracks or switches branches, the trace does not explicitly identify which earlier search state is being revisited. We show that adding simple parent pointers to explicitly represent the linearized tree (LinTree) structure improves both task performance and search efficiency relative to implicit reasoning models and LLM-heuristic-guided search. These results suggest that search history becomes most useful when its tree structure is made explicit, motivating more structure-aware representations for LLM reasoning.

Large Reasoning Models (LRMs) still struggle with fine-grained translation quality estimation (QE), even with long reasoning chains. We argue that LRMs already possess strong multilingual capabilities, while the core challenge stems from the intrinsic difficulty of learning the fine-grained QE task. In this paper, we propose $\textbf{RIEQE}$ ($\textbf{R}$easoning both $\textbf{I}$mplicitly and $\textbf{E}$xplicitly for $\textbf{QE}$), a simple two-stage training framework that enables the mutually boosting of implicit (layer-wise) and explicit (token-wise) reasoning capabilities. To make implicit reasoning feasible, we first decompose the complex QE task into straightforward subtasks. Based on this, our two-stage approach applies: (1) $\textit{NonThinking-SFT}$, Supervised Fine-Tuning (SFT) without reasoning chains to directly boost the model's implicit reasoning tendency and capability; and (2) $\textit{Thinking-RLVR}$, standard Reinforcement Learning with Verifiable Reward (RLVR) to subsequently strengthen explicit reasoning. On the WMT test sets, RIEQE based on Qwen3-4B-Thinking-2507 surpasses all baselines in explicit reasoning performance, while its implicit reasoning capability is also comparable to the best current encoder-based models. We further provide evidence for the mutually boosting between implicit and explicit reasoning, showing how they benefit each other in a bidirectional manner. Our code is available at https://github.com/NJUNLP/RIEQE.

Modular visual reasoning systems increasingly rely on shared working memory for multi-step collaboration, yet the failure dynamics of intermediate state evolution in low-capacity regimes remain underexplored. We study failure modes of collaborative reasoning with weak learners (4B--8B models) through the lens of noise accumulation. We introduce CoSee, an auditing framework that formalizes the read-write-verify loop to trace information flow in document visual question answering. Across multi-page, chart, and web-based benchmarks, we find a counter-intuitive degradation: naive shared workspaces often amplify hallucinations rather than resolve them. We identify two dominant failure modes: Noise Reinforcement, where ungrounded notes are reused as evidence, and Policy Collapse, where added context shifts the model toward under-specified, short-form answers. Using cost-accuracy Pareto frontiers, we show that increased compute can correlate negatively with performance without explicit verification. Our findings suggest that for resource-constrained agents, the bottleneck lies not in reasoning depth but in communication fidelity, providing trace-level diagnostics and a mechanistic baseline for reliable modular design.

Endowing large language models with compositional reasoning over specialized documents requires multi-hop training data at scale, where such data rarely exists outside of curated benchmarks built on structured sources. To construct it directly from plain, unannotated text, existing methods ask a single teacher model to jointly discover an evidence path through a document and verbalize it as a question-answer pair. However, these methods degrade sharply when documents are structured around repetitive templates and densely cross-referencing clauses, conditions that characterize most real-world specialized corpora. In this work, we decouple the two operations: reasoning paths are enumerated offline over a graph of contextual keyword centroids, and the teacher is invoked only to verbalize pre-validated paths. The graph enforces five geometric admissibility constraints, for which we provide Gram-matrix arguments establishing that local similarity bounds alone admit endpoint drift up to ${\sim}91^{\circ}$, and that an upper similarity bound is necessary to exit dense embedding cliques formed by boilerplate text. A matched-size ablation isolates the mechanism: at equal training scale, constrained and unconstrained chains yield indistinguishable downstream performance, and the gain at full scale comes from a 4.4$\times$ expansion of the usable corpus rather than from higher per-chain quality -- reframing the role of graph constraints, in this setting, as raising teacher synthesizability rather than improving chain content. Fine-tuning Qwen3-32B on 80K examples constructed from the CUAD legal contract corpus improves closed-book Token F1 from 21.66% to 38.58%. We have released our codes at https://github.com/hkgai-official/GCSCS.

While visually grounded Chain-of-Thought (CoT) has emerged as a promising paradigm to enhance fine-grained perception in multimodal large language models (MLLMs), its efficacy during the inference phase remains underexplored. In this work, we empirically find that mandating explicit object boxes in visually grounded CoT during inference often degrades performance compared to standard textual CoT, which reasons without explicit visual grounding. We hypothesize that the visual localization capability can be internalized into the textual CoT and that the mandatory explicit grounding introduces unnecessary interference with the model's primary objective of answer prediction. To address this problem, we propose Internalizing Visually Grounded Reasoning (\textbf{iVGR}), a novel reinforcement learning framework that transfers localization capabilities into the textual reasoning process. We employ a dual-stream training strategy, where a textual stream is aligned with a high-quality visually grounded stream via a proposed consistency reward, enabling the model to localize accurately without explicit grounding during inference. Extensive experiments demonstrate that our method significantly outperforms existing baselines on fine-grained benchmarks, while maintaining the flexibility to support tool-assisted inference workflows.

Large Language Models (LLMs) have significantly advanced online data services, particularly in the domain of financial question answering (FinQA). However, such systems remain susceptible to numerical reasoning hallucinations, which critically undermine reliability in high-stakes financial applications. Although retrieval-augmented generation (RAG) has been widely adopted to ground responses in external knowledge, it introduces three persistent challenges: noise sensitivity, calculation fragility, and an auditability crisis. Existing model-centric approaches, which primarily focus on optimizing either the retriever or generator in isolation, still struggle to address these issues in an integrated manner. In this work, we pioneer a data-centric paradigm and propose a novel framework, the Data-centric Reasoning Compiler (DCRC). The framework operates through three cohesive phases: (1) adversarial data construction, which synthesizes training examples with controlled noise to teach robustness; (2) multi-stage training that cultivates a Data-centric Structuring Agent (DSA) capable of explicit evidence auditing and program synthesis; and (3) a compile-and-execute inference process, where the DSA transforms user queries and retrieved documents into verifiable, executable reasoning programs. This data-driven framework ensures faithful numerical reasoning by design. We conduct extensive experiments on established offline benchmarks and further validate our framework through deployment in a real-world online financial QA system.

Large Language Models (LLMs) have achieved remarkable performance in complex reasoning tasks through Chain-of-Thought (CoT) prompting. However, this approach often leads to ``over-thinking,'' where models generate unnecessarily long reasoning traces for simple queries and incur avoidable inference cost. While recent work has explored adaptive reasoning, existing methods typically make a single query-level decision about whether to reason. This overlooks the dynamic nature of multi-step tasks, where the need for explicit reasoning varies across intermediate stages. To address this limitation, we introduce AdaptR1, a Reinforcement Learning (RL) based framework for adaptive interleaved thinking in multi-hop Question Answering (QA). Unlike previous approaches that require Supervised Fine-Tuning (SFT) for cold-start initialization, AdaptR1 uses a fully RL-based strategy with a quality-gated efficiency reward to dynamically allocate reasoning budgets at each step. Under the Graph-R1 setting, AdaptR1 reduces average think tokens by 69.71%, with a 90.35% reduction on HotpotQA, while maintaining performance comparable to or better than standard baselines. Furthermore, our analysis reveals that overthinking in multi-hop reasoning is not uniformly distributed but occurs predominantly during the initial planning stages, highlighting the effectiveness of step-wise adaptive budget allocation.

Large language models (LLMs) exhibit strong reasoning capabilities, yet most LLM-based agents are statically deployed and unable to improve through task interactions. Existing experience-driven methods often rely on memory or heuristics without enhancing the model's ability to learn, treating it as a passive executor and leading to early performance plateaus and limited long-term improvement. To address this issue, we propose MetaEvo, a two-stage framework for continual agent evolution that focuses on improving how the model learns from tasks experience, rather than solely on what it stores. MetaEvo first applies preference-based optimization to enhance the model's ability of principle abstraction, then enables the accumulation and reuse of these principles within a modular agent architecture. Experimental results on diverse reasoning benchmarks demonstrate that MetaEvo consistently outperforms strong baselines, maintains reliable improvement across iterations. These findings validate the effectiveness of meta-optimization in enabling agents to learn from experience and continually enhance their reasoning capabilities.

Recent advances in Large Reasoning Models have significantly improved chain-of-thought (CoT) capabilities via reinforcement learning (RL). However, generated reasoning chains frequently suffer from structural redundancy (i.e., \emph{overthinking}), incurring high computational overhead without improving answer correctness. Existing mitigation strategies typically rely on token-uniform length penalties, which provide coarse, segment-agnostic pressure toward shorter outputs and can inadvertently suppress useful reasoning alongside redundancy. To address this, we demonstrate that inefficiency concentrates in high-probability segments with low marginal utility. We derive a theoretical characterization of segment suboptimality under the correctness-length trade-off objective and propose \textsc{SLAT} (Segment-Level Adaptive Trimming), an RL framework that selectively suppresses redundant segments based on this criterion. Empirical results on standard benchmarks indicate that \textsc{SLAT} establishes a superior accuracy-efficiency Pareto frontier, reducing reasoning length by $50\%$ relative to uncompressed baselines while maintaining competitive accuracy. Overall, our results suggest that theoretically grounded, segment-aware trimming is a promising direction for efficient CoT reasoning in large language models.

Chain-of-thought prompting and looped Transformers both give a fixed model more test-time computation, but they differ in what they remember. Chain-of-thought stores intermediate state in generated tokens that remain in the context, whereas a looped Transformer carries state through recurrent hidden activations. We argue that this persistent mutable memory is a central resource for test-time reasoning. We compare three memory regimes, the compressed latent loop, the full sequence-state loop, and the chain-of-thought scratchpad. Our main result shows that a compressed loop is limited by the size of its recurrent state. Running the loop longer adds computation but does not by itself create a growing scratchpad, so a loop with a small recurrent state remains a small-space reasoner even when run for many steps. Under a standard complexity assumption, such loops cannot decide problems that are P-complete under logspace reductions, whereas polynomial-length chain-of-thought can. The separation is specific to compressed loops, as full sequence-state loops carry state at every input position and live in a memory-rich regime closer to explicit scratchpads. Controlled pointer-chasing and associative-recall sweeps illustrate this memory-budget view, with performance sensitive to whether the persistent-state budget matches the task's working-memory demand.

We study trajectory selection for reasoning distillation, where teacher-generated reasoning trajectories are selectively used as supervision for a student model. Existing methods rely on heuristics such as trajectory quality or model confidence, but they often overlook whether a trajectory is learnable by the student. In this paper, we present LARK, a learnability-grounded method for reasoning trajectory selection. LARK selects trajectories that the student can learn efficiently while preserving the generalization of the full training distribution. At the core of LARK is a learnability factor $ρ$, which characterizes the rate at which the student's training loss decreases. To estimate this rate efficiently and maintain generalization, we introduce a learnability proxy and a $χ^2$-regularized selection policy that balances learnability and distributional coverage, both with strong theoretical guarantees on their estimation error. Empirically, LARK consistently outperforms data selection baselines across multiple base models and reasoning tasks. Diagnostic analyses show that the LARK score predicts downstream training utility and that LARK-selected trajectories induce faster supervised fine-tuning loss reduction. Our code is available at https://github.com/Tianrun-Yu/LARK.

Large language models (LLMs) can reveal and amplify societal biases during chain-of-thought (CoT) generation. We present COFT (Chain of Fair Thought), a training-free decoding method that applies token-level fairness control at decode time, with distribution-free marginal validity guarantees (under exchangeability) for any frozen causal language model. COFT operates in three stages. First, it creates a masked counterfactual prompt by replacing sensitive spans with neutral tokens. Second, it compares the factual and masked logit distributions through lightweight logit fusion to attenuate attribute-driven biases. Third, it uses dual-branch split-conformal calibration to certify per-step candidate token sets at a user-chosen risk level. We evaluate COFT across six models and multiple bias benchmarks. Our method reduces standard bias metrics by 30-55% (median 38%) while preserving task utility and language quality. Reasoning accuracies remain unchanged within run-to-run noise margins. The computational overhead is modest, equivalent to one additional cached forward pass (<=11%). COFT offers a clear, auditable path to safer CoT generation with significant bias reduction, negligible utility loss, and no requirement for retraining, auxiliary classifiers, or weight access.

Machine unlearning evaluation is structurally skewed: Why-type questions, which probe causal and relational knowledge, comprise less than 0.06% of CounterFact, 0.6% of ZSRE, and less than 1.3% of TOFU, MUSE, and WMDP-Cyber. This near-zero representation means that methods that fail on causal knowledge can score highly in aggregate, and this failure is undetectable without balanced evaluation. We present 5WBENCH, a balanced 5,000-sample benchmark with 1,000 examples per 5W category (Who, What, When, Where, Why), making causal unlearning failures quantifiable for the first time. Using 5WBENCH, we show that no existing baseline simultaneously achieves high forgetting and high retention on Why-type questions: aggressive forgetting degrades retained knowledge, while conservative methods fail to forget causal facts. Why-type difficulty stems from multi-hop reasoning chains (44% of Why entries vs. less than or equal to 2% for others) and gradient dilution over 40.1-token answer spans. We present MAAT (Multi-phase Adapter-Aware Targeted Unlearning), a three-phase framework operating on LoRA adapter weights, combining gradient-projected ascent, SVD rank-dimension pruning, task vector negation, and hybrid KL-hidden-state retain repair. MAAT is the first method to simultaneously achieve high forgetting and high retention on Why-type causal knowledge, reaching a new operating point on the forget-retain Pareto frontier. We make our code publicly available.

Group Relative Policy Optimization (GRPO) is an effective recipe for training reasoning models with verifier-based outcome rewards, but its supervision is sparse: when all sampled trajectories for a prompt receive the same verifier reward, the group-relative advantage collapses to zero and learning stalls. Outcome-only rewards also provide no step-level credit assignment, limiting exploration and making it harder to learn robust reasoning. We present VeriGate (Verifier-Gated Step-Level GRPO), a verifier-gated extension of GRPO that addresses these limitations with three design choices. First, VeriGate keeps the verifier in charge whenever verifier rewards induce a meaningful preference among sampled trajectories, and uses process supervision only when verifier rewards are degenerate. Second, instead of collapsing Process Reward Model (PRM) step scores into a single trajectory reward, VeriGate converts them into future-cumulated rewards to assign continuation-aware credit. Third, VeriGate transforms these rewards into group-normalized token-level advantages, restoring informative gradients and fine-grained credit assignment while remaining less susceptible to reward hacking than methods that optimize aggregated PRM scores. Empirically, training on MATH with 1.5B and 7B Qwen2.5-Instruct models and evaluating on six reasoning benchmarks, VeriGate improves average accuracy by about 20% and 12% for 1.5B and 7B models respectively, substantially reduces zero-gradient failures, decreases reward-hacking behavior, and improves reasoning quality relative to outcome-only GRPO and PRM-as-outcome baselines.

To improve the reasoning capabilities of large language models, test-time compute is typically scaled by generating intermediate tokens before the final answer. However, this couples reasoning to autoregressive generation and thereby conflates internal computation with external communication. In contrast, human cognition can use working memory to hold and manipulate information internally without the need to externalize intermediate thoughts. Drawing on this principle, we introduce Reasoning in Memory (RiM), a latent reasoning method that replaces the autoregressive generation of reasoning steps with memory blocks. These memory blocks are fixed sequences of special tokens that unlock the working-memory capacity of large language models. Since they are fixed rather than generated, they can be processed in a single forward pass, enabling compute-efficient latent reasoning. To operationalize these memory blocks, we employ a two-stage curriculum. First, we ground them by predicting explicit reasoning steps after each memory block. Second, we discard this step-level supervision and iteratively refine the final answer after each memory block. Our experiments on reasoning benchmarks show that, across language models of different families and sizes, RiM matches or exceeds existing latent reasoning methods while avoiding the autoregressive generation of thoughts. These results demonstrate that large language models can be trained to use working memory as an effective mechanism for latent reasoning.

Frontier reasoning models are produced by posttraining base language models with reinforcement learning. Recent work has challenged this by showing that sampling from a sharpened version of the base model's distribution, a so-called power distribution, elicits comparable reasoning without additional training, curated datasets, or verifiers. However, making this method practical requires efficiently sampling from the power distribution. A sampler needs to "mix" to the power distribution, which necessitates moving between modes of the target distribution; intuitively, e.g., trying different reasoning strategies. The samplers proposed in prior works repeatedly select a "cut" position in the current reasoning trace uniformly at random and resample the suffix from that position onward. However, reasoning traces typically contain a few consequential decisions (e.g., the choice of proof strategy or algorithm), and we observe that a uniformly chosen cut tends to rewrite local details rather than revisit decision points. We introduce an algorithm (Entropy-Cut Metropolis-Hastings) that uses the base model's next-token entropy as a proxy to identify key decision points and resample from those positions. We empirically verify that entropy jumps are a useful proxy for decision points and, in a stylized model of reasoning, prove that our method's mixing time scales with the number of decisions in a trace rather than with the number of tokens, which can be much larger. Across MATH500, HumanEval, GPQA Diamond, and AIME26, our method consistently improves over baselines and RL-trained models.

Language model reasoning traces are rarely all-or-nothing; they frequently contain valid intermediate steps before a critical error occurs. Existing uncertainty quantification methods typically certify final answers or entire responses, failing to provide statistical guarantees for the proportion of a sequential trace that can be safely retained. To address this, we introduce CROP (Conformal Reasoning Output Prefixes), a verifier-agnostic calibration procedure for clean-prefix certification. Given any step-level risk proxy, CROP selects a calibrated threshold and returns the longest contiguous prefix whose step risk proxies remain below it, routing the uncertified suffix for downstream review or repair. Assuming exchangeability, CROP rigorously controls the marginal probability that the returned prefix contains an annotated error. Across six process-labeled reasoning datasets, we demonstrate that standard step-level metrics such as AUROC do not fully capture prefix utility, suggesting verifiers should instead be evaluated by certified prefix length. Furthermore, CROP balances over- and under-withholding, improving downstream repair accuracy by preserving valid intermediate reasoning while discarding misleading suffixes. Ultimately, this work positions prefix certification as a rigorous, practical bridge between process supervision, abstention, and repair.

The development of generative artificial intelligence technologies has propelled the visual realism of synthetic images to an unprecedented level. Although current interpretable detection methods based on Large Multimodal Models (LMMs) have made certain progress, they still rely on imitation learning derived from massive volumes of forged data. Consequently, they lack genuine causal reasoning capabilities and are prone to explanatory hallucinations. To overcome this bottleneck, we propose FakeVLM-R1, aiming to endow the model with human-like critical thinking capabilities when performing synthetic detection tasks. Building upon Supervised Fine-Tuning (SFT), this framework integrates Group Relative Policy Optimization (GRPO) with a Critical Thinking Chain-of-Thought (CoT) mechanism. During the inference phase, the model executes a "bidirectional dialectical reasoning" process: while proposing a forgery hypothesis, it must simultaneously invoke physical commonsense to construct an authenticity counter-proof. Furthermore, we constructed the FakeClue++ dataset with high-quality samples, which extensively introduces annotations guided by the physical laws of authentic images, providing a unified authenticity anchor for the model. Experiments confirm that FakeVLM-R1 achieves SOTA performance the evaluated models across multiple benchmarks. It not only achieves high-precision, logically interpretable detection but also resolves the over-rejection bias of existing methods against real images, demonstrating generalization and robustness against perturbations.

High-fidelity ECG interpretation is increasingly reliant on massive foundation models, yet their deployment in clinical edge-care remains hindered by extreme computational demands. While knowledge distillation (KD) is a promising solution, traditional methods fail to capture the complex spatio-temporal dependencies of ECG signals when transferring knowledge across heterogeneous architectures. In this paper, we propose EVL-ECG, a framework specifically designed for cross-architecture distillation of cardiac diagnostic logic. EVL-ECG introduces three ECG-aware innovations: (1) Multi-Head Cross-Attention Alignment, which harmonizes architectural discrepancies to preserve fine-grained morphological features; (2) Optimal Transport-based Visual Feature Matching, utilizing optimal transport to maintain global structural relationships across ECG leads despite mismatched token representations; and (3) Geometric Intra-Architecture Relation Matching, which distills the latent diagnostic reasoning of the teacher model. Evaluations across ECG benchmarks demonstrate that EVL-ECG yields improvements of up to 2.4% AUC and 1.1% clinical accuracy over existing baselines. Notably, EVL-ECG establishes an efficient 2B-parameter ECG foundation model, suitable for resource-constrained clinical environments.

Human reasoning has long been theorised to operate socially, not through isolated individual cognition, but through collective adversarial discourse, a framework known as the Argumentative Theory of Reasoning (ATR). Rather than relying on individual "intellectualist reasoners" as the primary vehicle for truth-seeking, ATR reconceptualises truth as an emergent property of social epistemology: the product of imperfect individual reasoning refined under the adversarial pressure of debate. This distributed method of collective intelligence has guided humanity to ever-greater epistemic heights and underpins the foundational principles of all democratic systems. This thesis breaks new ground by, for the first time, simulating ATR through the multi-agent debate (MAD) of large language models (LLMs). With rigorous empirical analysis, we demonstrate that, when correctly engineering an epistemically diverse set of models, LLM-MAD can significantly improve truth-seeking performance on questionnaire-based tasks, even when individual debate participants exhibit limited standalone performance. Furthermore, we present strong empirical evidence that this performance gain is mechanistically grounded in the central principles of ATR, suggesting that collective reasoning may be universally favourable over individualist reasoning, rather than a quirk in biology or evolution. Finally, drawing on our analysis of debate dynamics, we propose a novel benchmarking methodology that leverages LLM-MAD to measure intrinsic model properties (such as hallucination propensity) in order to compare models in ways that current static benchmarking approaches cannot support.

Large Language Models (LLMs) excel at understanding natural language but struggle with optimisation tasks involving multiple constraints and user-defined preferences, which commonly arise in domains such as robotics. We propose a hybrid reasoning approach in which LLMs externalise reasoning through code generation. Given a natural language problem description, an LLM generates Python code that encodes user-defined constraints and preferences as a preference-based Maximum Satisfiability (MaxSAT) problem, which is then solved by an exact MaxSAT solver. To ensure correctness, solutions returned by the model-generated code are independently verified for feasibility and optimality against a canonical MaxSAT encoding, allowing for different encodings and multiple optimal solutions. We evaluate our approach using both open-source and closed-access LLMs on three families of preference-based reasoning tasks, and compare it against direct-answer, chain-of-thought, and program-of-thought baselines using the same models. While these baselines rarely produce feasible solutions, the MaxSAT-based pipeline achieves substantially higher acceptance rates, in some cases exceeding 80%. Our results demonstrate that LLM-driven code generation combined with preference-based MaxSAT enables solver-verifiable optimisation with respect to generated encodings, and substantially improves correctness under independently verified reference semantics.

Evaluating open-ended outputs from large language models (LLMs) remains challenging due to the absence of ground truth. Existing metrics rely on final-answer accuracy or surface-level statistics, leaving the reasoning process itself unexamined. We introduce TRACE (Toulmin-based Reasoning Assessment through Constructive Elements), a metric that analyzes Chain-of-Thought (CoT) reasoning processes. Rather than judging outcomes, TRACE inspects how arguments are constructed by integrating Toulmin's argumentation theory with Flavell's metacognitive framework to assess reasoning structure. Experiments on 26.3K QA samples across 7 reasoning models show strong correlation with benchmark accuracy (r=0.74). Furthermore, TRACE is effective as a reinforcement learning reward signal, outperforming accuracy-only baselines. Together, these results indicate that logically sound reasoning leads to higher-quality answers. TRACE thus serves as a complementary metric for evaluating open-ended outputs. Code is available at https://github.com/hyyangkisti/trace.

Heuristic search is the dominant paradigm in symbolic AI planning, and the strongest heuristics are the result of decades of work by planning researchers. Recent work has shown that large language models (LLMs) can design heuristics for individual planning domains, but no LLM-generated heuristic has so far worked on arbitrary planning tasks. In this paper, we use evolutionary search to produce the first LLM-generated domain-independent heuristics that exceed the hand-engineered state of the art. We let an LLM mutate parent heuristics written in C++, store candidates in a MAP-Elites archive keyed on informedness and speed and calculate fitness scores by blending coverage with solving time. To place the evolved programs in context, we additionally benchmark a broad set of hand-engineered heuristics on their informedness-speed tradeoff, which to our knowledge has not been done before. On unseen testing domains, our best evolved heuristic solves more tasks than even the strongest baseline, with our full heuristic suite spanning the Pareto frontier of said tradeoff. We also find that seeding evolution from the trivial blind heuristic outperforms seeding from the strong FF heuristic, even when the resulting program is itself an FF variant, and that LLM reasoning effort affects how often candidates compile much more than the quality of those that do. Because the evolved programs are plain C++, they slot into existing planners as drop-in replacements and inherit the soundness and completeness guarantees of the underlying search.

Explaining why dense retrievers assign high relevance scores remains challenging because retrieval decisions are made through opaque high-dimensional embeddings. Existing explanations often focus on surface signals, such as lexical matches, token alignments, or post-hoc textual rationales, and thus provide limited insight into the latent factors that shape dense retrieval behavior at the embedding level. We propose \textit{Xetrieval}, an embedding-level mechanistic framework for explaining dense retrieval. \textit{Xetrieval} first introduces a lightweight reasoning internalizer that approximates Chain-of-Thought reasoning directly in the embedding space with a single forward pass, enriching sentence embeddings with reasoning-oriented information while avoiding expensive autoregressive generation. It then decomposes these reasoning-enhanced embeddings into sparse, human-interpretable features, each associated with a coherent natural language description. By aggregating sparse feature overlaps across multiple document-side views, \textit{Xetrieval} provides feature-level explanations of individual retrieval decisions. Experiments on diverse retrievers and benchmarks show that \textit{Xetrieval} uncovers coherent interpretable features, yields stronger pair-level intervention effects, and supports task-level feature steering. The project page and source code are available at https://hihiczx.github.io/Xetrieval .

Efficient Distillation (EDistill) compresses large language models (LLMs) by structured pruning parameters and tuning lightweight modules with high training efficiency. Although these EDistilled LLMs achieve state-of-the-art (SOTA) performance on general ability benchmarks relative to similarly sized LLMs, we identify a severe degradation in their multi-step reasoning ability, which we term reasoning collapse. We systematically analyze the geometric origins of reasoning collapse and show that the SOTA EDistill method based on width-reducing projection matrices suffers from eRank collapse, in which the effective rank (eRank) of hidden representations drops. We theoretically explain how singular values of randomly initialized projection matrices become unevenly distributed, leading to eRank collapse and thus token indistinguishability. To address this issue, we propose RED (Reasoning-preserved Efficient Distillation) for LLMs, which introduces activation-aware initialization to initialize projection matrices as channel-selection matrices, thus theoretically mitigating eRank collapse. Experiments on Llama and Qwen series demonstrate that RED substantially recovers reasoning while maintaining high training efficiency and SOTA general ability.

Large Reasoning Models (LRMs) achieve strong performance on table reasoning tasks but incur substantial inference cost due to long reasoning traces. Stepwise model routing mitigates this issue by dynamically assigning reasoning steps to smaller or larger models. However, stepwise model routing for table reasoning remains underexplored. Through empirical analysis, we find that reasoning steps involving tables contain two types of tokens with distinct uncertainty distributions: table tokens grounded in table structure, such as cell values and headers, and text tokens representing surrounding natural-language reasoning. The uncertainty of both token types is correlated with the risk that the model makes an error in the next reasoning step. However, existing methods fail to model them separately, leading to suboptimal routing decisions. To address this, we propose EcoTab, a table-aware stepwise routing framework for efficient table reasoning. At each reasoning step, EcoTab separately estimates the uncertainties of table tokens and text tokens, maps them to next-step failure risks for the small model, and combines the two risks for routing. Experiments on multiple table reasoning benchmarks show that EcoTab consistently outperforms strong baselines and achieves a better balance between accuracy and efficiency.

Stepwise model routing improves the efficiency of Large Reasoning Models (LRMs) by assigning each reasoning step to a suitable model. Recent methods formulate routing as a sequential decision process and train the router with reinforcement learning. However, although they model routing as a process, they still supervise the router with outcome rewards. Such rewards only reflect final answer correctness and fail to evaluate intermediate routing decisions, which can weaken performance and generalization. To address this gap, we propose RoRo, a rubric-guided process reward framework for stepwise model routing. RoRo first collects diverse routing trajectories and constructs preference pairs based on outcome, cost, and process quality. It then trains a Rubricor to generate a query-specific evaluation rubric and a Judge to score routing trajectories under this rubric through alternating optimization. The resulting process rewards are combined with outcome rewards to optimize the routing policy via GRPO. Experiments on five reasoning benchmarks under both same-family and cross-family settings show that RoRo consistently outperforms strong baselines and achieves better accuracy and cost trade-offs.

Reasoning distillation transfers complex reasoning abilities from large language models (LLMs) to smaller ones, yet its success depends on how well the training data align with the student model. This paper introduces the Data-Model Compatibility (DMC) metric, which can be used to assess the suitability of a dataset for reasoning distillation on a student model. DMC provides an assessment by jointly considering data quality, relative difficulty, and student capability. We validated the effectiveness of DMC from two perspectives: (1) DMC exhibits a strong correlation with reasoning distillation performance; and (2) using DMC as the criterion for data selection leads to improved reasoning distillation performance. Both findings are consistently demonstrated across multiple student models and tasks. Moreover, since the DMC of each dataset dynamically changes during training, our experiments demonstrate that dynamically selecting datasets based on DMC can further enhance performance.

Group-advantage-based reinforcement learning methods, such as GRPO and DAPO, have demonstrated strong performance across diverse domains, including mathematical reasoning and text-to-image generation. However, their reliance on sample-level rewards introduces a key limitation as uniform credit assignment across all tokens fails to capture fine-grained, token-level contributions. To address this issue, we propose Guidance Contrastive Policy Optimization (GCPO), a novel algorithm that enables per-token credit assignment by contrasting model predictions under positive and negative prompts. Rather than uniformly broadcasting sample-level advantages, GCPO assigns token-level advantages proportional to the difference between these contrastive predictions, allowing more precise and informative learning signals. Empirically, we find that GCPO emphasizes semantically relevant regions such as visual areas aligned with textual prompts in text-to-image generation, and critical keywords within reasoning traces for chain-of-thought tasks. Through extensive experiments, GCPO consistently outperforms GRPO and DAPO baselines on both text-to-image generation and chain-of-thought reasoning benchmarks, demonstrating its effectiveness as a general and scalable optimization strategy for discrete policy learning.

Chain-of-thought traces from large reasoning models can span tens of thousands of tokens, yet we lack a vocabulary for describing their internal structure. Previous methods developed to analyze chain-of-thought traces are either too rigid or not expressive enough, failing to capture features across domains and models. To remedy this, we develop ReasonOps, an unsupervised, expressive method for annotating chain-of-thought traces, providing succinct universal operators. Using ReasonOps, we analyze 44,662 traces from 12 thinking LLMs spanning 6 families across 8 reasoning benchmarks and discover that they share a common compositional structure: 7 recurring reasoning operators -- discourse-level moves such as backtracking, inferring, and hypothesizing -- that emerge from unsupervised clustering of sentence-initial 3-token pivots. These operators appear across every model family and benchmark domain, confirmed by three independent LLM judges who classify held-out samples at 70 -76% accuracy. We analyze the structure of operators on easy vs. hard problems, revealing that reflective operators are more helpful on hard problems and harm performance on easy problems. Operator sequences are highly model-identifying: a classifier trained on operator distributions alone recovers the source model with macro-AUC, revealing that each model family has a distinctive reasoning fingerprint. Structural operator features predict within-problem answer correctness well above baselines. Classifiers built on these operators reach WP-AUC and on AIME specifically. ReasonOps further enables early quality estimation well before the trace completes: we predict at WP-AUC for only 50% of the trace. The ReasonOps pipeline is unsupervised and annotation-free, enabling deep insights into LLM reasoning traces as well as strong downstream results on model identification and correctness prediction.

Reinforcement learning using verifiable rewards (RLVR) improves LLM reasoning, but the conditions under which it transfers across domains -- and why it does so -- remain under-explored. We study cross-domain transfer in a 7B model whose SFT and RL post-training stages use only constraint-satisfaction puzzles, with no mathematics problems in the post-training data. To analyze how transfer emerges, we introduce a reasoning primitive-level framework that combines a 9-class span classifier with motif extraction, allowing us to segment chain-of-thought traces into primitive motifs and track their evolution across training stages and domains. We find that puzzle SFT induces a reasoning-primitive vocabulary, yielding a $+7$pp \texttt{pass@32} gain on OlymMATH-Hard. Vanilla GSPO then composes these primitives into longer compute-verify chains, adding a further $+6$pp. However, this RL stage also suppresses exploratory primitives such as \textit{hypothesize} and \textit{backtrack}. To address this, we introduce a novelty bonus that rewards diverse correct rollouts, using perplexity under the reference model as a signal. This restores recovery primitives during RL and adds a further $+7$pp \texttt{pass@32} relative to vanilla GSPO. Finally, the end-to-end recipe raises the hard-math capability ceiling from $16.0\%$ at the OLMo3-7B-Instruct-SFT base to $36.0\%$, without adding any mathematics problems during the SFT or RL stages.

Masked diffusion language models (MDMs) uniquely support any-order generation, with confidence-based decoding currently serving as the de facto standard inference policy. To optimize for this, recent training schemes attempt to align training mask patterns directly with those observed during generation. However, we argue that confidence-based decoding is inherently misaligned with the logical-flow trajectories required for complex reasoning, and that confidence-aligned training actively entrenches this misalignment. We make this concrete using multi-digit addition, where the decoding strategy prematurely predicts locally easy digits before resolving their long-range dependencies, producing high-confidence errors on challenging inputs. While traditional random masking keeps the failure rate low on this challenging tail, confidence-aligned training amplifies the error rate by an order of magnitude. Across five distinct reasoning tasks, this same pattern emerges with task-dependent severity: confidence-based decoding induces failures on highly complex inputs, and confidence-aligned training exacerbates them. In contrast, random masking -- despite its perceived inefficiency -- robustly preserves the reasoning-trajectory conditionals essential for solving the challenging tail.

When multiple LLM agents solve the same problem, standard practice compresses each agent's reasoning into a majority vote or layered synthesis, treating agreement as the finish line. We show this is unnecessarily lossy: an LLM aggregator that reads complete reasoning traces recovers correct solutions even when agents unanimously agree, with beneficial corrections consistently outweighing harmful ones -- the \emph{aggregation paradox}. Majority voting has a ceiling that perturbation diversity does not raise (error correlations are identical); the aggregator's gain comes from trace-level complementarity, assembling correct intermediate steps from minority chains that voting discards. These findings motivate Self-Consistent Mixture of Agents which generates trace diversity through semantic-preserving input perturbations, safeguards the majority via anchored refinement with provable non-degradation guarantees, and always synthesizes -- never gates on consensus. A single model with perturbation-induced trace variation outperforms heterogeneous model pools across structured reasoning, PhD-level science, competition mathematics, and competitive programming. The unit of aggregation should be the reasoning trace, not the answer.

Reasoning models are evaluated on single-turn benchmarks but deployed in multi-turn dialogue, where users push back on correct answers. Under sustained adversarial pressure we find a previously undocumented failure mode: the chain-of-thought stays factually correct from first turn to last while the emitted answer flips wrong. We call this unfaithful capitulation (UC) and isolate it with a $2\times 2$ latent-versus-behavioral framework that flip-rate metrics and single-turn faithfulness probes both miss. Across three datasets (MT-Consistency, MMLU-Pro, GSM8K), the latent-correct rate at the behavioral flip clusters near 50% in think mode and collapses to 11-15% under no_think -- paired, within-model causal evidence that reasoning creates the gap. Across models the effect tracks the reasoning channel (high in Qwen3-32B and GPT-OSS-20B, low in inline-CoT Gemma-4-31B-it). An independent GPT-4o judge corroborates $86\%$ of UC labels; a token-level probe shows the answer-slot argmax is correct in $84\%$ of UC cells; and a naive trace-anchored defense backfires. We release all trajectories, traces, and judge labels.

Personalized tutoring, teacher training, and education research need access to \emph{targeted} synthetic misconceptions, but privacy and IRB constraints make labelled corpora of real student errors scarce. LLMs could in principle generate synthetic errors at scale, but producing an arbitrary wrong answer is easy for a modern LLM while producing one that matches a specified cognitive failure mode is much harder. We present a framework that generates errors targeted to a five-class taxonomy adapted from the revised Bloom's taxonomy, evaluated on questions from the TheoremQA dataset. A Generation Agent (GA) drafts a candidate erroneous solution conditioned on a target class, and an Examination Agent (EA) judges whether the draft is incorrect and class-consistent. The framework yields a reusable recipe for building class-stratified synthetic error datasets where authentic student corpora are unavailable. As a secondary diagnostic, targeted error generation is substantially harder than free-form incorrect-answer generation, and answer-grounding contributes more than expanded examples or external textbook content.

A paraphrase-quality audit of MathCheck (ICLR 2025) detected 4 semantically incorrect paraphrases in 129 groups (3.1%); removing them drops GPT-4o from rank 2 to rank 4 and elevates Claude Haiku and DeepSeek V3 above it; these ranking changes are invisible to any single-model evaluation. Cross-model unanimity found these errors automatically (>= 3/4 models for MathCheck; >= 6/9 for our primary evaluation) for under $10; in our own dataset the same protocol found that 47% of auto-generated connective-variation paraphrases were semantically incorrect. That flaw compounds a deeper measurement gap: Claude Haiku 4.5 achieves 86% accuracy yet SCR=50%, meaning half its theorems are answered differently under semantically equivalent restatements, while aggregate accuracy across 9 models spans only 86-96% yet Semantic Consistency Rates (SCR) span 50-82% -- a 32-point gap invisible to standard benchmarks. Formally, for any target ranking over 9 frontier models there exists a weighting over paraphrase families that realizes it (No-Free-Benchmark corollary), because no model Pareto-dominates all families -- so benchmark designers who select families are implicitly choosing which model wins. FormInv supplies the audit protocol (replicated on external benchmarks at 100% recall), SCR and per-theorem Cochran's Q as primary invariance measures evaluated on 9 models across 366-811 items (on Lean4-verified theorems), and FormInvSelector for regime-aware model selection.

On-policy self-distillation (SD) improves LLM reasoning by using teacher-side privileged information (PI) to turn sparse verifier outcomes into dense token-level supervision. Existing methods usually assume trusted PI, such as reference answers or successful traces. We ask whether PI can instead come from an experience-derived skill bank, where retrieved skills are compact and reusable but may also be irrelevant or misleading. We propose Skill-Conditioned Gated Self-Distillation (SGSD), which formulates skill-based SD as teacher hypothesis validation rather than unconditional imitation. SGSD retrieves skill-mistake pairs, constructs a multi-teacher pool, and lets all skill-conditioned teachers score the same plain-prompt student rollout. The verifier validates each teacher's polarity: supporting a success or suppressing a failure gives positive supervision, while the opposite stance is reversed. A robust gated objective then distills informative teacher-student disagreements while suppressing uncertain or extreme signals. Experiments on multiple mathematical reasoning benchmarks show that SGSD consistently improves over GRPO and remains competitive with answer-conditioned OPSD under a weaker PI assumption. For example, on Qwen3-1.7B, SGSD outperforms GRPO by 6.2% and OPSD by 1.7% on average on AIME24, AIME25, and HMMT25.

Large reasoning models (LRMs) often generate extensive chain-of-thought (CoT) traces before producing a final answer. As explicit textual artifacts, these traces can be passed to other models to solve the same task, enabling cross-model reasoning transfer. Yet successful transfer alone does not reveal how the provided CoT contributes to another model's answer. We study this question with a controlled provider--receiver framework, where a provider generates a reasoning trace and a receiver solves the same problem from increasingly longer trace prefixes. We compare force-answer, where the receiver answers directly from the prefix, with free-generation, where it may continue reasoning before answering. Across models and benchmarks, full traces often transfer successfully, but prefix trajectories reveal distinct mechanisms. In force-answer mode, AIME transfer is largely driven by explicit answer availability. MMLU-Pro instead reflects a larger role for receiver competence, while ZebraLogic depends on partial structured-answer information rather than complete-answer leakage alone. In free-generation mode, partial CoTs improve performance across benchmarks, indicating that prefixes can guide continued reasoning. Finally, answer agreement among receivers provides a gold-free signal for stopping provider reasoning early. Overall, cross-model CoT transfer is not a single phenomenon: it can reflect answer extraction, reasoning scaffolding, or receiver-dependent competence.

Language models can use verifiable rewards to improve at a wide variety of reasoning tasks. However, both parametric (e.g. RLVR) and non-parametric (e.g. prompt optimization) approaches to doing so typically require hundreds of training samples and thousands of model rollouts, making them expensive in the best case and intractable in the worst. To address this challenge, we introduce Contrastive Reflection (CORE), a non-parametric learning algorithm that compares past reasoning traces to generate insights: short natural-language descriptions of reasoning strategies and constraints that capture differences between successful and unsuccessful problem attempts. Across four reasoning tasks, we demonstrate that CORE enables more rapid improvement than both parametric (GRPO) and non-parametric (GEPA, episodic RAG, and MemRL) methods, while using fewer rollouts. Under fixed rollout budgets with as few as five training samples, CORE achieves the strongest performance in most task-data regimes. Finally, we highlight how CORE is substantially more context-efficient than non-parametric baselines, requiring fewer prompt tokens while storing learned knowledge as compact, interpretable natural-language insights. Our results therefore suggest that distilling contrasts between successful and unsuccessful reasoning traces into abstract and useful insights can provide a more efficient and interpretable route to model self-improvement than weight updates, prompt optimization, or direct reuse of stored reasoning traces.