Large Language Model Reasoning

Chain-of-thought (CoT) reasoning improves the problem-solving ability of large language models (LLMs), but generated reasoning traces may not faithfully reflect the model's actual decision process. Existing CoT unfaithfulness detectors mainly rely on external signals from generated rationales, such as textual plausibility or answer consistency, while overlooking evidence from the model's internal computation. Although recent circuit tracing methods provide a way to obtain model-internal evidence by tracing how information flows through model components during reasoning, constructing full reasoning circuits for long CoTs is costly and difficult to scale. To address these challenges, we propose Circuit-guided Internal-External Discrepancy Scorer (CIE-Scorer), a framework for instance-level CoT unfaithfulness detection. The key idea is that faithful reasoning traces should align with the model's computational process, whereas unfaithful traces may diverge from it. CIE-Scorer efficiently traces compact sentence-level circuits from informative reasoning tokens, constructs internal and external reasoning graphs, and measures their discrepancy using Fused Gromov--Wasserstein distance. Experiments on four datasets from FaithCoT-Bench show that CIE-Scorer achieves state-of-the-art performance while reducing the cost of circuit construction, demonstrating the effectiveness of combining mechanistic interpretability signals with external reasoning traces for CoT unfaithfulness detection.

Post-training via Supervised Fine-Tuning (SFT) and Reinforcement Learning (RL) is crucial for enhancing reasoning in Multimodal Large Language Models (MLLMs), yet existing paradigms often reach a performance bottleneck due to the limitations of static data. While current methods leverage self-reflection or self-evolution to push these boundaries, they still suffer from cognitive drift and hallucinated reasoning paths caused by low-quality synthetic data. To address these challenges, we propose Anchor Evolution (AnE), a new paradigm that integrates truth-anchored data curation and model evolution, achieving faithful and steady performance gains at the reasoning frontier. Specifically, we propose Truth Anchor Expansion, which pinpoints the model failing frontier via trajectory rollouts and leverages ground-truth databases to retrieve high-fidelity anchors for faithful data curation. Subsequently, we introduce the Scaffold-Stripping Mechanism to internalize reasoning capabilities. This mechanism first anchors reasoning paths via scaffold-augmented supervision to mitigate the learning complexity and distribution drift of direct SFT on raw data, then leverages RL to strip the scaffold template, thereby effectively transitioning the reasoning paths into intrinsic model capabilities. Experimental results on multimodal reasoning benchmarks show that our method substantially advances the model performance frontier, improving the base model by 10.3% across eight multimodal benchmarks and achieving state-of-the-art results. The code will be made publicly available.

Clinical decision-making requires reasoning over incomplete, imprecise, and linguistically expressed patient narratives. While large language models (LLMs) excel at extracting latent information from natural language, they lack the verifiability and interpretability essential for trustworthy medical AI. We propose a neuro-symbolic reasoning framework that aligns LLMs with formal logic to enable explainable and formally verifiable medical diagnosis. Patient descriptions and clinical guidelines are embedded into a neural knowledge base, where LLMs extract structured medical entities, temporal relations, and fuzzy symptom patterns, which are decoded into a symbolic knowledge base expressed in fuzzy logic and declarative rules. We perform two-stage reasoning: (1) inductive symbolic generalization to capture diagnostic patterns from encoded narratives, and (2) inference verification via a logic programming engine to derive and validate diagnoses consistent with clinical standards. Each symptom is treated as a fuzzy predicate with probabilistic weights, and inference paths are auditable, adjustable, and compatible with physician feedback. Unlike purely statistical methods, our system supports iterative refinement: misalignment between LLM-generated diagnoses and ground truth can be traced, explained, and corrected through formal rules. By combining logic-based transparency, LLM adaptability, and probabilistic robustness, the framework enables human-aligned healthcare inference with strong generalization and verifiable, step-by-step reasoning chains. We validate our framework on public benchmarks, demonstrating effective reconciliation of symbolic reasoning and LLMs with real-world clinical narratives. Results show performance comparable to state-of-the-art LLMs, while additionally providing interpretable reasoning paths and formally verifiable diagnostic conclusions.

High-quality expert chain-of-thought (CoT) data is one of the core bottlenecks in large language model (LLM) post-training. Existing data production methods each have structural limitations: crowdsourced annotation lacks deep reasoning paths; expert solo writing is constrained by the "expert blind spot" -- experts structurally skip reasoning steps they consider obvious; RLHF only produces preference signals rather than reasoning chains. This paper proposes the BC Protocol -- a structured dual-expert elicitation method for LLM post-training data production. The method carefully pairs a domain expert (crystallized intelligence) with a knowledge engineer (fluid intelligence), systematically externalizing the expert's implicit judgments as natural language reasoning chains. We introduce the Participant Aptitude Model, which defines six participant characteristic dimensions that affect elicitation quality. "Calibrated Ignorance" is an original concept proposed in this paper. We further propose "Selection-over-Prescription" as a methodological principle: for implicit knowledge elicitation tasks, investing quality-control resources in personnel selection yields a higher return than investing the same resources in process design. In a controlled experiment in the narrative fiction domain, we directly compared CoT produced by BC Protocol dual dialogue (Group A, (n=20)) against CoT written independently by the same domain expert (Group B, (n=20)). Three cross-vendor judge models -- GPT-4o, Claude Opus 4.5, and Gemini 2.5 Pro -- conducted blind evaluation across five dimensions (600 ratings total). Results show that the BC Protocol achieves an overwhelming advantage in "naturalness of reasoning process" (Group A mean 4.80 vs. Group B mean 1.30, (p=2.4\times10^{-8}), Cliff's (δ=1.0)).

Reliable spatial reasoning remains a core bottleneck for vision-language models (VLMs). Existing mainstream training paradigms for spatial reasoning largely rely on outcome alignment or process imitation, lacking explicit constraints on the reasoning process, and therefore struggle to ensure genuine visual dependence and stable reasoning trajectories. In this paper, we construct a high-quality CoT dataset covering diverse spatial phenomena and diagnose the model's reasoning process, revealing two typical types of process degradation during reinforcement learning optimization: Spurious Grounding, which bypasses visual evidence, and Tail Instability, where uncertainty abnormally rises in the later stage of reasoning. To address these issues, we propose ProSR, a process-shaping optimization framework for spatial reasoning. Through a Counterfactual Invariance Penalty and a Tail Drift Penalty, ProSR extends the optimization objective from single answer correctness to two process-level dimensions: visual dependence and trajectory stability. Experiments on multiple complex and out-of-distribution spatial reasoning benchmarks show that ProSR improves answer accuracy while generating reasoning trajectories that are more stable and more dependent on visual evidence.

Contemporary reinforcement learning with verifiable reward methods post-train language models on multi-step reasoning by assigning a single outcome reward uniformly across all tokens in a trajectory. Such uniform assignment ignores which steps contributed to success or failure. Improving credit assignment can address this limitation by enabling targeted refinement of faulty reasoning steps, rather than updating entire trajectories uniformly. Resets are one such simple mechanism, enabling more precise credit assignment by returning to an intermediate state and resampling counterfactual continuations, so that outcome differences can be attributed to decisions made at that point. We propose two such methods: Random-Reset Policy Optimization (RRPO), where reset states are drawn randomly from reasoning steps, and Self-Reset Policy Optimization (SRPO), where the model self-localizes the erroneous step in an incorrect trajectory and resets there. We analyze these methods within the Conservative Policy Iteration (CPI) framework. Extending CPI with a credit-assignment oracle that targets improvable states yields provable improvements over random resets. Across models and reasoning benchmarks, SRPO consistently outperforms standard GRPO and RRPO by sampling multiple suffix continuations at a self-localized reset and learning from their rewards, using only the model itself with no external supervision.

Post-training has significantly enhanced the reasoning capability of Large Reasoning Models (LRMs), especially with Reinforcement Learning (RL) like Group Relative Policy Optimization (GRPO). However, GRPO-style RL methods in multi-domain settings often fail to achieve consistent improvements across all domains due to inherent interference in policy optimization. Prior studies on multi-domain RL primarily focus on alleviating cross-domain interference, while often neglecting the pivotal role of knowledge sharing, which we argue is the key to transforming cross-domain interactions from harmful competition into beneficial transfer. To address this limitation, we propose Multi-domain Contrastive Policy Optimization (MCPO), which analyzes the structural relationships among rollouts and promotes cross-domain knowledge sharing and in-domain knowledge consolidation in a contrastive manner. Specifically, for a given prompt, MCPO identifies transferable reasoning trajectories from other domains as positive examples, while treating incorrect rollouts as negative ones. It then encourages consistent representations for positive pairs and pushes negative pairs apart, thereby facilitating knowledge transfer and reducing interference. Moreover, MCPO aligns intra-domain correct rollouts to build a consolidated representation space. In this way, MCPO contrastively learns a harmonious representation space that can accommodate diverse multi-domain knowledge. Empirical results show that MCPO improves the reasoning capabilities of LRMs across multiple domains and even outperforms single-domain training in some cases. Code is available at https://github.com/Maricalce/MCPO.

Mathematical reasoning is a hallmark of human intelligence, requiring logical deduction, symbolic manipulation, and abstract thinking. Recent multimodal large language models (MLLMs) have demonstrated strong performance on geometry problems through multi-step reasoning. To better emulate human problem-solving, intermediate steps can incorporate auxiliary visual constructions, such as additional lines or points, which improve geometric interpretation and educational clarity. In this work, we introduce the GeoMathCode, where programmatic representations serve as intermediate visual outputs. We further conduct an in-depth analysis of the underlying reasoning geometry. Experimental results show that reasoning and code generation steps can be disentangled in the latent space, while supervised fine-tuning (SFT) makes the reasoning manifold more structured and informative. Moreover, hierarchical syntactic code structures emerge as disentangled latent subspaces, and contain more mathematical symbolic information than visual representations.

While LLMs excel at reasoning over prompts using static pretrained knowledge, they struggle significantly with context learning-the ability to dynamically extract, internalize, and apply new knowledge from complex, task-specific contexts. Recent evaluations on the CL-Bench reveal a critical capability gap: frontier models solve only 17.2% of context-dependent tasks on average.

Recent work on recursive architectures has shown that tiny neural networks can be surprisingly powerful on structured reasoning tasks. The trick is to model reasoning trajectories with a latent dynamical system. We argue that the inference-time behaviour of these architectures is best understood as approximate inference over latent reasoning trajectories, with deterministic recursion as the one-particle, zero-noise limit. We make this view operational through guided stochastic exploration: stochastic perturbations of the reasoning dynamics propose neighbouring trajectories, and the model's existing early-stopping head reweights them online. The framework yields three label-free diagnostics: local stability, guide alignment, and cloud-token entropy. These predict, from inference traces alone, whether the procedure will help and which of its outputs to trust. On Sudoku-Extreme it lifts exact-solve accuracy from $85.9\%$ to $98.0\%$ without retraining; on Maze-Hard the diagnostics flag a misaligned guide, as validation performance later confirms. The same machinery thus characterises both when recursive reasoning has room to improve at the trajectory level and when the model's internal guide can recover it.

Multi-agent LLM systems improve reasoning by combining outputs from multiple agents, but interaction-heavy methods can introduce error propagation and high communication overhead. When agents exchange raw responses or reasoning traces, incorrect intermediate reasoning may be adopted and amplified, leading to confident but wrong consensus; multi-round communication also increases token consumption, latency, and inference cost. In this paper, we propose a controlled-communication coordination framework named DarkForest. DarkForest first keeps agents independent, so each agent produces an answer without seeing the others' outputs. It then parses the raw responses into structured candidate records, groups semantically equivalent candidates into clusters, and estimates a calibrated belief distribution over these clusters using agent reliability, confidence, parse quality, support-pattern reliability, and independence corrections. A coordinator receives only policy-permitted evidence from this belief state with controlled communication. Experiments on six reasoning benchmarks show that DarkForest achieves leading overall quality, improves the strongest baseline by up to 30.7% on benchmark metrics, and reduces token consumption by up to $6.5\times$ compared with communication-heavy baselines.

Knowledge graph (KG) is an abstraction that can be extracted from text corpora and used for in-depth reasoning. Prior work has leveraged KGs to fine-tune language models (LMs), enabling domain-specific superintelligence. In this work, we explore whether KG-driven in-depth reasoning capabilities can emerge in neuroscience using only information contained within a single authoritative textbook. The central hypothesis is that structured knowledge, when distilled into a high-quality KG and converted into KG-grounded question-answer (QA) supervision, is sufficient to produce expert-level reasoning through a fine-tuned LM that surpasses large language models (LLMs) in accuracy, while employing orders of magnitude fewer parameters. We construct a textbook-derived KG via a dual-LLM validation pipeline, expand it with a masked LM trained on the KG topology, generate multi-hop QA items, which include QA pairs and reasoning traces, to fine-tune an LM exclusively on KG-derived supervision, and apply reinforcement learning using path-derived KG signals as implicit reward models. Our results demonstrate that deep, mechanistic neuroscience understanding can be induced in the model without reliance on large, heterogeneous web-scale corpora. The KG-based synthetic neuroscience curriculum that readers can quiz themselves on, and the fine-tuned LM, are available at the following GitHub location: https://kg-bottom-up-superintelligence.github.io/neuro-bench.

Test-time scaling improves language model reasoning by spending additional compute to explore multiple solution trajectories. The key challenge is to maximize accuracy while minimizing the total number of generated tokens during reasoning. Recent PRM-guided methods score intermediate prefixes to steer this search, but most are frontier-only: they keep only the current active prefixes and irreversibly prune or resample away the rest using noisy PRM scores. This can cause premature commitment, diversity collapse, and the loss of prefixes that still admit correct continuations. We introduce stochastic backtracking over a persistent pool of historical prefixes, allowing test-time compute to revisit previously generated states instead of only expanding the current frontier. To make this efficient, we propose two complementary mechanisms. Subpool Selection strengthens greedy PRM-guided search by applying Top-N selection within random subpools, giving historical prefixes a chance to bypass over-scored frontier candidates. Power Backtrack Sequential Monte Carlo extends SMC-style resampling to the persistent pool using powered PRM scores and mixture-corrected weights. Across mathematical reasoning benchmarks and model scales, our methods consistently achieve higher accuracy per token count, and the same level of accuracy using only a fraction of the token count in comparison to strong PRM-guided baselines, demonstrating that persistent-pool stochastic backtracking provides a simple and effective way to improve the accuracy-token trade-off in test-time scaling.

Self-improvement training enables the large reasoning models (LRMs) to improve themselves by self-generating reasoning trajectories as training data without external supervision. However, we find that this method often falls short in complex reasoning tasks and even leads to model collapse. Through a series of preliminary analyses, we reveal two problems: (1) data imbalance, where most training samples are simple, but the challenging yet crucial samples are scarce; (2) overthinking, where many undesired samples with redundant reasoning steps are used for self-training. To this end, we propose HSIR, which effectively Harnesses Self-Improvement in large Reasoning models via two simple-yet-effective approaches. Specifically, HSIR introduces a verify-then-exit sampling strategy to mitigate data imbalance by efficiently collecting more accurate solutions for difficult queries, and designs an Intrinsic Diversity score to quantify overthinking and filter out the undesired solutions. We apply HSIR to various post-training paradigms, among which we further propose H-GRPO, an enhanced GRPO algorithm that leverages the intrinsic diversity as an external reward to encourage concise and diverse reasoning via reinforcement learning. Extensive results show that HSIR not only effectively enhances the reasoning performance, i.e., bringing up to +10.9% average performance gains, but also significantly improves the reasoning efficiency by reducing up to 42.4% relative inference overhead.

Chain-of-Thought (CoT) faithfulness, i.e., whether CoTs genuinely reflect large language models' (LLM) underlying behavior, is typically evaluated under two disjoint paradigms: contextual faithfulness, measured by perturbing the input or CoT trace, and parametric faithfulness, assessed by intervening on a model's parametric knowledge. Yet prior work compares them only descriptively. We fill this gap by proposing FaithMate, a unified preference-alignment interface for optimizing models towards either faithfulness paradigm. It enables us to investigate the interplay between the two paradigms, examining whether and to what extent faithfulness gains generalize within and across paradigms. Across three models, two datasets, and six faithfulness metrics, we find that the two paradigms are positively coupled, yet asymmetric: optimizing towards parametric faithfulness yields consistent gains across both paradigms, whereas the contextual counterpart delivers more variable gains. Within the contextual paradigm, faithfulness gains on one metric do not consistently transfer to others, implying that existing contextual metrics capture disjoint facets of faithfulness and exposing inherent trade-offs. These findings imply that CoT faithfulness is not a monolithic objective and therefore requires multifaceted optimization and evaluation.

Reasoning-enabled LLMs perform strongly on medical reasoning benchmarks, but it remains unclear whether these gains transfer to structured clinical documentation; we investigate this question using SOAP note generation from clinical dialogue in a source-aware benchmark spanning OMI Health, ACI-Bench, and PriMock57. We evaluate GPT-5.4, DeepSeek-V4-Flash, and Gemma-4-E4B in a controlled 2x2 design that independently toggles provider-native reasoning and same-source retrieval-augmented generation (RAG). Outputs are assessed using seven automatic metrics alongside two reference-aware LLM judges. Both evaluation approaches agree that a non-reasoning GPT-5.4 configuration achieves the highest overall quality, while DeepSeek-V4-Flash performs best among reasoning-enabled configurations. Enabling reasoning significantly degrades GPT-5.4 performance across all three datasets, whereas same-source RAG yields smaller, model-dependent improvements. Overall, the findings indicate that stronger reasoning capability should not be assumed to improve fidelity-sensitive SOAP note generation without dedicated, task-specific evaluation.

Despite the importance of causal reasoning, training LLMs to reason causally remains underexplored. Existing data efforts mostly focus on benchmarking LLMs on specific aspects of causality, making them less suitable for training generalizable causal reasoners. To address this, we propose UniCo, a data generation framework that both (1) addresses 18 causal query types across Pearl's Causal Ladder and (2) translates natively symbolic examples into code and natural language forms to simulate real-world use cases where causal terms are not explicitly specified. To ensure data quality, UniCo grounds answers with exact causal inference and filters cases with reasoning shortcuts. Upon supervised finetuning with 66.6K UniCo-generated instances, Qwen3-4B, Qwen3-8B and Olmo-3-7B-Instruct achieve an average of 22.9% improvements across all 18 in-distribution query types, and 8.1% over state-of-the-art causal data generation frameworks on 7 established causal benchmarks outside the training distribution. More importantly, in real-world medical understanding, legal decision, and tabular reasoning, UniCo-trained models consistently display more faithful reasoning traces, outperforming the base models by an average of 20.2% in faithfulness metrics. These suggest that causality-centered training not only strengthens causal reasoning, but also equips LLMs with a causal mindset in general reasoning tasks.

Chain-of-Thought (CoT) prompting has shown promise in enhancing the reasoning capabilities of large language models (LLMs) on text-attributed graphs (TAGs). This work reframes CoT-based graph learning through the principle of clustering as reasoning, offering a $k$-means interpretation of how iterative reasoning operates over graph-structured data. We observe that existing graph CoT methods rely on disjoint architectures and fixed graph representations, limiting step-by-step semantic-topological interaction and interpretability. To overcome this limitation, we propose a unified framework named KCoT that integrates CoT reasoning with graph representation learning. Our key theoretical result reveals a formal mathematical correspondence between a Transformer block and the $k$-means algorithm, allowing reasoning to be interpreted as iterative assignment and update steps. Based on this insight, we introduce a Semantic Discriminating Prompt that explicitly formulates these steps as structured CoT reasoning, together with a structure-grounded alignment strategy to fuse topological priors with evolving thought-conditioned representations. Experiments on standard benchmarks demonstrate consistent improvements over state-of-the-art methods, validating clustering as a principled mechanism for CoT-based graph learning.

While general-purpose Large Language Models (LLMs) applied to Geology often hallucinate when reasoning about subsurface structures and deep-time evolution, current AI in Earth sciences predominantly targets surface remote sensing and GIS. To bridge this gap, we introduce Geo-Expert, a family of parameter-efficient geological LLMs fine-tuned on a custom-curated, high-quality instruction dataset processed using our custom instruction synthesis pipeline. We investigate the impact of model scaling and architecture by fine-tuning three base models: Qwen3-8B, Qwen3-32B, and Gemma-3-27B, with Low-Rank Adaptation (LoRA) method. Our extensive evaluation on a novel domain-specific benchmark, Geo-Eval, reveals that a domain-aligned 8B model can outperform open-weight 70B generalists and proprietary GPT-4o on specialized geological reasoning, while a 32B variant approaches frontier reasoning models. The optimized 8B model further offers a competitive cost-performance ratio for deployment. This work provides a reproducible recipe for democratizing scientific LLMs and establishes a baseline for geological artificial intelligence.

With the continuous advancement of Large Language Models (LLMs), intelligent agents are becoming increasingly vital. However, these agents often fail in environments governed by implicit rules--hidden constraints that cannot be observed directly and must be inferred through interaction. This causes agents to fall into repetitive trial-and-error loops, ultimately leading to task failure. To address this challenge, we propose Test-Time Exploration (TTExplore), a framework where a thinker component analyzes interaction history to infer these implicit rules and guide an actor. Effective exploration in this setting critically depends on the reasoning ability of the thinker. However, evaluating deep reasoning trajectories is inherently unstable and difficult, which poses a major obstacle to effective training. To overcome this issue, we introduce a novel and stable reinforcement learning pipeline. The core idea is to use accurate task-level scores as indirect rewards to bypass the difficulty of evaluating intermediate reasoning, and to retain only a single thinking node per trajectory to alleviate reward sparsity. Using this pipeline, we train a specialized 7B model, Exp-Thinker. Experiments on five text-based embodied tasks show that TTExplore equipped with Exp-Thinker improves baseline agent performance by an average of $14$-$19$ points, demonstrating the effectiveness of explicitly reasoning about implicit rules.

Despite remarkable progress on reasoning benchmarks, current LLM evaluation practice remains anchored to final-answer correctness, providing limited insight into how models reason, how reliably they behave under contextual variation, or how efficiently they reach conclusions. This paper proposes a unified multi-dimensional framework for measuring LLM reasoning quality from a behavioral perspective, operationalizing six theoretically grounded dimensions rooted in cognitive science: Correctness (CQ), Consistency (CS), Robustness (RS), Local Logical Coherence (LS), Efficiency (ES), and Stability (SS). The framework introduces deployment-aware aggregation, enabling context-specific model selection beyond accuracy-based leaderboards. Experiments across multiple LLMs and benchmarks reveal behaviors systematically concealed by single-metric evaluation, including the orthogonality of local logical coherence and correctness, deployment-context-dependent ranking inversions, and non-trivial dimensional profiles in small locally-deployed models. Discriminant validity analysis confirms that the proposed dimensions capture largely non-redundant signals. The resulting pipeline provides a foundation for diagnosing LLM reasoning behavior across deployment contexts, with domain-specific validation as a direction for future work.

Medical large language models hold promise for reducing healthcare disparities, yet Hindi remains severely underrepresented. While medical LLMs excel in high-resource languages, their performance degrades sharply in Hindi, particularly on Indian systems of medicine. We argue that robust cross-lingual medical transfer requires Hindi reasoning. To this end, we introduce HiMed, a Hindi reasoning medical corpus and benchmark suite covering both Western and Indian medicine. We further propose HiMed-8B, a Hindi-form medical reasoning LLM, through the design of decaying scaffolding reward. Extensive experiments demonstrate improvement in Hindi medical reasoning performance and reduction in the English--Hindi accuracy gap. Ablation studies validate the contribution of each training stage and reward component. All data and code are available on GitHub: https://github.com/FreedomIntelligence/HiMed.

Post-hoc repair of LLM mathematical reasoning introduces an asymmetric risk: fixing an incorrect reasoning trace is useful, but replacing a trace that was already correct can be harmful. We study this problem under a selective replacement setting, where a system must decide whether a repaired candidate is safer than preserving the original cached trace. We present GuardedRepair, a guarded best-of-N repair framework that diagnoses cached reasoning traces, selectively triggers repair, and accepts answer-changing candidates only when deterministic verification guards support replacement. The framework combines lightweight symbolic checks, surface semantic-risk diagnostics, bounded candidate generation, and conservative acceptance policies. On the full GSM8K test set, where the initial reasoner already achieves 95.60% accuracy, GuardedRepair improves final accuracy to 96.89%, fixing 17 of 58 remaining errors without measured broken-correct cases in the main run. On a weak-reasoner ASDiv setting, accuracy improves from 78.40% to 87.60%. Direct regeneration baselines show that this gain is not explained by stronger-model re-solving alone: re-solving all GSM8K examples lowers accuracy to 93.03% and breaks 47 initially correct answers. Additional analyses show that guarded repair substantially improves the fixed/broken tradeoff, while also revealing that replacement risk is reduced rather than eliminated. These results support viewing post-hoc repair as harm-aware selective replacement rather than unconstrained re-solving.

Many applications of large language models (LLMs) require deductive reasoning, yet models frequently produce incorrect or redundant inference steps. We frame natural language inference as a search problem where the final answer is the valid proof itself, requiring a reasoning procedure in which intermediate inferences are correct. Specifically, we investigate whether LLMs can learn to generate correct and efficient proofs with guidance from A* search -- an algorithm that guarantees an optimally efficient path to a goal. We explore two training techniques: supervised fine-tuning on execution traces from A* and reinforcement learning with A*-informed process reward models. Empirically, we find that Llama-3.2 models in the 1B--3B range benefit substantially from A* post training, going from near-zero accuracy to outperforming DeepSeek-V3.2 -- a much larger model. Our analysis uncovers a trade-off: while simple correctness rewards maximize accuracy, A*-informed signals strike a balance between accuracy and efficiency. Furthermore, we find that on larger search spaces, models trained with imperfect heuristics exhibit superior accuracy. Our results demonstrate a promising direction towards reasoning guided by principles derived from classical search algorithms.

Efficiently updating Large Language Models (LLMs) with new or evolving factual knowledge remains a central challenge, as even parameter-efficient adaptation can erode previously acquired reasoning abilities. This tension reflects a plasticity-stability dilemma: models must incorporate new knowledge while preserving skill-critical representations. In this work, we study this trade-off through the spectral structure of multilayer perceptron weight matrices. We show, both theoretically and empirically, that information essential for reasoning is not localized only in dominant singular directions, but is instead distributed across the singular spectrum. Motivated by this observation, we introduce PALoRA, a two-stage framework for knowledge injection with reduced interference. PALoRA first trains a Singular Value Fine-Tuning (SVF) expert on a reasoning dataset and uses its learned singular scaling vector as a frozen geometric probe to identify components that are critical for the target skill. It then performs factual knowledge injection with Low-Rank Adaptation (LoRA) under a structural orthogonality constraint, ensuring that updates avoid the identified skill-relevant subspace. Across Llama 3.1 8B and Mistral 7B, and across mathematical, coding, and scientific reasoning benchmarks, PALoRA preserves on average 95% of the SVF expert's reasoning performance while maintaining competitive factual recall. It consistently improves skill retention over prior spectral Parameter-Efficient Fine-Tuning (PEFT) methods while adding less than 0.006% parameter overhead.

Reinforcement learning with verifiable rewards can improve LLM reasoning, but learning remains sample-inefficient when terminal rewards are sparse. This has motivated a growing line of work on RL with textual feedback, where a critic model generates natural language feedback to guide a reasoning model (the actor), augmenting scalar rewards with richer learning signals. However, existing methods typically treat feedback as fixed or auxiliary, which misses a key property: feedback should not merely be correct, but should improve the policy (actor model) when provided in context. This motivates a paradigm of learnable textual feedback for RL. Yet the learnability and usefulness of feedback depend on the policy's ability to learn from it, making RL with learnable feedback an inherently bilevel problem. We formalize this coupling as a Stackelberg bilevel program and derive Bilevel Natural Language Actor-Critic (Bi-NAC), which jointly trains a critic to generate reward-improving feedback and an actor to exploit it. Across MATH-500, MBPP, and GPQA, Bi-NAC improves sample and parameter efficiency over RL and fixed-critic baselines: our 2B model outperforms the 3B GRPO baseline, achieving 46.6% versus 41.4% on MATH-500, while our 6B model surpasses the 7B GRPO baseline, achieving 49.3% versus 43.6% on GPQA.

Large Reasoning Models (LRMs) have demonstrated remarkable capabilities in reasoning and generation tasks and are increasingly deployed in real-world applications. However, their explicit chain-of-thought (CoT) mechanism introduces new security risks, making them particularly vulnerable to jailbreak attacks. Existing approaches often rely on static CoT templates to elicit harmful outputs, but such fixed designs suffer from limited diversity, adaptability, and effectiveness. To overcome these limitations, we propose an adaptive evolutionary CoT jailbreak framework, called AE-CoT. Specifically, the method first rewrites harmful goals into mild prompts with teacher role-play and decomposes them into semantically coherent reasoning fragments to construct a pool of CoT jailbreak candidates. Then, within a structured representation space, we perform multi-generation evolutionary search, where candidate diversity is expanded through fragment-level crossover and a mutation strategy with an adaptive mutation-rate control mechanism. An independent scoring model provides graded harmfulness evaluations, and high-scoring candidates are further enhanced with a harmful CoT template to induce more destructive generations. Extensive experiments across multiple models and datasets demonstrate the effectiveness of the proposed AE-CoT, consistently outperforming state-of-the-art jailbreak methods.

Long chains of thought (CoT) from current language models frequently contain logical gaps and unjustified leaps, limiting the gains from additional test-time compute. Improving reasoning quality directly would require process reward models, but the step-level annotations needed to train them are expensive and scarce. We find such a signal in how the model's confidence evolves during reasoning: premature confidence, the tendency to commit to an answer early and use the remaining tokens to rationalize it, strongly predicts flawed reasoning across tasks and model scales. We exploit this in progressive confidence shaping, a reinforcement learning objective that trains models to update their confidence as they reason rather than commit early -- rewarding gradual confidence growth and penalizing early commitment, with no external labels or reward models. The method improves accuracy and reasoning quality from 1.5B to 8B parameters across arithmetic (Countdown), math (DAPO, AIME), and science (ScienceQA): on Countdown, accuracy improves 3.2x (+42.0pp) and flawed reasoning drops 48pp; on AIME, Pass@64 improves 6.6pp. Consistent with this mechanism, the method also improves faithfulness: on a safety benchmark, our models more transparently surface misleading content in their reasoning traces rather than concealing it. Controlled experiments reveal that the problem and its remedy scale together: premature confidence grows with model size and task difficulty, and so do the gains from addressing it.

Context or prompt-level reweighting has emerged as a central algorithmic lever in Reinforcement Learning with Verified Rewards (RLVR) for improving the reasoning capability of large language models, yet the principle determining what constitutes an optimal weighting remains poorly understood. We address this gap by formulating prompt reweighting as a functional derivative of a utility functional defined in the pass-rate function space, yielding a unified optimality framework that accommodates existing schemes, including REINFORCE and GRPO. Building on this optimality framework, we propose a distribution-aware prompt reweighting approach, called CurveRL, based on a quantile coordinate transform, in which the weight assigned to each prompt depends not on the absolute value of pass rates but on its rank and density to reflect the distributional structure of the pass rates in the learning dynamics. Extensive experiments across multiple benchmarks demonstrate that our proposed CurveRL consistently outperforms GRPO and other RLVR baselines. Our study identifies context-distribution control as a principled axis for analyzing and designing prompt-reweighted RLVR algorithms. The code is released in https://github.com/zhyzmath/CurveRL.

Standard accuracy on binary reasoning benchmarks hides critical failure modes: prior collapse, inconsistency under paraphrase, and inability to reason about parameter-dependent dynamics. We present ChaosBench-Logic v2, a 40,886-question benchmark over 165 dynamical systems with 27 FOL predicates and 78 axiom edges, together with CARE (Calibration- and Adversarial-Robust Evaluation), a protocol that surfaces these pathologies. Evaluating 14 models, we find that regime-transition reasoning remains near random (MCC = 0.05) even for frontier models, whereas FOL deduction with given premises reaches MCC = 0.52. Per-family decomposition shows that the proprietary-model advantage concentrates on cross-indicator (+0.40) and consistency tasks, while open-source Qwen 2.5-32B dominates indicator diagnostics (0.91 vs. 0.45). Two models exhibit negative MCC on bifurcation questions, confirmed as systematic anti-correlation via confusion-matrix analysis.

Multi-step reasoning remains a central challenge for large language models: single-pass generation is efficient but lacks accuracy; tree-search methods explore multiple paths but are computation-heavy. We address this gap by distilling reasoning progress into a hyperbolic geometric signal that guides step-by-step generation. Our approach is motivated by a structural observation: in combinatorial reasoning trees, solution-bearing states are few while dead ends are exponentially numerous. The hyperbolic space matches this asymmetry, with compact volume near the origin and exponentially expanding capacity toward the boundary, so that distance-to-origin naturally encodes solution proximity while angular separation distinguishes branches requiring different next operations. We train a lightweight head to project LLM hidden states into this space, then fine-tune a low-rank adapter interactively on its own reasoning attempts to act on the injected signal. Across multiple benchmarks, the geometric signal yields consistent gains, with larger improvements on deeper reasoning chains. Our code is publicly available at https://github.com/yuyuliu11037/HyperGuide.

Recent RL methods have substantially improved the reasoning abilities of LLMs. Existing reward designs mainly follow two paradigms: (1) Reinforcement learning with verifiable rewards (RLVR) derives outcome signals from executable checks or ground-truth answers, but provides limited guidance for intermediate reasoning behaviors. (2) Rubrics-as-reward (RaR) goes beyond final-answer checking by using natural-language rubrics to assess reasoning quality and task compliance, but often requires instance-specific rubrics and substantial design effort. To address these issues, we introduce Metacognition-as-Reward (MaR), a metacognition-inspired RL framework that guides LLM reasoning through two general process dimensions: i) metacognitive knowledge, which identifies task-relevant information without hand-crafted instance-specific rubrics, and ii) metacognitive regulation, which plans and adjusts the reasoning process to provide reward guidance beyond final-answer outcomes. MaR scaffolds model rollouts into explicit metacognitive components and optimizes them with a trajectory-level reward over task knowledge coverage, regulation fidelity, and final-answer correctness. In this way, MaR extends reward feedback to reasoning trajectories while grounding the reward signals in general metacognitive dimensions. Experiments on 22 benchmarks show that MaR consistently improves model performance, achieving up to a 7.7% gain over the base model and up to an 11.0% gain over vanilla DAPO. Notably, Qwen3.5-9B + MaR narrows the gap to frontier models, surpassing GPT-OSS-120B on overall average and outperforming stronger models on several individual benchmarks. Process-level analysis further shows substantial improvements in reasoning process quality. MaR also generalizes to out-of-domain datasets, where MaR-trained models improve over their corresponding base models on average.

Retrieval-augmented generation (RAG) has emerged as a paradigm for grounding large language models in external knowledge, yet most existing RAG systems assume centralized knowledge access and ample computation. These assumptions break down in edge environments, where knowledge is fragmented across devices, raw data cannot be shared, and repeated LLM calls are prohibitively expensive. We propose FD-RAG, a federated dual-system RAG framework that decouples lightweight memory access from on-demand LLM reasoning for decentralized deployment. Specifically, FD-RAG learns semantic-aware adaptive hypergraphs over local corpora and distills them into compact QA memories. At inference time, it answers well-covered queries via direct memory matching and invokes LLM-based reasoning only when necessary, while tracing retrieved memories to hypergraph-grounded evidence. To mitigate cross-device knowledge fragmentation, FD-RAG aggregates anonymized memories across devices without exposing raw documents. Experiments on QA benchmarks show that FD-RAG improves accuracy by up to 7.8% while reducing latency by 8.4$\times$ compared with strong local and federated baselines. We also provide theoretical analysis establishing an $\mathcal{O}(1/ε^{2})$ convergence rate for the proposed hypergraph learning, supporting its tractable deployment in edge settings.

Position-controlled evaluation is standard for retrieval tasks such as Needle-in-a-Haystack and RULER, but mainstream reasoning benchmarks do not control positional placement of target tasks in long contexts. We audit 11 long-context benchmarks and find none jointly controls task position, filler content, and context length for reasoning. An audit of four flagship long-context releases finds no main result-table entry for NIAH, RULER, or LongBench-family benchmarks, while agentic and coding benchmarks appear in main result-tables across all four. We propose Context Rot Evaluation (CRE), a controlled framework varying all three factors, and evaluate nine LLMs on GSM8K and ARC-Challenge across two rounds: an initial five-model set and four newer vendor releases. Models can drop sharply when the target task moves from end to middle, and the drop grows worse with context length for vulnerable models. MiMo-v2-Flash drops 88pp at 64K under with_solutions filler (middle accuracy 8%). Newer releases show smaller drops: at 64K, three of four stay within +/-6pp of end-position accuracy; MiMo-V2.5-Pro narrows the MiMo-v2-Flash 88pp drop to 32pp. Under questions_only_v2 filler, middle-position drops persist across all four (range -16pp to -56pp across 8K, 32K, 64K). At 8K, a diagnostic probe adding a target-task copy at the end brings middle accuracy within +/-4pp of end baseline across all nine models, consistent with a positional explanation. In the initial five-model set, 76% of middle-position errors match surrounding filler text versus 22% at the end position, consistent with filler-answer interference as a dominant error mode. These results expose a structural evaluation gap in current reasoning benchmark design and vendor evaluation practice: positional vulnerabilities that grow with context length cannot be measured when task position is not controlled.

The emergence of Large Reasoning Language Models (LRMs) has paved the way for tackling complex reasoning tasks through test-time scaling by generating long-form Chain-of-Thought (CoT) trajectories during inference. Meanwhile, these trajectories often contain explicit reflection markers such as wait'', but'', and ``alternatively'', signaling hesitation, revision, and the consideration of alternative explorations, respectively. Recent studies on test-time control leverage such markers as lightweight handles for steering reasoning, typically treating them as a single coarse-grained category rather than distinguishing their distinct functional roles. In this paper, we conduct type-wise suppression and fixed-prefix intervention, revealing that reflection markers differ not only in their functional roles but also in when they exert the greatest influence. Specifically, different marker classes affect accuracy and generation length in distinct ways, and marker choices are most consequential before the model settles into a stable reasoning trajectory. Motivated by these findings, we introduce PathCal, a novel training-free decoding controller that calibrates reasoning paths by distinguishing marker types and intervening only at locally uncertain states. At each decoding step, PathCal utilizes the distribution over reflection-markers to estimate local competition between maintaining the current reasoning trajectory and initiating a competing branch, and softly rebalances marker logits when competing-branch evidence becomes excessive. Experiments across six reasoning benchmarks demonstrate that PathCal achieves a better efficiency--performance trade-off, improving or preserving accuracy while reducing generation length, without relying on external verifiers or additional sampling.

We aim to improve the reasoning capabilities of diffusion language models (DLMs). While SFT is a popular post-training recipe for autoregressive models, its use in DLMs faces challenges and can even hurt performance, though the underlying causes remain understudied. Our analysis reveals that vanilla SFT overlooks learnability, namely what and when tokens are learned. Specifically, rare tokens are difficult to learn when most of the input is masked, whereas it is straightforward and thus of little value to learn common tokens when most of the input is unmasked. Motivated by our analysis, we propose LIFT, an efficient SFT-based post-training algorithm for DLMs. LIFT learns easy tokens when most of the input is masked and hard tokens when more context is available, thus aligning the training with the information available at different diffusion time steps. Our results show that LIFT outperforms existing SFT baselines across six reasoning benchmarks, achieving up to a 3x relative gain on AIME'24 and AIME'25. Our code is publicly available at https://github.com/divelab/LIFT.

Persuasive dialogue requires reasoning about others' latent mental states, a capability known as Theory of Mind (ToM). However, due to reliance on simple prompting strategies and insufficient ToM knowledge, existing LLMs often fail to capture the intrinsic dependencies among mental states, leading to fragmented representations and unstable reasoning. To address these challenges, we introduce the ToM-based Persuasive Dialogue (ToM-PD) task, grounded in the Belief-Desire-Intention (BDI) framework, which explicitly models the sequential dependencies among mental states in multi-turn dialogues. To facilitate research on this task, we construct a large-scale annotated dataset, ToM-based Broad Persuasive Dialogues (ToM-BPD), capturing fine-grained mental states and corresponding persuasive strategies. We further propose Think Thrice Before You Speak (TTBYS), a knowledge-enhanced stepwise reasoning framework that leverages both explicit and implicit prior experiences to improve LLMs' inference of desires, beliefs, and persuasive strategies. Experimental results demonstrate that Qwen3-8B equipped with TTBYS outperforms GPT-5 by 1.20%, 22.80%, and 16.97% in predicting desires, beliefs, and persuasive strategies, respectively. Case studies further show that our approach enhances interpretability and consistency in reasoning.

Reinforcement learning has proven effective for enhancing multi-step reasoning in large language models (LLMs), yet its benefits have not fully translated to multilingual contexts. Existing methods struggle with a fundamental trade-off: prioritizing input-language consistency severely hampers reasoning quality, while prioritizing reasoning often leads to unintended language drift toward English. We address this challenge with LANG, a novel framework that leverages language-conditioned hints to guide exploration in non-English reasoning tasks. Our method incorporates two key mechanisms to prevent dependency on these hints: a progressive decay schedule that gradually withdraws scaffolding, and a language-adaptive switch that tailors learning horizons to specific language difficulties. Empirical results on challenging multilingual mathematical benchmarks reveal that LANG substantially enhances reasoning performance without compromising language consistency. Moreover, we show that our framework generalizes beyond mathematics, fostering more consistent language alignment across model layers

Making high-stakes personal decisions involves cognitive, emotional, and intuitive processes, and individuals differ in how they allocate attention across these modes. Integration of these processes has shown to benefit decision making. Yet, most current decision-support systems focus primarily on supporting cognitive aspects, rather than adapting to the individual's thinking profile to support integration of different types of thoughts. In this study, we investigate an agent designed to encourage integration by adapting to the individual user's thought patterns. We explore its effects on participants' perceptions of the agent and their reflective behavior, in comparison with unaided pre-reflection and a baseline agent. In a between-subjects study (N = 128), our agent, which fostered broad and elaborated thinking, enabled more personalized reflective trajectories, elicited more integrative reflective language, and was perceived as providing stronger support for holistic reflection. In contrast, the baseline agent produced homogenized profiles dominated by cognitive language across participants.

Effectively training Large Language Models (LLMs) for complex, long-CoT reasoning is often bottlenecked by the need for massive high-quality reasoning data. Existing methods are either computationally expensive or fail to reliably distinguish high- from low-quality reasoning samples. To address this, we propose High-Entropy Sum (HES), a training-free metric that quantifies reasoning quality by summing only the entropy of the top (e.g., 0.5%) highest-entropy tokens in each reasoning sample. We validate HES across three mainstream training paradigms: Supervised Fine-tuning (SFT), Rejection Fine-tuning (RFT), and Reinforcement Learning (RL), with extensive results demonstrating its consistent effectiveness and significantly reduced computational overhead. In SFT, training on the top 20% HES-ranked data matches full-dataset performance, while using the lowest-HES data degrades it. In RFT, our HES-based training approach significantly outperforms baseline methods. In RL, HES-selected successful trajectories enable the model to learn strong reasoning patterns, significantly surpassing other compared methods. Our findings establish HES as a robust, training-free metric that enables a unified, effective, and efficient method for developing advanced reasoning in LLMs.

On-policy self-distillation (OPSD) is an emerging LLM post-training paradigm in which the model serves as its own teacher: conditioned on privileged information such as a reference trace or hint, the same policy provides dense token-level supervision on its own rollouts. However, recent studies show that OPSD degrades complex reasoning by suppressing predictive uncertainty, which supports exploration and hypothesis revision. Our token-level analysis shows that this failure arises from applying a uniform direction of teacher supervision across tokens with different uncertainty levels: conformity to the privileged self-teacher suppresses exploration at high entropy, while deviation from the teacher degrades step accuracy at low entropy. Accordingly, we propose \textbf{Direction-Adaptive Self-Distillation} (\textbf{DASD}), which reframes privileged self-distillation from uniform teacher imitation into entropy-routed directional supervision: high-entropy tokens are pushed away from the privileged teacher to preserve exploration, while low-entropy tokens are pulled toward the teacher to stabilize step-level execution. Across six mathematical reasoning benchmarks, DASD achieves the best macro Avg@16 over strong RLVR and self-distillation baselines. Pass@$k$, reasoning-health, and generalization analyses show that these average gains come from preserving exploration without sacrificing step-level execution.

Graph of Thoughts (GoT), a generalized form of recent prompting paradigms for large language models (LLMs), has been shown to be useful for elaborate problem solving. By executing a graph of operations, thoughts of the LLM are structured as an arbitrary graph, forming the actual graph of thoughts. Originally, the graph of operations is defined manually, which requires in-depth knowledge about the solution of the problem to solve. Such a static graph of operations is rigid and therefore lacks adaptability. We propose Reinforced Graph of Thoughts (RGoT), an automated approach to the GoT prompting paradigm that leverages reinforcement learning (RL) to adaptively generate a graph of operations from a human-defined set. Results indicate that, under certain constraints, it is possible to construct graphs of operations adaptively to the task's complexity in an automated way.

Recent progress in LLM reasoning has increasingly shifted from single-pass generation to explicit search over intermediate reasoning states. Tree-of-Thoughts (ToT) organizes inference to tree-structured search with branching and backtracking, but it substantially amplifies the Key--Value (KV) cache: retaining KV states for a frontier of partial trajectories quickly becomes a memory bottleneck that limits throughput and constrains search depth and width under fixed hardware budgets. We address this challenge by observing that KV reuse in ToT-style inference is governed by search dynamics: near-term decoding depends primarily on the active branch and its ancestors, whereas inactive subtrees have low short-term reuse probability yet must remain recoverable for backtracking. Motivated by this, we propose ArborKV, a structure-aware eviction framework that couples a lightweight value estimator with a tree-aware allocation policy, and performs purely token-extractive eviction with lazy rehydration to support revisits. Experiments on ToT-style reasoning benchmarks show that ArborKV achieves up to ~4x peak KV-memory reduction while preserving near-full-retention accuracy, enabling larger search configurations under fixed device budgets that would otherwise run out of memory.

A common failure mode in long-horizon agentic test-time scaling is error propagation, where factual errors or invalid deductions introduced at intermediate steps persist in the agent's belief state and contaminate later reasoning. Existing test-time scaling methods provide limited control over this process, as they often rely on agents to detect their own mistakes, select among flawed trajectories, or refine solutions only after errors have already shaped the reasoning path. We propose ExComm, a communication protocol for exploration-stage agentic test-time scaling. ExComm is motivated by the empirical observation that the majority of intermediate errors in parallel agentic reasoning produce detectable cross-agent factual conflicts. Leveraging the iterative structure of agentic workflows, ExComm periodically audits agent belief states to detect such conflicts, resolves them through a dedicated tool-based verification loop, and returns concise, targeted feedback to the involved agents. Corrections are incorporated through soft belief updates, which append verified feedback rather than overwriting existing beliefs. Furthermore, to prevent collapsing trajectory diversity due to communication, ExComm further introduces a trajectory diversification module that redirects redundant trajectories toward orthogonal strategies. Experiments on AIME 2024, AIME 2025, and GAIA with Gemini-2.5-Flash-Lite and Qwen3.5-4B show that ExComm consistently outperforms strong test-time scaling baselines, achieving average performance gains of 5.7% and 5.0% over the best-performing baselines, respectively. Further analyses demonstrate improved error recovery, favorable scaling behavior, stronger diversity than adapted communication baselines, and the best performance-cost trade-off among the evaluated methods.

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.

Understanding 3D point clouds through language remains a fundamental challenge in computer graphics and visual computing, due to the irregular structure of point cloud data and the lack of explicit reasoning in existing 3D multimodal models. While Chain-of-Thought (CoT) reasoning has shown strong effectiveness in LLMs and image-based MLLMs, its extension to 3D understanding remains largely underexplored. In this paper, we propose a data-centric framework for constructing large-scale CoT supervision tailored to 3D point cloud understanding. Our framework consists of a two-stage pipeline that first refines point-text instruction data via vision-language-model-based quality evaluation and reference-guided refinement, and then synthesizes high-quality reasoning paths through Human-in-the-Loop Prompt Optimization (HiLPO). Using this approach, we build PoCoTI, a CoT-enhanced point-text instruction-following dataset containing 55K samples with explicit reasoning paths. Fine-tuning PointLLM on PoCoTI yields PointLLM-R, a reasoning-capable 3D multimodal language model. Extensive experiments on generative 3D classification and captioning demonstrate that PointLLM-R achieves state-of-the-art performance and generalizes robustly to real-world scanned point clouds and multi-turn dialogue scenarios.

Financial markets are characterized by extreme non-stationarity, low signal-to-noise ratios, and strong dependence on external information such as news, company fundamentals, and macroeconomic signals. Yet, existing approaches either abstract time-series into text or decouple forecasting from language-based reasoning, leading to a fundamental mismatch between qualitative reasoning and quantitative outcomes. To address this, we introduce StockR1, a time-series-enhanced LLM that unifies stock forecasting and financial reasoning through a verifiable forecast action. Based on a tool-call design, the model first emits a forecast action, which is a structured and interpretable representation of its qualitative market outlook. It then invokes a time-series decoder conditioned on this action to generate distributional future trajectories, leading to more informed question answering and financial reasoning. We optimize the full pipeline with reinforcement learning, where rewards jointly reflect answer validity, forecast accuracy, and consistency between generated actions and observed time-series dynamics. In addition, rewards are reweighted by a sample-level uncertainty scalar, encouraging the model to accommodate varying uncertainty in market dynamics. We evaluate StockR1 on financial question answering and stock forecasting over a large-scale 10-year benchmark. Our method consistently outperforms time-series baselines and general-purpose LLMs, improving reasoning accuracy by 17.7% (4B) and 25.9% (8B). These findings demonstrate that structuring the forecast actions establishes a powerful synergy between language reasoning and temporal prediction, enabling LLMs to reason through verifiable, interpretable, and numerically grounded decisions.

Reinforcement learning with verifiable rewards has become the standard recipe for improving LLM reasoning, but the dominant algorithm GRPO assigns a single trajectory-level advantage to every token, diluting the signal at pivotal reasoning steps and injecting noise at uninformative ones. Critic-free alternatives derived from on-policy distillation supply per-token signals through oracle-conditioned likelihood ratios, yet apply each signal in isolation from the trajectory-level evidence accumulated up to that position. We propose Oracle-Prompted Policy Optimization (OPPO), which rests on a single observation: the oracle signal used by prior distillation-style methods for local discrimination is also the natural Bayesian update of the model's belief about eventual success. Accumulating the signal along a trajectory yields, in closed form and at the cost of one extra forward pass, a running estimate of the success probability at every position, together with a token-level advantage that requires no learned value network and no additional rollouts. A first-order analysis factorizes the advantage into the per-token discrimination signal used by distillation methods modulated by a state weight that concentrates credit on genuinely pivotal tokens, with a directional variance-reduction guarantee. The framework admits two estimators differing only in which model scores the evidence: a \textit{self-oracle} that reuses the student and recovers the on-policy distillation reward as a strict special case, and a \textit{teacher-oracle} that delegates scoring to a stronger frozen model. On two base LLMs across seven mathematics, science, and code reasoning benchmarks, OPPO improves over GRPO, DAPO, and SDPO by up to $+6.0$ points on AMC'23 and $+5.2$ points on AIME'24, with gains that widen monotonically with response length.

Large language models frequently produce errors in reasoning tasks despite possessing the underlying knowledge required for correct reasoning. One possible approach to improve reasoning consistency is through activation steering. However, existing activation steering approaches apply fixed, pre-computed correction vectors, ignoring where the model currently sits along its generation trajectory; the result is indiscriminate perturbation that disrupts already-correct steps as freely as erroneous ones. We propose Manifold-Guided Attention Steering (MAGS), a trajectory-aware inference-time intervention grounded in a geometric observation: the output activations of specific attention heads diverge from a low-dimensional correctness manifold at the point of error, and this deviation compounds through subsequent steps. For each identified attention head, we learn a low-dimensional subspace from contrastive pairs of correct and incorrect traces that capture the directions along which error behavior deviates from correct behavior. During inference, we monitor each head's proximity to this manifold and apply a targeted projection correction when deviation exceeds a learned threshold, steering the attention output back toward the correct subspace before the error propagates. MAGS consistently outperforms both unsteered baselines and static steering approaches across benchmarks spanning mathematical reasoning (MATH-500, GSM8K), code generation (HumanEval, MBPP), and molecular generation (SMILES), suggesting that correctness manifolds are a general feature of LLM attention geometry.

Although LLMs have made substantial progress in reasoning, systematically producing frontier-level reasoning data remains difficult. Existing synthesis methods often have limited visibility into the structural factors that govern problem difficulty, which can result in narrow diversity and unstable difficulty control. In this work, we view the difficulty of a reasoning problem as arising from the accumulation of atomic knowledge-reasoning transformations, which we term thought modes. Building on this perspective, we propose MindLoom, a framework for synthesizing frontier-level reasoning data through compositional thought mode engineering. Given a collection of hard problems with verified solutions, MindLoom first decomposes those solutions into thought mode chains that reveal each problem's construction logic. It then trains a retrieval model that matches problem states to compatible thought modes, providing guidance on which reasoning challenges to introduce during synthesis. New problems are composed by iteratively applying retrieved thought modes to seed questions, with distribution-aligned sampling to encourage diverse reasoning coverage. Finally, a rollout-based judging stage labels generated questions by difficulty and supplies judged-correct responses for supervised fine-tuning. We evaluate MindLoom on nine benchmarks covering five STEM disciplines and four mathematical reasoning tasks across multiple model families and sizes. Models fine-tuned on MindLoom-generated data achieves favorable performances over base models, distillation, and external-data baselines across the reported benchmarks. Ablation studies indicate the contribution of each component, and further analysis suggests that MindLoom covers a broad range of reasoning patterns while maintaining useful difficulty control. We have open-sourced our implementation at https://github.com/EachSheep/MindLoom.

Scaling test-time compute by iteratively updating a latent state has emerged as a powerful paradigm for reasoning. Yet the internal mechanisms that enable these iterative models to generalize beyond memorized patterns remain unclear. We hypothesize that generalizable reasoning arises from learning task-conditioned attractors: latent dynamical systems whose stable fixed points correspond to valid solutions. We formalize this process through Equilibrium Reasoners (EqR), which enable test-time scaling without external verifiers or task-specific priors. EqR scales internal dynamics along two axes: depth, by running more iterations, and breadth, by aggregating stochastic trajectories from multiple initializations. Empirically, gains from test-time scaling are tightly coupled with stronger convergence toward solution-aligned attractors. This attractor perspective allows neural networks to adaptively allocate test-time compute based on task difficulty. While simple cases converge within 1 to 5 iteration steps, harder cases benefit from massive test-time scaling. By unrolling up to the equivalent of 40,000 layers, scalable latent reasoning boosts accuracy from 2.6% for feedforward models to over 99% on Sudoku-Extreme. These results suggest that learned attractor landscapes provide a useful mechanistic lens for understanding scalable reasoning in iterative latent models.

Can post-trained large language models (LLMs) further improve themselves using only unlabeled prompts, without external teachers or feedback from tools? We study this setting starting only from unlabeled seed questions with no ground-truth solutions, across three reasoning domains: math, science, and coding. We propose Self-Verified Distillation, a simple post-training refinement algorithm in which the model generates candidate solutions to these seed questions, filters them using prompt-based self-verification, and trains on the resulting self-curated dataset. Inspired by the UQ benchmark's use of multiple validators to screen candidate answers to hard unsolved questions, we adapt this validation-based filtering idea to self-training: the model filters its own generated solutions through a three-stage cascade of cycle-consistency, factuality, and correctness checks, accepting a solution only if it passes all stages with unanimous judge votes. We find that sampling more candidate generations and using a larger verification budget during training data construction produces higher-quality self-curated data and, in turn, better reasoning models. We then train Qwen3 models at multiple scales with Self-Verified Distillation and obtain gains across all three domains. For Qwen3-4B, our method improves aggregate held-out pass@1 by +16.7 points in math (AIME26 and HMMT), +11.1 points in science (GPQA Diamond and HLE), and +8.3 points in coding (LCBv5 and LCBv6), with gains also extending to 0.6B and 8B models. Compared to our test-time-only baseline (UQ-TTC), which improves performance by spending extra compute at inference time, Self-Verified Distillation achieves better performance in most settings while requiring only a single inference call at test time.

Humans effortlessly go beyond literal meanings: If you mow the lawn, I will give you fifty dollars, is typically understood as implying that the speaker will pay only if the lawn is mowed, whereas If you are hungry, there is pizza in the oven implies that pizza is available regardless of the hearers hunger. Large Language Models - LLMs - show human-like performance on many tasks, yet it remains unclear whether they reason like humans. To address this, we conducted a population-matching experiment assessing how twentyfive LLMs compute conditional inferences across four languages, compared to an equal number of humans per language. We find that humans enrich logical reasoning through pragmatic inferences across languages. Model behavior is more variable. Some LLMs perfectly follow the truth-table of conditionals but they ignore pragmatic inferences, while others deviate from the truth-table, adhering to a single interpretation across the board, thus reflecting accurate rule-based processing but not human-like reasoning. Overall, LLMs are accurate semantic operators, but fail to capture the pragmatic enrichments characteristic of human reasoning. Crucially, LLM accuracy is neither predicted nor boosted by open vs. closed status, training orientation, or architecture type, suggesting that pragmatic reasoning is still an emerging ability in the cognitive toolkit of artificial systems.

We develop a learning-theoretic framework for understanding Chain of Thought (CoT). We model CoT as the interaction between an answer map and a chain rule that generates intermediate questions autoregressively, and define the reasoning risk of a hypothesis under this interaction. Our first result is a tight canonical decomposition of this risk into two terms with opposing roles: an oracle-trajectory risk (OTR), which captures the benefit of CoT and reduces to a target-domain risk in a domain adaptation problem, and a trajectory-mismatch risk (TMR), which captures the cost of CoT through error accumulation along mismatched reasoning trajectories. We then show that this cost is unavoidable without structure: if any one of the loss, the hypothesis answer map, or the chain rule lacks stability, the TMR can be arbitrarily large even when the OTR is zero and the hypothesis is uniformly close to the ground truth. Conversely, under stability, we prove a tight upper bound on the TMR governed by an exact amplification factor that identifies bounded, linear, and exponential error-growth regimes. Together, these results give a precise theory of when CoT helps, when it hurts, and what controls the transition between the two.

Reinforcement learning with verifiable rewards (RLVR) has become an effective paradigm for improving reasoning language models on tasks such as mathematics, coding, and scientific question answering. However, widely used group-relative objectives, such as GRPO, summarize each sampled group with scalar statistics and therefore discard fine-grained relational information among candidate responses. This weakens credit assignment under sparse outcome rewards, especially when multiple generated solutions differ only subtly in reasoning quality. We propose \textbf{LamPO}, a \textbf{Lambda-Style Policy Optimization} method that replaces scalar group advantages with a \emph{Pairwise Decomposed Advantage}. LamPO aggregates pairwise reward gaps within each response group and modulates each comparison by a confidence-aware weight computed from sequence log-probability differences, while retaining the critic-free and clipped-update structure of PPO-style optimization. When reference solutions are available, we further add a lightweight ROUGE-L-based dense auxiliary reward to reduce reward sparsity. Experiments on AIME24, AIME25, MATH-500, and GPQA-Diamond with Qwen3-1.7B, Qwen3-4B, and Phi-4-mini show that LamPO consistently improves over GRPO and recent RLVR variants, with more stable training dynamics and better sample efficiency.

Explicit reasoning models are trained to produce intermediate reasoning traces before final answers, but downstream fine-tuning is often performed on ordinary instruction-response data that contains no such traces. We show that this mismatch can induce reasoning-trace collapse: a fine-tuned model continues to produce plausible final answers while losing the structurally valid explicit reasoning traces that made it a reasoning model in the first place. We introduce a structural evaluation framework that separates answer correctness from reasoning-trace validity, measuring valid, empty, missing, and truncated reasoning alongside reasoning-conditioned task performance. Using this framework, we study four open-weight reasoning models and find that standard supervised fine-tuning can rapidly suppress valid reasoning traces, and that answer-only metrics can substantially obscure this failure: in several settings, performance conditional on valid reasoning remains high while the rate of valid reasoning falls sharply. We further show that simple loss-masking strategies can substantially mitigate collapse without requiring teacher-generated reasoning traces. These results suggest that evaluations of fine-tuned reasoning models should report structural reasoning reliability metrics in addition to final-answer performance, especially when adaptation data does not contain explicit reasoning traces.

Vision-language models solve geometry problems with rising accuracy, yet their intermediate states remain latent and unverifiable: a relation expressed in textual reasoning or drawing code carries no guarantee that a constraint-satisfying configuration realizes it. We observe that existing externalization methods based on rendered pixels or one-shot scripts fail to provide exact, per-action geometric guarantees. Enforcing geometric relations by algebraic definition closes this gap: the workspace becomes a constraint-checked evolving canvas. We present Draw2Think, a framework that recasts geometric reasoning from latent spatial inference into agentic interaction with the GeoGebra constraint engine. In a Propose-Draw-Verify loop, Draw2Think externalizes hypotheses onto an executable canvas, measures exact geometric quantities, and feeds structured observations back to the model, so subsequent reasoning proceeds from checked canvas state grounded by the shared workspace. This externalization makes two properties separately auditable: model-level Construction Fidelity (whether the canvas realizes the intended configuration) and engine-level Measurement Faithfulness (exact values and relations from canvas constraints). Across construction, outcome, and rendering evaluations, Draw2Think builds canvases that pass 95.9% predicate-level and 84.0% strict problem-level construction checks on GeoGoal, improves outcome accuracy by up to 4.1%/16.4% on planar/solid benchmarks, and attains 68.2%/90.5% strict/relaxed rendering scores on GenExam-math. Project page is available at https://draw2think.github.io/

Reinforcement learning improves LLM reasoning, but PPO/GRPO typically use fixed clipping and decoding temperature, which makes training brittle and tuning-heavy. We propose Adaptive Group Policy Optimization (AGPO), a critic-free refinement of GRPO that uses group-level statistics to control both update magnitude and exploration. AGPO uses a shared probe-derived statistical state to drive two controllers: (i) adaptive clipping, which sets the trust-region size from reward dispersion and skewness, probe vote entropy, policy entropy, and step-wise KL drift; and (ii) bidirectional adaptive temperature sampling, which heats or cools decoding around a base temperature according to centered uncertainty relative to a running baseline. On nine English and Chinese math/STEM benchmarks, Qwen2.5-14B trained with AGPO outperforms PPO/GRPO under the same generated-token budget, reaching 67.3% on GSM8K and 40.5% on MATH. Gains transfer to Llama-3-8B and Gemma-2-9B, and ablations confirm both modules are complementary. Our implementation is publicly available at https://github.com/wandugu/paper_agpo.

Chain-of-thought (CoT) reasoning has become the default strategy for enhancing LLM capabilities, yet its application raises a fundamental question: when is explicit reasoning actually beneficial? Empirical evidence reveals a striking paradox: CoT often provides marginal or even negative gains on factual and open-ended tasks while multiplying token consumption. In this work, we show that LLM reasoning is not a static property of tasks or models, but a \emph{dynamic decoding state} that emerges during generation. Through systematic analysis, we find early-stage entropy dynamics provide a reliable signal of this state: tasks benefiting from CoT exhibit consistent entropy reduction, while others display unstable or increasing patterns. This behavior can be interpreted as a phase-transition-like shift from a high-entropy exploratory regime to a low-entropy structured reasoning regime. Based on these insights, we propose \textbf{EDRM} (Entropy Dynamics-based Reasoning Manifold), a lightweight and training-free routing framework that leverages early decoding entropy to adaptively select inference strategies. EDRM embeds entropy trajectories into a compact and interpretable manifold representation, enabling both zero-shot deployment and fine-grained instance-level adaptation. Across 15 benchmarks and 4 LLMs of varying scales and architectures, EDRM consistently outperforms static baselines. At the dataset level, EDRM achieves \textbf{41--55%} token reduction while improving accuracy with as few as 50 calibration samples. At the instance level, it further improves accuracy by up to \textbf{4.7%} while maintaining \textbf{27--45%} token savings. These results suggest that reasoning should be invoked selectively rather than by default, and demonstrate the effectiveness of entropy-driven decoding control for efficient and adaptive LLM inference.

Neural networks can be trained to rank the choices made by logical reasoners, resulting in more efficient searches for answers. A key step in this process is creating useful embeddings, i.e., numeric representations of logical statements. This paper introduces and evaluates several approaches to creating embeddings that result in better downstream results. We train embeddings using triplet loss, which requires examples consisting of an anchor, a positive example, and a negative example. We introduce three ideas: generating anchors that are more likely to have repeated terms, generating positive and negative examples in a way that ensures a good balance between easy, medium, and hard examples, and periodically emphasizing the hardest examples during training. We conduct several experiments to evaluate this approach, including a comparison of different embeddings across different knowledge bases, in an attempt to identify what characteristics make an embedding well-suited to a particular reasoning task.