Reasoning Chain

Reasoning traces from chain-of-thought models appear to offer a legible window into how a model arrives at its answer. A growing body of work treats them as such, using LLM judges to diagnose errors, evaluate faithfulness, and provide step-level supervision via process reward models and generative critics. These practices rely on the text of a reasoning step carrying information about its functional role. But does the text actually encode information about which reasoning steps matter? We operationalize the importance of a reasoning step as its advantage: the change in expected reward, e.g., producing the correct final answer, from including that step, estimated via Monte Carlo rollouts. Basing ground truth on these estimates, we evaluate whether LLM judges can identify high-advantage steps and find that sufficiently capable LLMs can outperform a prevalence baseline but fall well short of a noise ceiling. Fine-tuning a model as a step-level critic yields strong improvement for incorrect responses but remains distant from ceiling for correct responses, suggesting that step importance is only partially recoverable from the text of the reasoning trace. Our findings contribute to a growing body of chain-of-thought faithfulness work that cautions against treating the legibility of reasoning traces as interpretability, especially with implications for process reward modeling.

Chain-of-thought (CoT) reasoning improves multi-step problem solving, but long reasoning traces inflate inference cost. Token-level CoT compression reduces this cost by pruning full reasoning chains into shorter traces for model adaptation, making token selection the central challenge. Existing methods often rely on external scorers or heuristic signals only indirectly tied to the model's internal answer computation. We instead adopt a model-internal perspective: as the model forms an answer, each reasoning token leaves a ripple in the residual stream, the model's \emph{stream of thought}, and the magnitude of this ripple reflects the token's contribution to the answer computation. Building on this view, we propose \textsc{MIST} (Model-Internal Saliency for Token-level CoT compression), which defines token importance along two complementary axes: \emph{necessity}, the drop in answer likelihood when a token's internal contribution is removed, and \emph{sufficiency}, the gain in answer likelihood when that contribution alone is provided. Combining the two yields a unified importance score for pruning. Across four reasoning benchmarks and four models, \textsc{MIST} consistently outperforms baseline methods, suggesting that model-internal saliency provides an effective proxy for reasoning-token importance.

Large Reasoning Models produce Long Chains-of-Thought (LCoTs) which involve breaking down the problem into smaller reasoning steps before reaching the conclusion. However, these steps often contain contradictions, unsupported inferences, or irrelevant steps, even when the final answer is correct. We propose Long Chain-of-Thought Graph Verifier (LCoT-GV), a graph-based framework that represents LCoTs as reasoning graphs. Each node in the graph represents a reasoning step and the edges encode semantic and logical relations. A Graph Attention Network is then trained to predict chain-of-thought correctness from the reasoning graph. We construct a new graph-oriented verification dataset from multiple reasoning benchmarks for question answering in various domains. The results show that our method is competitive with the most similar approaches.

A benchmark should deliver more than a scalar score: what makes an evaluation trustworthy is the reasoning that justifies the score. This is especially critical for world models, where judging a rollout requires understanding whether physics, causality, and world state evolve correctly. Humans spot such violations naturally, yet no existing benchmark automates this capability: metrics are computed brute-force, leaving no reasoning chain that can be examined or verified. We introduce HarnessEval-W, an agentified evaluation pipeline that brings the harness paradigm from the LLM ecosystem to world model benchmarking. Rather than applying a fixed rubric, HarnessEval-W interprets the context of each evaluation case, decomposes the evaluation question into measurable subproblems, and spawns specialized sub-agents, each equipped with tailored context and diagnostic tools to reason over its own subproblem. The parent agent then validates the gathered evidence and summarizes it into the final verdict. This hierarchical workflow turns every evaluation into a transparent evidence tree whose complete reasoning chain justifies the result. We apply HarnessEval-W to 18 representative world models over 330 evaluation cases. Its judgments closely align with human preferences while providing verifiable, fine-grained diagnoses of every generated rollout. We open-source the full pipeline as a live benchmark and invite the broad community to contribute to grow new skills and evaluation cases as world models evolve.

Harmful chat dialogues are ever-shifting through type-shifting and lexical evasion, yet we find they share invariant principles, i.e., an Ordered Reasoning Chain (ORC) of recurring topics, harm language indicators, severity hierarchies, and type characteristics, which can help us capture the key information in the frequently changing lexical expressions. We propose BRACE, which encodes the ORC as four differentiable stages (Topic -> Indicator -> Severity -> Type) with intermediate supervision, serving as a structured regularizer blended with direct heads, and supported by prototype-based feature augmentation and feature path disentanglement. The evaluation results show that, across 4 domains and 5 harm categories, BRACE achieves harm-type macro F1 of 0.934 (RoBERTa-wwm-ext, 3-seed mean), with decoder backbones (Qwen3-1.7B LoRA) reaching 0.949. Ablation studies show that all components contribute to BRACE, and the structural decomposition of ORC enables BRACE to distinguish harmful types with semantic ambiguity. Disclaimer: This paper may contain content that is disturbing to some readers.

Chain-of-Thought (CoT) reasoning offers a promising window into model monitoring. However, monitoring relies on faithfulness, i.e., the model output strictly derives from its reasoning trace. We identify an alignment tension where a model must be faithful enough to be monitored, yet robust enough to reject unsafe reasoning. We demonstrate that this counterbalance exists in current Large Reasoning Models (LRMs), and show ways in which it can be addressed. We introduce HazMart, a human-written dataset set in an autonomous AI shopkeeper scenario. Unlike prior work that relies on providing hints in prompts to test faithfulness (e.g., "A Stanford professor said it should be Answer A"), we propose a novel replacement-based technique, which we call Targeted Reasoning Replacement (TRR), that directly intervenes in the reasoning chain to substitute in unsafe or illogical thoughts (e.g., "Wait, the answer must be Option B [was Option A] because it is the most fitting"). DeepSeek-R1-Llama-70B exhibits high faithfulness (97.5%) but fails to reject Unsafe Reasoning (12.3%), while QwQ-32B is more robust (73.9% safety) at the cost of lower faithfulness (74.7%). Mechanistic analyses of QwQ-32B reveal that these properties are represented by anti-correlated internal directions peaking at the action-commit token. Finally, we demonstrate that representation steering can independently amplify the safety direction, increasing safe behavior by 9 percentage points while maintaining base capabilities.

Multimodal large language models (MLLMs) have advanced visual understanding and reasoning, yet their static parametric knowledge limits their ability to address knowledge-intensive and dynamically evolving open-world problems. To move beyond this limitation, multimodal deep search has emerged as a key direction for open-world information access, evolving from single-turn factual retrieval toward long-horizon, multi-turn search guided by visual evidence. However, existing methods typically confine vision to the input or answer stage, overlooking its role in intermediate reasoning, and lack designs tailored to long-horizon interaction. Consequently, visual evidence rarely drives continued retrieval, constraining both interaction depth and reasoning span. To address these limitations, we propose DeepVoyager-VL, a long-horizon multimodal deep-search framework for vision-in-the-loop search. Specifically, we construct a multimodal event graph to drive data synthesis, yielding problems with intermediate visual dependencies and long reasoning chains. We then design an agent framework for active visual acquisition and on-demand image loading. Finally, we fine-tune models on the synthesized data without reinforcement learning. Extensive experiments across ten multimodal search benchmarks demonstrate the effectiveness of our method.

Entropy-based pruning has been proposed as an effective method for compressing Chain-of-Thought (CoT) reasoning with negligible accuracy loss. We test the robustness of low- and high-entropy CoT step selection methods across various models and reasoning tasks, showing that entropy offers no advantage over random pruning in any evaluated setting. Moving from sentences to tokens, we then show that retaining low-entropy tokens seems effective only on mathematical benchmarks. We find this is due to the inherently low-entropy nature of numeric tokens, which also convey semantic content in such problems. Finally, we demonstrate that patching a subset of a few CoT tokens with their original activations recovers near-perfect full-trace performance, providing causal evidence that task information is not concentrated in a small set of CoT tokens identifiable by heuristics, but rather distributed across the full reasoning chain.

Large Language Models (LLMs) explore problems through chain-of-thought, but this exploration is buried in unstructured prose. On high-stakes tasks, users cannot tell which steps are well-supported, which alternatives were seriously considered, or how the final conclusion compares to those the model discarded. We propose a framework that ensembles the reasoning structure, not just the answers, of multiple LLMs by weighted merging of Directed Acyclic Graphs (DAGs) extracted from reasoning chains. We weight each step by how many traces independently attest to it, to return "Consensus Reasoning". Across six benchmarks spanning statutory interpretation, graduate-level science, narrative multi-hop reasoning, and first-order logic, our ensemble outperforms a matched-budget majority-vote baseline, with a maximum accuracy gain of 3.1% on MuSR-MM (narrative multi-hop reasoning). On a single model, the framework matches or exceeds self-consistency at the same trace budget while additionally exposing an inspectable consensus reasoning graph. Ensemble weights correlate with LLM-judge rankings of reasoning quality at Spearman $ρ= 0.30$-$0.51$, and consensus subgraphs are preferred over alternatives leading to the majority-vote answer in 54.4-65.4% of head-to-head comparisons across five of six datasets. We observe that our framework can also be used to analyze diverse reasoning perspectives for a problem.

Chain-of-thought (CoT) prompting enables large language models (LLMs) to tackle multi-step reasoning tasks, yet the generated intermediate steps are not guaranteed to be logically sound. We present Reason Popper-ly, a neurosymbolic framework that uses inductive logic programming (ILP) to learn relation composition rules from reasoning traces and deploys them as an online verifier for step-level correction. Given an LLM-generated trace, the method checks each inferred step against the learned rule table, diagnoses the violation type, rewrites incorrect steps with symbolically derived repairs, and regenerates the remaining suffix so that the model can produce its final answer conditioned on a verified trace. We evaluate on CLUTRR, a multi-hop kinship reasoning benchmark, using five language models over reasoning chains of 2 to 10 hops. Across all models, Reason Popper-ly consistently improves terminal accuracy over standard CoT, with gains of up to 48 percentage points for small models and 15 points for frontier models on the longest chains. Compared with a fully exogenous symbolic pipeline, our method performs better on harder instances by preserving the model's successful grounding while correcting only verifiable reasoning failures. In addition, step-level ILP verification yields a fine-grained error taxonomy that provides diagnostic insight beyond final-answer accuracy.

Large language models (LLMs) are increasingly used as technical assistants, but their competence in solid waste management (SWM) remains difficult to assess because existing benchmarks emphasize general knowledge rather than professional decisions under engineering, environmental, and policy constraints. We introduce WuYuEval, a multi-level benchmark for evaluating LLMs in SWM across foundational knowledge, domain reasoning, and expert decision-making. After quality auditing, WuYuEval contains a Foundation Module with 4,590 closed-ended multiple-choice questions across six task types and eight domain categories, together with an Expert Module with 247 scenario-based open-ended questions involving multi-objective optimization, constraint trade-offs, and system design. For expert tasks, we combine anchor-calibrated LLM-as-a-Judge scoring with Elo-based pairwise comparison. Across 33 LLMs, performance varied widely. The leading model reached 94.64% accuracy on the Foundation Module, but average accuracy still fell from 84.14% on easy questions to 42.50% on hard questions, with lower performance concentrated in calculation, experimental design, urban planning, and open-ended expert tasks. Reasoning-oriented Thinking modes improve most matched model pairs after auditing, but the gains depend on baseline capability and are not uniformly positive. These results suggest that visible deliberation helps only when it remains anchored to units, assumptions, and engineering constraints; otherwise, it may drift from decisive answer boundaries. WuYuEval therefore provides both an evaluation resource and an empirical basis for developing SWM-oriented foundation models with professional reasoning chains and explicit constraint control.

Chain-of-thought (CoT) reasoning is widely used to improve both the performance and interpretability of large language models (LLMs), yet the generated reasoning may not faithfully support the final answer. We study this problem from a causal perspective, where a faithful CoT process should follow the chain $Z\rightarrow X\rightarrow Y$, with $Z$, $X$, and $Y$ denoting the instruction, reasoning chain, and final answer, respectively. In this process, the instruction should affect the answer only through the reasoning chain. However, conventional autoregressive LLMs condition answer generation on both the instruction and the CoT, which still allows a direct instruction-to-answer shortcut. To address this issue, we propose CASE, a framework that combines training-time causal alignment and inference-time structural enforcement. During training, CASE builds counterfactual-CoT, biased-instruction, and empty-instruction datasets, and applies selective-loss fine-tuning to strengthen CoT-to-answer dependence while suppressing instruction shortcuts. During inference, CASE masks direct attention from instruction tokens to answer tokens, preventing the model from bypassing the generated CoT. We provide an information-theoretic analysis showing how these components promote faithful chains. Experiments on three models and four benchmarks show that CASE achieves a 37% average per-setting relative improvement in overall CoT faithfulness over the strongest baselines, exhibits stronger cross-dataset faithfulness transfer, and maintains competitive average accuracy. Code is available at https://github.com/oddwang/CASE.

Chain-of-Thought (CoT) prompting has significantly advanced the reasoning capabilities of Large Language Models (LLMs), yet it often incurs substantial computational costs due to over-reasoning: the generation of redundant, verbose, or irrelevant steps. While existing reasoning step evaluators effectively detect logical fallacies and factual errors, our analysis reveals a critical blind spot: they fail to penalize valid but inefficient reasoning steps that inflate token usage without contributing to the solution. To systematically diagnose this limitation, we introduce RIV-GSM8K, a diagnostic benchmark injected with five distinct types of inefficiencies, including circular reasoning and excessive decomposition. Diagnostic experiments reveal that state-of-the-art evaluators struggle to distinguish these inefficiencies from necessary reasoning. To address this gap, we propose CAID (Context-Aware Information Density), a training-free metric grounded in information theory that identifies low-utility steps. To validate the metric's practical utility, we apply it within PACE, a post-hoc compression strategy. Additional control experiments show that the gains of PACE are not explained by trivial pruning: compared with random step removal and PRM-based compression baselines, it preserves accuracy at substantially higher compression rates. Empirical results on GSM8K, StrategyQA, and ARC-Challenge demonstrate that PACE reduces token consumption by 31-53% while maintaining accuracy, confirming that CAID successfully distills informational froth from reasoning chains without compromising deductive validity.

Large Language Models (LLMs) have achieved remarkable success in complex reasoning tasks through Chain-of-Thought (CoT) prompting. However, these models often exhibit "computational overthinking," generating redundant reasoning steps that increase latency and cost without improving accuracy. Recent studies suggest that CoT trajectories can be significantly pruned, yet existing methods often rely on forcing a static thinking budget, heuristic filtering, sub-optimal early exit via classification, or expensive re-training. In this paper, we introduce OS-Pruner, a lightweight plug-in framework that formulates chain-of-thought pruning as an optimal stopping problem. Given a reasoning prefix, OS-Pruner learns whether further reasoning is worth its token cost by optimizing an explicit utility that trades off final-answer accuracy against generated length. Our novel formulation enables the model to dynamically assess the sufficient point of termination for a reasoning chain. OS-Pruner is designed to be lightweight during both training and inference, and to provide users with fine-grained control over the reasoning-effort vs. accuracy trade-off. On diverse reasoning benchmarks and base models, OS-Pruner achieves 20-60% reduction in generation length with minimal accuracy sacrifice.

Selecting the correct answer from a pool of candidate reasoning chains is the engine of test-time scaling, yet the standard selectors each carry a cost: self-consistency inherits the errors of the single model it resamples, and trained reward models need labeled data and transfer poorly off-distribution. We study a third signal, free at inference time: cross-model consensus, the degree to which independently trained models, each solving the problem once, agree on a final answer. We treat the panel as an LLM-jury, in which the structure of agreement, not any model's score of another, is the verification signal. Across seven benchmarks it selects correct answers better than self-consistency and far better than a model scoring its own candidates: on competition math it closes the entire gap to an oracle selector, while self-scoring closes almost none. The mechanism is error decorrelation: independently trained models err differently, so their wrong answers scatter while the correct one accumulates agreement. We make this precise with a parameter-free law, derived in closed form, that predicts consensus accuracy from three measured panel statistics to a mean absolute error of $0.03$ and exposes the method's ceiling: a shared-error floor where models share a misconception, near zero on math but non-trivial on science. Against four trained verifiers spanning discriminative, outcome, and generative reward models, the free LLM-jury matches the strongest inside their math training domain and is the top selector outside it. Cross-model consensus is thus a verifier we can characterize in advance: a law that says when to trust it, and a floor that marks where it cannot.

Uncertainty quantification for visual language models (VLMs) conventionally targets the answer token distribution. We provide the first three-family empirical characterisation of answer entropy behaviour in thinking-mode VLMs. Running four models on identical POPE adversarial samples, we find three qualitatively distinct patterns: Qwen3-VL-8B-Thinking shows complete collapse (ans H AUROC = 0.492); GLM-4.1V-9B-Thinking shows no collapse (0.716); and InternVL3-8B shows selective thinking (chains on only 50% of samples, ans H = 0.675 full / 0.602 thinking-only). Across all three thinking-mode models, thinking chain entropy outperforms answer entropy on the subset where chains are generated (0.647, 0.759, 0.608 vs. 0.492, 0.716, 0.602 respectively), suggesting chain signals are the more reliable predictor whenever chains are present. This holds strongly for Qwen and GLM, but with only marginal and statistically unreliable advantage for InternVL3 (n_FP = 17). A 300-sample VQAv2 pilot confirms chain entropy (0.680) outperforms answer entropy (0.595) on VQAv2 questions, with the gap largest for free-form answers (0.733 vs. 0.467). On harder reasoning tasks (HallusionBench) both Qwen models show moderate signal (approx. 0.64), consistent with incomplete pre-commitment on difficult questions. We additionally document structured abstention affecting 12-22% of queries with asymmetry toward absent-object queries, and a practical abstention gate raising accuracy from 71.0% to 93.8% at 62.7% coverage with no additional inference cost.

Glaucoma is a leading cause of irreversible blindness worldwide, yet most automated diagnosis systems rely on opaque deep-learning models that offer little clinical interpretability. We present GlaKG, a biomarker-centric fundus knowledge graph that integrates structural biomarkers, clinically grounded rules, and image features to produce traceable reasoning for glaucoma diagnosis and risk stratification. GlaKG encodes six entity types (Fundus Image, Optic Disc, Neural Rim, Pathology, Diagnosis, Risk Level), eight relation types, and 11 clinically validated rules into a unified graph, so that every prediction is accompanied by an explicit reasoning chain linking biomarker evidence to activated clinical rules. To keep knowledge-based reasoning strictly separate from label information, we adopt a post-processing fusion framework that combines ResNet50 image embeddings with a normalized KG reasoning-chain score via a tunable weight alpha, with all fitting confined to the training split. On a publicly available, AI-annotated fundus dataset, GlaKG reaches F1 = 0.9953 for binary glaucoma classification and 0.930 accuracy with 0.922 weighted F1 for four-class risk stratification; we report openly that the dataset's biomarker annotations are highly label-correlated, and therefore frame these figures as an upper bound attainable with clean structured biomarkers rather than as leakage-free image-only performance. Feature-importance analysis shows KG-derived and biomarker features contributing near-equally (51.1% vs. 48.9%), and the reasoning chain flags borderline cases by exposing low chain scores rather than failing silently. GlaKG's central contribution is therefore a clinically auditable reasoning framework that complements raw predictive performance by explicitly exposing the biomarker evidence and rule activations behind each decision.

Multi-step symbolic reasoning is essential for robust financial analysis, yet most benchmarks neglect intermediate reasoning steps. FINCHAIN introduced verifiable Chain-of-Thought (CoT) evaluation but is limited to English. FINESSE-Bench includes a Russian block but relies on multiple-choice questions without step-level supervision. We present RusFinChain, the first Russian-language symbolic benchmark for verifiable CoT reasoning in finance. It spans 17 domains, 172 topics, and comprises 5,280 parameterized examples from executable Python templates, ensuring contamination-free evaluation. Each example includes a gold-standard reasoning chain with intermediate numeric values for automatic verification. We also introduce enhanced metrics: Fuzzy Numeric Alignment and Soft-Attention Alignment. We evaluate 8 open-weight LLMs on a stratified sample, generating 8,100 responses. Results reveal a substantial reasoning gap: models achieve Hard F1 of ~0.65 for step alignment, but only ~29% of final answers are correct. Our fuzzy and soft metrics show stronger correlation with final-answer correctness (Spearman rho approx 0.48) than the original ChainEval (rho approx 0.38-0.46), demonstrating superior diagnostic power. We release dataset, code, and evaluation framework to foster verifiable financial AI for the Russian-speaking community.

Understanding and localizing subtle changes between paired images is critical for tasks such as surveillance and image editing. However, traditional Image Change Captioning (ICC) methods lack spatial grounding, limiting their precision. We introduce Image Change Captioning and Segmentation (ICCS), a new multimodal task that jointly requires structured change description and pixel-level localization. To address ICCS, we propose the Change-aware Captioning and Reasoning Chain (CCRC), a dual-chain framework that decouples semantic reasoning from spatial segmentation. The first chain, Chain-of-Change-Captioning (CCC), enhances fine-grained change perception via a visual fusion module based on Multi-Head Change-aware Attention inserted between the visual and language components of a Multimodal Large Language Model (MLLM). CCC also determines whether a change is segmentable. If not, it alone generates the caption. Otherwise, the second chain, Chain-of-Change-Segmenting (CCS), is activated, leveraging spatial priors from CCC and refining masks with a Change-aware Token Refiner for accurate boundary localization. We evaluate CCRC on both synthetic and real-world change detection benchmarks with pixel-level supervision. Experiments show CCRC achieves state-of-the-art performance.

Process reward models (PRMs) enhance the reasoning capabilities of large language models (LLMs) by providing fine-grained feedback, yet training PRMs typically requires expensive stepwise annotations. Outcome-supervised PRMs offer a scalable alternative by learning from final-answer correctness alone, but this introduces a fundamental credit assignment challenge, i.e., attributing outcomes to responsible reasoning steps. Existing approaches rely on either uniform or causal assignment, both of which fail to anchor credit in step correctness and thus hinder process error identification. In this work, we propose Outcome-Supervised Process Reward Modeling via Learnable Credit Assignment (LCA), an outcome-supervised PRM framework that jointly learns credit assignment and reward modeling under the principle of Weakest Link Assignment: a reasoning chain is as strong as its weakest link. To address mutual dependence between credit assignment and reward modeling, we formalize outcome-supervised PRM as a Multiple Instance Learning (MIL) problem and introduce Softmax-Weighted-Sum (SWS) pooling, an MIL pooling technique tailored for strong dependence and redundancy among reasoning states. We prove Bayes consistency of our algorithm under mild assumptions. Extensive experiments demonstrate that LCA consistently outperforms state-of-the-art outcome-supervised PRMs across multiple tasks and backbones. Code is available at https://anonymous.4open.science/r/LCA.

Recent advances in large language models (LLMs) have demonstrated that reinforcement fine-tuning of pretrained base models can lead to significant gains in reasoning performance at inference time. In this work, we theoretically analyze why reinforcement fine-tuning induces better reasoning ability than purely supervised fine-tuning (SFT) methods. We model chain-of-thought (CoT) reasoning as a pathfinding problem on graphs and compare the popular method of reinforcement learning with verifiable rewards (RLVR) against traditional SFT. We prove that SFT, when trained on golden shortest paths without negative examples, fails to learn how to efficiently backtrack. In contrast, an RLVR-trained model can learn how to efficiently backtrack from dead ends using only outcome reward. This leads to an exponential separation in inference-time compute between the two methods, and demonstrates that RLVR leads the model to learn the location of difficult decisions in a reasoning chain, ultimately allowing for better allocation of inference-time compute. Finally, we show that the reasoning traces of an RLVR model can be distilled to train a base model to backtrack efficiently as well.

Current evaluations of Large Language Models (LLMs) on logical fallacy detection focus on predicted labels, but do not establish whether those labels are supported by the reasoning the models provide. We propose ForEx (Formal Verification for Explainable Reasoning), a framework that translates LLM-generated explanations into Lean4 and verifies whether the translated rationale is derivable under encoded premises, not the logical validity of the original natural language argument. To distinguish prediction outcomes from the formal status of the supporting reasoning, we introduce the LLM Argument Verification Matrix, which separates label consistency from formal verification status. Experiments on LOGIC-Climate show that over 90% of LLM outputs can be translated into formal reasoning chains that pass verification, while agreement with human annotations remains around 20%. These results expose a systematic gap between formal derivability and label agreement, a distinction invisible to prediction-based metrics. ForEx moves LLM evaluation beyond label correctness toward machine-checkable analysis of formalized reasoning chains.

Visual reasoning requires integrating evidence distributed across regions, attributes, and relations, making single-chain reasoning prone to early perceptual commitment and hallucination. We propose Visual Para-Thinker++, a single-policy multi-agent framework in which one shared MLLM policy is instantiated as role-conditioned Main, Worker, and Summary Agents. The Main Agent decomposes the task with fixed allocation patterns; Worker Agents reason in parallel under context isolation; and the Summary Agent reconciles full Worker reasoning traces rather than majority-voting on final labels. The shared policy is trained by Multi-Agent Capability Injection and Role-Decoupled Multi-Agent Optimization, which assign role-specific rewards and advantages to corresponding token segments to reduce gradient conflict among collaborative roles. A native inference engine enables efficient multi-agent rollout through shared visual prefix and KV cache reuse. Across V*, CountBench, the RefCOCO family, and HallusionBench, Visual Para-Thinker++ consistently outperforms single-trajectory and inference-time parallel baselines, with especially strong gains on hallucination-sensitive visual reasoning.

Autoregressive chain-of-thought (CoT) reasoning in large language models (LLMs) is fundamentally forward-directed: each step conditions only on prior tokens. This unidirectional inductive bias renders even capable models susceptible to error snowballing, wherein a single logical or arithmetic mistake in an early step irreversibly corrupts the entire reasoning chain. We introduce Teleological Reasoning Infilling (\TRI{}), a training framework that endows decoder-only transformers with a native \emph{goal-conditioned bridging} capability. The key insight is to reframe erroneous reasoning segments as fill-in-the-middle (FIM) tasks: given a verified prefix premise $P$, a verified downstream milestone $S$, and the original query $Q$, the model must synthesise the logical bridge $M$ that connects $P$ to $S$ rigorously and completely. To achieve this with standard causal architectures, we introduce a Prefix-Suffix-Middle (PSM) sequence rearrangement with three non-overlapping sentinel tokens, enabling $M$ to attend to both $P$ and $S$ without any structural modification to the self-attention mechanism. Training proceeds in two stages: (i) Supervised Fine-Tuning (SFT) on symbolically verified $(P, S, M)$ triples extracted from formal mathematics corpora, and (ii) Direct Preference Optimisation (DPO) with a deterministic symbolic verifier (Lean 4 / Python) as the sole reward oracle, eliminating LLM-judge sycophancy. At inference, TRI operates as a surgical repair module within a dual-system loop: a causal draft model generates an initial trace, the verifier pinpoints failures, and TRI infills only the damaged segment, leaving verified sections intact. Comprehensive experiments on three benchmarks demonstrate that TRI achieves state-of-the-art performance across all tasks, while reducing per-problem token expenditure by 31.2%.

Large language models have made substantial progress on mathematical reasoning, but existing benchmarks typically evaluate well-specified problems with final answers, step-by-step solutions, or complete proofs. They do not capture collaborative open-problem solving: a setting in which participants propose partial arguments, identify gaps or errors in prior steps, repair flawed reasoning, and gradually synthesize incremental contributions into a proof. We introduce CrowdMath, a dataset of 164 expert-annotated progress chains from the MIT PRIMES--Art of Problem Solving (AoPS) CrowdMath program (2016-2025), a collaborative research initiative whose discussions have led to peer-reviewed publications. Each chain traces a multi-participant forum discussion from an open-problem statement to a completed proof. Posts are labeled by their functional roles in the evolving solution process, including partial progress, proof completion, erroneous reasoning, and error identification. We define evaluation tasks and benchmark six frontier models. Models achieve 83-88% accuracy on next-post prediction, suggesting that they can follow the local flow of mathematical discussion. However, they struggle to identify the functional significance of individual contributions with the best model achieving only 0.42 macro-F1 on post-role classification. CrowdMath exposes a gap between solving well-specified mathematical problems and understanding collaborative mathematical progress as it unfolds.

Large Reasoning Models (LRMs) have achieved remarkable progress thanks to Reinforcement Learning with Verifiable Rewards (RLVR) on Chain-of-Thoughts (CoTs). However, since long CoTs naturally contain trial and errors and mainstream RLVR approaches choose outcome-correct CoT trajectories for memorization, the redundant explorations in long CoTs are inevitably reinforced, which results in the over-thinking issues of LRMs. Previous attempts to resolve this issue mainly give more advantage to shorter trajectories, yet their learning signals are still outcome-based and cannot reduce the memorization of redundant explorations in long CoTs. Therefore, we propose ThoughtFold, a framework that leverages fine-grained preference learning to mitigate redundant explorations for efficient reasoning. ThoughtFold employs an introspective strategy to identify redundancy within each correct trajectory, which yields a spectrum of candidate sub-trajectories. Leveraging this spectrum, we introduce a masked preference optimization objective that explicitly penalizes redundant explorations and encourages the model to directly bridge essential reasoning segments, effectively folding its reasoning chains into a more concise path. Extensive experiments show that ThoughtFold significantly enhances efficiency. It reduces the token usage of DeepSeek-R1-Distill-Qwen-7B by approximately 56% while maintaining state-of-the-art accuracy.

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.

Reinforcement learning from verifiable rewards (RLVR) has shown strong promise for LLM reasoning, but outcome-based RLVR remains inefficient on hard problems because correct final-answer rollouts are rare and sample-level credit assignment cannot use partial progress in failed attempts. We introduce SCRL (Subproblem Curriculum Reinforcement Learning), a curriculum RL framework that derives verifiable subproblems from reference reasoning chains and fixes the final subproblem as the original problem. This turns partial progress on hard problems into verifiable learning signals. Algorithmically, SCRL uses subproblem-level normalization, which normalizes rewards independently at each subproblem position and assigns the resulting advantages to the corresponding answer spans, enabling finer-grained credit assignment without external rubrics or reward models. Our analysis shows that subproblem curricula lift hard problems out of gradient dead zones, with larger relative gains as the original problem becomes harder. Across seven mathematical reasoning benchmarks, SCRL outperforms strong curriculum-learning baselines, improving average accuracy over GRPO by +4.1 points on Qwen3-4B-Base and +1.9 points on Qwen3-14B-Base. On AIME24, AIME25, and IMO-Bench, SCRL further improves pass@1 by +3.7 points and pass@64 by +4.6 points on Qwen3-4B-Base, indicating better exploration on hard reasoning problems.

Multimodal large language models often generate reasoning chains containing subtle errors that lead to incorrect answers. Current verification approaches have notable limitations. Learned critics need extensive labeled data and show inconsistent performance across different tasks. Meanwhile, existing training-free methods simply average scores from different sources, missing a key insight: when these scores disagree, that disagreement itself carries important information about whether a reasoning step is truly valid or not. We propose a training-free verification approach that treats step-wise verification as a coordination problem among specialized judges. We formalize these judges' interaction as a Nash equilibrium game where agreement signals valid steps while disagreement reveals instability. Our method computes equilibrium scores through a closed-form solution, enabling both disagreement-aware filtering and stability-conscious ranking of reasoning steps. Evaluated across six benchmarks, our approach achieves consistent improvements of 2.4% to 5.2% over baseline models and shows competitive performance against learned critics, demonstrating that cross-modal agreement (not just average confidence) provides robust verification signals without task-specific adaptation.

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.

The rapid spread of memes makes harmful content detection increasingly crucial, as effective identification can curb the circulation of misinformation. However, existing methods rely heavily on high-volume annotated data, which leads to substantial training costs and limited generalization. To address these challenges, we propose PrismAgent, a zero-shot, multi-agent, interpretable framework. PrismAgent conceptualizes this task as a criminal case investigation, employing four specialized agents responsible for the analysis, investigation, prosecution, and judgment stages within a structured collaborative workflow. In the first stage, the analyst agent paraphrases each meme under benevolent and malicious assumptions to probe its underlying intent. The investigator agent then retrieves supporting evidence from an unannotated dataset and constructs contextual interpretations for the meme and its variants. Next, the prosecutor agent performs three independent preliminary judgments by pairing the original meme with each of the three interpretations. Finally, the judge agent deliberates across all evidence to render a final verdict. Moreover, PrismAgent's explicit multi-stage reasoning chain makes the model inherently interpretable, as every intermediate step is explicitly explained rather than only producing a final detection result. Extensive experiments on three public datasets show that PrismAgent significantly outperforms existing zero-shot detection methods.

Chain-of-Thought (CoT) prompting has emerged as a simple and effective way to elicit step-by-step solutions from large language models (LLMs). However, CoT reasoning can be unstable across runs on long, multi-step problems, leading to inconsistent answers for unchanged task. Most prior work focuses on improving the forward reasoning chain within a single pass, with less attention to iterative and contrastive correction. To address this gap, we propose CAP-CoT, a Cycle Adversarial Prompt optimization framework designed to improve both CoT reasoning accuracy and stability of a single deployed solver. In each cycle, a forward solver generates candidate reasoning chains, an adversarial challenger constructs plausible but deliberately flawed chains using targeted error strategies, and a feedback agent contrasts the two chains and produces step-aligned structured feedback. This feedback closes the optimization loop in two directions, including updating the solver prompt based on errors exposed by the challenger, and updating the challenger prompt to generate increasingly targeted errors in subsequent cycles. Unlike safety-oriented adversarial prompting such as jailbreak or prompt-injection attacks, our adversarial component is task-semantic and aims to expose logical vulnerabilities in reasoning chains. Experiments across six benchmarks and four LLM backbones demonstrate that within two to three adversarial prompt optimization cycles, CAP-CoT consistently reduces variability across runs while improving reasoning accuracy and robustness to prompt perturbations.

While LLMs demonstrate impressive reasoning capabilities, they remain fragile in multi-step logical deduction, where a single transition error can propagate through the entire reasoning chain, leading to unstable performance. In this work, we identify logical connectives as primary points of this structural fragility. Through empirical analysis, we show that connective tokens function as high entropy forking points, at which models frequently struggle to determine the correct logical direction. Motivated by this observation, we hypothesize that intervening in logical connective selection can guide LLMs toward more correct logical direction, thereby improving the overall reasoning chain. To validate this hypothesis, we propose a multi-layered framework that intervenes specifically at these logic-critical junctions in the reasoning process. Our framework includes (1) Gradient-based Logical Steering to guide LLMs internal representations towards valid reasoning subspaces, (2) Localized Branching to resolve ambiguity via targeted look-ahead search, and (3) Targeted Transition Preference Optimization, a surgical reinforcement learning objective that selectively optimizes single-token preferences at logical pivots. Crucially, by concentrating intervention solely on logic-critical transitions, our framework achieves a favorable accuracy--efficiency trade-off compared to global inference time scaling methods like beam search and self-consistency.

The rapid advancement and widespread adoption of Large Language Models (LLMs) have elevated the need for reliable AI-generated content (AIGC) detection, which remains challenging as models evolve. We introduce AIGC-text-bank, a comprehensive multi-domain dataset with diverse LLM sources and authorship scenarios, and propose REVEAL, a detection framework that generates interpretable reasoning chains before classification. Our approach uses a two-stage training strategy: supervised fine-tuning to establish reasoning capabilities, followed by reinforcement learning to improve accuracy, improve logical consistency, and reduce hallucinations. Extensive experiments show that REVEAL achieves state-of-the-art performance across multiple benchmarks, offering a robust and transparent solution for AIGC detection. The project is open-source at https://aka.ms/reveal

Large reasoning models (LRMs) produce complex, multi-step reasoning traces, yet safety evaluation remains focused on final outputs, overlooking how harm emerges during reasoning. When jailbroken, harm does not appear instantaneously but unfolds through distinct behavioral steps such as suppressing refusal, rationalizing compliance, decomposing harmful tasks, and concealing risk. However, no existing benchmark captures this process at sentence-level granularity within reasoning traces -- a key step toward reliable safety monitoring, interventions, and systematic failure diagnosis. To address this gap, we introduce HarmThoughts, a benchmark for step-wise safety evaluation of reasoning traces. \ourdataset is built on our proposed harm taxonomy of 16 harmful reasoning behaviors across four functional groups that characterize how harm propagates rather than what harm is produced. The dataset consists of 56,931 sentences from 1,018 reasoning traces generated by four model families, each annotated with fine-grained sentence-level behavioral labels. Using HarmThoughts, we analyze harm propagation patterns across reasoning traces, identifying common behavioral trajectories and drift points where reasoning transitions from safe to unsafe. Finally, we systematically compare white-box and black-box detectors on the task of identifying harmful reasoning behaviours on HarmThoughts. Our results show that existing detectors struggle with fine-grained behavior detection in reasoning traces, particularly for nuanced categories within harm emergence and execution, highlighting a critical gap in process-level safety monitoring. HarmThoughts is available publicly at: https://huggingface.co/datasets/ishitakakkar-10/HarmThoughts

Language models often solve complex tasks by generating long reasoning chains, consisting of many steps with varying importance. While some steps are crucial for generating the final answer, others are removable. Determining which steps matter most, and why, remains an open question central to understanding how models process reasoning. We investigate if this question is best approached through model internals or through tokens of the reasoning chain itself. We find that model activations contain more information than tokens for identifying important reasoning steps. Crucially, by training probes on model activations to predict importance, we show that models encode an internal representation of step importance, even prior to the generation of subsequent steps. The internal representations of importance in different models yield high agreement on which steps are important. The representation is distributed across layers, and does not correlate with surface-level features, such as a step's relative position or its length. Our findings suggest that analyzing activations can reveal aspects of reasoning that surface-level approaches fundamentally miss, indicating that reasoning analyses should look into model internals.

Long Chain-of-Thought (CoT) reasoning is pivotal for the success of recent reasoning models but suffers from high computational overhead and latency. While prior works attempt to compress CoT via external compressor, they often fail to align with the model's internal reasoning dynamics, resulting in the loss of critical logical steps. This paper presents \textbf{C}ompressing \textbf{R}edundancy in Chain-of-Thought via \textbf{I}ntrinsic \textbf{S}aliency \textbf{P}runing (\textbf{CRISP}), a framework that compresses CoT by exploiting the model's intrinsic saliency. Our analysis reveals a distinct phenomenon: the reasoning termination token \texttt{[object Object]} acts as an information anchor, where its attention pattern effectively demarcates essential reasoning from redundancy. Based on this finding, we design a policy that utilizes these intrinsic attention signals to guide atomic compression operations. In contrast to coarse-grained pruning strategies, CRISP strategically distills the reasoning chain to maximize information density while preserving logical coherence. Empirical results across various backbone models and mathematical datasets demonstrate that CRISP achieves a 50-60% reduction in token count without compromising accuracy, effectively mitigating the efficiency bottleneck of long-context reasoning. We open-source our implementation to facilitate further research in efficient reasoning.

Large language models exhibit systematic limitations in structured logical reasoning: they conflate hypothesis generation with verification, cannot distinguish conjecture from validated knowledge, and allow weak reasoning steps to propagate unchecked through inference chains. We present a symbolic reasoning scaffold that operationalizes Peirce's tripartite inference -- abduction, deduction, and induction -- as an explicit protocol for LLM-assisted reasoning. The framework enforces logical consistency through five algebraic invariants (the Gamma Quintet), the strongest of which -- the Weakest Link bound -- ensures that no conclusion in a reasoning chain can exceed the reliability of its least-supported premise. This principle, independently grounded as weakest link resolution in possibilistic logic and empirically validated for chain-of-thought reasoning, prevents logical inconsistencies from accumulating across multi-step inference. We verify all invariants through a property-based testing suite of 100 properties and 16 fuzz tests over 10^5+ generated cases, providing a verified reference implementation of the invariants suitable as a foundation for future reasoning benchmarks.

Large language models have demonstrated remarkable progress in mathematical reasoning, leveraging chain-of-thought and reinforcement learning. However, many open questions remain regarding the interplay between reasoning token usage and accuracy gains. In particular, when comparing models across generations, it is unclear whether improved performance results from longer reasoning chains or more efficient reasoning. We systematically analyze reasoning chain length across o1-mini and o3-mini variants on the Omni-MATH benchmark, finding that o3-mini (m) achieves superior accuracy without requiring longer reasoning chains than o1-mini. Moreover, we show that accuracy generally declines as reasoning chains grow across all models and compute settings, even when controlling for difficulty of the questions. This accuracy drop is significantly smaller in more proficient models, suggesting that new generations of reasoning models use test-time compute more effectively. Finally, we highlight that while o3-mini (h) achieves a marginal accuracy gain over o3-mini (m), it does so by allocating substantially more reasoning tokens across all problems, even the ones that o3-mini (m) can already solve. These findings provide new insights into the relationship between model capability and reasoning length, with implications for efficiency, scaling, and evaluation methodologies.