LLM Reasoning

LLM: Large Language Model

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68 papers in the last four weeks, up 143% on the four weeks before. 0.7% of all new papers.

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Latest papers 654

Oct 8, 2026cs.AI

Looking Inside LLMs: Small-World Connectivity as a Signature of Reasoning Performance

Understanding large language model (LLM) reasoning requires looking beyond behavioral performance to examine how reasoning ability is reflected in internal organization. Inspired by neuroscience findings linking higher intelligence to stronger small-world organization in functional brain networks, we investigate small-world connectivity as a structural signature of LLM reasoning. We construct functional graphs from attention-head activation similarities and find that a higher small-world index (SWI), capturing local clustering and short global paths, consistently correlates with better fluid reasoning performance across models and training checkpoints. Since local clustering is central to small-world organization, we further examine how heads important for model performance connect within and across communities. We find that these heads tend to have a larger share of connection weight within their own communities (high core scores) and a more concentrated weight distribution across communities (low bridge scores). These observations motivate the hypothesis that high core and low bridge scores serve as structural indicators of head importance for reasoning capability. We validate this hypothesis through pruning, introducing Small-World Allocation (SWA), a hierarchical sparsity allocation method guided by these scores. Across six LLMs, SWA better preserves small-world organization and model performance than competing allocation strategies, reducing WikiText perplexity by up to 20%. Together, these findings identify small-world functional connectivity as a measurable signature of LLM reasoning performance, offering a structural perspective that complements behavioral evaluation.

Zheng Huang, Sansheng Cao, Enpei Zhang +7

Dartmouth College · Yale University · New York University +2

LLM Reasoning LLM Interpretability LLM Pruning Attention Head Pruning

Oct 8, 2026cs.CL

Probing for Long-Horizon Deductive Reasoning Capabilities in Language Models with Prolog

Current frontier LLMs can theoretically process long contexts with 1M tokens or more. But to what extent can they go beyond simple retrieval and perform deeper reasoning over such long contexts? We empirically investigate long-horizon reasoning capabilities of LLMs, focusing on deductive logic expressed in Prolog. We construct ProloNg, a synthetic testbed to probe Prolog Long Reasoning, which systematically varies the complexity (reasoning depth) of problems, where the hardest case has a reasoning depth of 22 and 62k context length. We study 8 reasoning models across 5 families of frontier LLMs, and find that performance degrades substantially as reasoning depth grows, with the majority of models approaching chance beyond depth 10.

Hadeel Al-Negheimish, Jasna Ilieva, Yoon Kim

King Saud University · Massachusetts Institute of Technology

LLM Reasoning Long-Context Language Model Inference Language Model Probing Logic Programming

Oct 8, 2026cs.AI

Safe, Persistent, and Evolving Agent Harness for Understanding Partially Observable Worlds

Large language model agents can invoke tools fluently, but enterprise workflows demand more than selecting the right tools: actions must strictly comply with organizational policies, tool feedback often conceals hidden side effects under partial observability, and long-horizon tasks require persistent state tracking across multiple records. To address these challenges, we introduce E-Ledger, a multi-agent harness for safe and persistent execution. E-Ledger employs a code approval layer that checks every proposed action against policy before execution, and maintains a world ledger of verified hidden rules alongside evidence-backed dynamic state. Because hidden rules are typically unknown a priori, we further propose WorldAbduct, an abductive, world-model-driven harness evolution framework. WorldAbduct diagnoses execution trajectories across four complementary views (state consistency, world-observation gap, policy-gate correctness, and goal judgment) to hypothesize latent rules, and verifies them through targeted abductive interactions before integrating them into the ledger. On the enterprise benchmark World of Workflows, E-Ledger with WorldAbduct improves safe task completion across four LLM backbones, outperforming the strongest evolution baseline by 5--15 percentage points. Experiments in ScienceWorld and DiscoveryWorld further show that abductive harness evolution carries over to scientific environments. Our code is available at https://github.com/HKUST-KnowComp/E-LEDGER-WorldAbduct.

Yisen Gao, Yue Guo, Qing Zong +2

The Hong Kong University of Science and Technology · LIGHTSPEED · Independent Researcher

LLM Agent Harnesses LLM Agent Safety Runtime Enforcement for AI Agents Long-Horizon LLM Agents LLM Reasoning

Oct 8, 2026cs.AI

SynCo: Data Synthesis Co-Training for Self-Evolving LLMs via Multi-Agent Reinforcement Learning

Self-evolving LLM agents promise to improve autonomously through continual interaction and learning, reducing their dependence on manually curated supervision. Realizing this promise requires not only updating the agent, but also evolving its training experience as its capabilities change. However, most existing pipelines rely on static datasets or separately updated synthesis models, causing previously useful tasks to become trivial while overly difficult tasks remain uninformative. This growing mismatch between agent capability and training experience limits sustained self-improvement. To address this problem, we propose SynCo, an agentic data synthesis co-training framework for self-evolving LLMs based on multi-agent reinforcement learning. SynCo jointly optimizes two independently parameterized agents: a Synthesizer that constructs training tasks from the Reasoner's evolving capability state, and a Reasoner that learns from the resulting experience. Each synthesized task induces multiple Reasoner rollouts whose outcomes provide complementary rewards to both agents. Correctness feedback improves the Reasoner, while task quality, answer reliability, and outcome-grounded teachability guide the Synthesizer. Their updates are fed back into subsequent synthesis rounds, allowing the task-solving policy and its training distribution to evolve together. Extensive experiments across eight mathematical reasoning benchmarks demonstrate that SynCo substantially outperforms a broad range of existing synthetic-data methods and controlled baselines, achieving the strongest overall performance while deriving most of its gains from previously unsolved problems.

Wei Yang, Shawn Li, Yuehan Qin +8

University of Southern California · The George Washington University · Georgia Institute of Technology

Self-Evolving Agents Synthetic Data Generation for Language Models LLM Reasoning RL for Language Model Reasoning

Oct 8, 2026cs.CL

ReCal: Calibrating Structured Pruning for On-Policy Distillation Recovery

Structured pruning reduces the deployment cost of reasoning language models, but the resulting capability degradation can hinder subsequent on-policy distillation (OPD) recovery. Because OPD relies on student-generated trajectories, pruning damage that persists after offline distillation can limit its effectiveness. We propose RECAL, Recovery-Aware Calibration, a simple plug-and-play approach that improves OPD recovery by adjusting calibration before pruning. RECAL uses forward KL between an unpruned teacher and a pruned probe to identify teacher-supported predictions disrupted by pruning, then reweights calibration statistics to guide existing pruning criteria toward preserving these predictions. Across multiple models and pruning methods, RECAL consistently improves mathematical reasoning after OPD, achieving gains of up to 16.7 percentage points on AIME, alongside improvements in most code-generation comparisons. Further analysis shows that RECAL reduces residual damage at heavily affected tokens and establishes performance advantages that persist through recovery. These results demonstrate the value of recovery-aware calibration for improving on-policy distillation recovery of pruned reasoning models.

Houcheng Jiang, Mao Zheng, Mingyang Song +4

Zhongguancun Academy · Foundation Model Department, Tencent · University of Science and Technology of China +1

LLM Pruning LLM Reasoning Language Model Calibration On-Policy Distillation

Oct 8, 2026cs.AI

Balancing Reference Guidance and Free Generation in Trajectory Rollouts for Reasoning RL

A verified reference solution provides a correct trajectory for training a reasoning model. Alternatively, a prefix of the reference can guide the model in generating a trajectory of its own. How much reference guidance should we provide? We study this question through prefix continuation, where the model continues from a reference prefix and keeps the resulting trajectory if it passes verification, falling back to the reference otherwise. Since both procedures produce correct trajectories, we compare their distributions with the ideal distribution, the model's own distribution conditioned on successful verification. For one continuation, we derive the KL divergence in closed form, which, up to a bounded term, decreases with the product of the probability of generating a different correct trajectory and the reference surprisal, the negative log probability of the reference suffix given the prefix. Since a longer prefix tends to raise the former but lowers the latter, continuation success alone does not determine the preferred amount of guidance. From this analysis, we learn a prefix selector shared across training questions from continuation outcomes, without estimating success probabilities or additional generation. The resulting Adaptive Reference Guidance (ARG) constructs correct trajectories within a fixed generation budget, and we apply it to all-failure groups in Group Relative Policy Optimization (GRPO). Experiments on Qwen3-4B and Qwen3-8B across five mathematical reasoning benchmarks show that ARG achieves the highest aggregate pass@12 among the evaluated methods with competitive average sampled accuracy.

Hanyu Wang, Nakul Agarwal, Hossein Nourkhiz Mahjoub +4

The Pennsylvania State University · Honda Research Institute USA · Honda Research Institute Japan

LLM Reasoning RL for Language Model Reasoning Text Generation Conditional Generation

Oct 7, 2026cs.LG

SemanticFold: Latent Sequence Compression SeparatesLanguage Modeling, Decodability, and Reasoning

We study whether latent sequence compression of prompt prefixes preserves the capabilities that large language models rely on during inference. We introduce SemanticFold, a compression scheme that folds prefix hidden states at learned boundaries, and evaluate it across five model scales: Qwen3-1.7B, Qwen3-8B, SmolLM2-1.7B, Pythia-1.4B, and Pythia-6.9B. We use a fixed-target protocol: a frozen prefix is executed natively or compressed, and both arms teacher-force identical continuation tokens. This design rules out target-selection explanations for likelihood changes. We examine five endpoint families: fixed-target negative log-likelihood, finite-label reasoning accuracy, linear probe accessibility, open-ended generation, and systems-level memory and latency. We find that compression moves these endpoints non-monotonically and that they do not share a single compression threshold. On Qwen3-1.7B at compression ratio R=1.7, compressed-minus-native mean NLL decreases by 0.135 under paired bootstrap with 10000 draws. On SmolLM2 at R=1.2, the mean change is 0.013 higher than native. On both Pythia checkpoints, NLL is effectively unchanged. An NLL decomposition separating sequence shortening from the learned residual transform shows that the favorable Qwen likelihood is attributable primarily to residual adaptation rather than to shortening alone. MLP-only, which applies the transform without shortening, achieves 0.082 lower NLL than Full SemanticFold. Linear probe accuracy and macro AUC change by less than 0.03 in absolute value across conditions, with confidence intervals crossing zero. We conclude that preservation under latent compression has no single scalar certificate: language-model fit, decodability, and reasoning behavior answer different questions and can move in different directions under the same compression operation.

Mingyan Liu, Min Huang

LLM Compression LLM Inference LLM Reasoning

Oct 7, 2026cs.CL

SAPD: Step-Aligned Privileged Distillation

On-policy post-training can improve large language models by learning from their own trajectories, but requires costly rollout generation. We ask whether fixed demonstrations can support competitive off-policy learning through better supervision. Our premise is that their usefulness depends not only on the training trajectories, but also on whether supervision provides informative preferences among continuations and connects this guidance to the reasoning decision being learned. We introduce Step-Aligned Privileged Distillation (SAPD), a rollout-free self-distillation method that turns demonstrations into step-aligned distributional supervision. Its key insight is to use the known progression of a reference solution to associate each reasoning transition with targeted privileged guidance, rather than treating the solution as undifferentiated context. On mathematical reasoning benchmarks, SAPD outperforms supervised fine-tuning and label smoothing on average while remaining competitive with on-policy reinforcement learning and self-distillation. Analyses support both the value of context-dependent distributional guidance and the benefit of aligning privileged information with the current step. SAPD also largely preserves out-of-domain coding performance and achieves approximately 2x training-loop speedups over the on-policy baselines. These findings suggest that carefully constructed supervision can make fully off-policy post-training a competitive and computationally efficient alternative. Our code is available at https://github.com/Miaow-Lab/SAPD.

Tianle Wang, Jiayu Liu, Ruizhi Zhao +1

Department of Data Science, City University of Hong Kong · Hong Kong Institute of AI for Science, City University of Hong Kong · Shenzhen University

LLM Post-Training Language Model Distillation Knowledge Distillation LLM Reasoning Self-Distillation

Oct 7, 2026cs.CL

Which Language Should a Skeleton Speak? Language Choices in Multilingual Reasoning

Skeleton-based reasoning prompting is a promising training-free approach for structuring LLM reasoning, but prior work largely assumes an English-centric setting. We propose the Language-Aware Skeleton Exploration Framework (LASEF) to study skeleton-language choice in multilingual mathematical reasoning. Across math benchmarks, model scales, and languages, we show that English skeletons yield a small positive tendency on average, most visible for smaller models and low-resource languages. However, few language-level gains remain significant after correction, and English is not universally optimal. Combining greedy decoding, multi-rollout evaluation, translation ablation, and cross-benchmark validation, we further find three patterns of skeleton-language effects: directionally consistent, evaluation- and benchmark-dependent, and asymmetric negative. These effects cannot be fully explained by generation quality alone. Overall, skeleton language is a context-dependent design variable that requires multi-level exploration. All resources are released at https://github.com/lhsstn/LASEF.

HyeonSeok Lim, SeungWoo Song, Inho Won +3

ETRI · KAIST · Department of Artificial Intelligence, Dankook University

LLM Reasoning Cross-Lingual Reasoning in Language Models Multilingual Language Model Evaluation

Oct 7, 2026cs.LG

Collaborative Reasoning Distillation via Cross-Feedback and Coherent Curation

Reasoning capabilities are critical for advancing Large Language Models, yet current approaches either require massive computational budgets or struggle to effectively distill reasoning to smaller models. Standard distillation methods rely on outcome-based rewards, failing to distinguish between sound reasoning and lucky guesses. We propose Collaborative Reasoning Distillation (CRD), a framework that enhances reasoning in compact models through three innovations: (1) interactive cross-feedback where teachers iteratively critique each other's reasoning, (2) fine-grained step-wise quality assessment capturing logical validity independent of final answers, and (3) coherence-aware step stitching that synthesizes complementary strengths. Students are trained via Reasoning Quality Optimization (RQO) with budget constraints. Our model, CRD-4B, achieves 97.3% on MATH-500 and 70.3% on AIME'25, surpassing baselines while using only 50K training examples, up to 12 times smaller than the datasets of comparable models.

Taehoon Kim, Seunggeun Cho, Dongsu Han

KAIST

Reasoning Distillation LLM Reasoning Multi-Teacher Knowledge Distillation Process Supervision

Oct 6, 2026cs.LG

The Dichotomy Between Pattern Recognition and Step-by-Step Reasoning

We argue that pattern recognition and step-by-step reasoning are two ends of a spectrum. A large language model (LLM) learns to reason step-by-step when data is structured such that the next token depends on a small amount of preceding context. Inference in LLMs resembles pattern recognition when the next token depends on a large amount of preceding context. If the next token depends on only the

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most recent tokens, reasoning traces are paths on a De Bruijn graph whose nodes are

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-length contexts and edges are next-token transitions between contexts. The set of reasoning traces of a task forms a directed acyclic subgraph of the De Bruijn graph. An LLM that has learned all edges of this subgraph can compose them to solve longer, unseen tasks, i.e., it reasons step-by-step. We prove that the number of edges is vanishingly small compared to the number of reasoning traces. Empirically, the number of training samples a transformer needs is a power law in the number of edges, so learning to reason step-by-step is sample efficient. We can induce De Bruijn structure in any task by maintaining a ``state'' that makes future reasoning independent of the past. The frequency of states in the reasoning trace determines

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. We show, by fine-tuning Qwen2.5-1.5B-Instruct to solve equations and answer questions about stories, that frequent states (small

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) result in higher accuracy but greater fragility to perturbations at test time. LLMs trained with a large

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are only as good as models that perform pattern recognition without reasoning. A moderate density of states balances accuracy and robustness. We show that real-world data has De Bruijn structure: Qwen3-14B and Qwen3-32B retain over 75% of their accuracy on GSM8K, MATH-500 and GPQA-Diamond when attention is restricted to a sliding window less than 15% as long as the full reasoning trace.

Amrut Nadgir, Pratik Chaudhari, Vijay Balasubramanian

University of Pennsylvania

LLM Reasoning Efficient Language Model Reasoning Neural Algorithmic Reasoning LLM Reasoning with Graphs Language Model Robustness

Oct 6, 2026cs.AI

ThinkFuse: Trajectory-Aware Test-Time Fusion for Small Reasoning Models

Small reasoning models (SRMs) have shown strong performance on complex reasoning tasks by generating extended chain-of-thought trajectories, but they often fail to recover once their reasoning enters an erroneous path. Existing test-time fusion methods rely on local fusion signals to determine when to trigger fusion, which can be misled by transient uncertainty fluctuations and may reinforce unstable reasoning trajectories. We propose ThinkFuse, a training-free test-time fusion framework that selectively intervenes in unreliable reasoning segments. ThinkFuse compares segment-level uncertainty shifts with trajectory-level uncertainty trends to identify unstable reasoning points and fuse auxiliary reasoning paths into the primary model's trajectory. Extensive experiments demonstrate that ThinkFuse outperforms baselines on mathematical and knowledge-intensive reasoning benchmarks, with consistent gains across model-family combinations, and remains robust with a smaller primary model. Our analysis shows that ThinkFuse requires fewer fusion triggers and generates fewer tokens, highlighting the efficiency of selective triggering. Our code is available at https://github.com/js-lee-AI/ThinkFuse.

Myunghoon Kang, Jungseob Lee, Jaehyung Seo +1

Department of Computer Science and Engineering, Korea University · Department of Computer Science and Engineering, Konkuk University · Human-inspired AI Research

Efficient Language Model Reasoning LLM Reasoning

Oct 5, 2026cs.CL

Can Language Models Learn to Reject Their Own Bad Reasoning Steps?

Verifier-guided decoding can prevent harmful reasoning steps from contaminating subsequent generation, but typically relies on an external learned verifier. We ask whether a language model can instead reject its own bad reasoning steps. We define a prefix's recoverability as the probability that the frozen generator can complete it correctly. Diagnostics show that adjacent recoverability changes are often difficult to resolve with practical Monte Carlo budgets, while same-prefix candidates exhibit a sparse low-recoverability tail. We introduce Self-Step Rejection (SSR), which trains a lightweight LoRA acceptance gate on the generator backbone while keeping the base model frozen. SSR uses confidence-qualified first-passage supervision: steps before the first resolved crossing of a root-relative recoverability barrier are accepted, the crossing step is rejected, and unresolved steps and suffixes are excluded. Training combines pointwise classification, same-prefix pairwise learning, and group-relative policy refinement using final-answer correctness. At inference, SSR accepts candidates or resamples from the unchanged prefix under rejection budgets, without an external learned verifier. Across three reasoning models and five mathematical reasoning benchmarks, SSR improves macro-average accuracy over single-pass decoding by 5.4--10.1 points using 1.21--1.40x as many generated tokens, and achieves the highest macro-average accuracy among evaluated step-level methods. Full-solution scaling methods require 4.47--8.27x the single-pass token cost for comparable performance.

Siheng Xiong, Xiaoze Liu, Yiqiao Jin +2

Georgia Institute of Technology · Purdue University

LLM Self-Correction Language Model Decoding Efficient Language Model Reasoning LLM Reasoning Reasoning Verification

Oct 4, 2026cs.LG

Expanding LLM Reasoning

Extra inference compute is usually spent on sampling more reasoning chains. We study where inside an existing chain an additional continuation should begin. We define expansion utility, the change in correctness from restarting a chain at a stored step, and measure it at every eligible step for nine models on six benchmarks (41 model and benchmark cells). Restart position matters: steps selected on one set of continuations beat uniform placement when scored on disjoint ones, in held-out audits on 5, 16, and 38 cells (+4.25 points [+2.51, +6.63] in a fresh five-cell audit). A fixed rule that restarts from the last eligible steps, always-last, is a strong baseline: our learned router beats uniform placement but shows no detected gain over it, and on DeepSeek-R1-Distill-Qwen-14B/MATH-500 always-last exceeds the exact self-consistency frontier at matched aggregate generated output by +0.052 [+0.008, +0.098], using 0.774x the aggregate generated output of four-sample self-consistency. Cross-fitted oracle selection still finds held-out headroom beyond declared positional classes, a target for future selectors. Finally, breaking step-label ties by earliest index flips the sign of a pointwise selector's gain over uniform placement in every seed of a five-seed diagnostic with four rollouts per step; randomized ties remove the bias.

Rian Atri, Evan Luo

Keiji AI · University of California, Berkeley

LLM Inference Efficiency Inference-Time Scaling Efficient Language Model Reasoning Inference-Time Compute Allocation LLM Reasoning

Oct 4, 2026cs.AI

Safe Context Switching for Agents in the Wild: Mitigating Subspace Interference via Orthogonal Adaptation

Most Large Language Models exhibit a fundamental tension between two sequential tasks, such as logical reasoning and safety alignment. The high-variance internal states required for sophisticated Chain-of-Thought (CoT) deduction can geometrically interfere with latent representations encoding safety constraints. We identify this phenomenon as Sequential Subspace Interference, showing that standard fine-tuning on logical tasks such as multi-step mathematics and code generation can result in a 23.3% interference penalty on alignment benchmarks, substantially weakening the model's safety priors. This Reasoning Drift is not adequately captured by current adaptation methods because gradients for logical tasks are rarely orthogonal to safety objectives. To address this issue, we propose AURA (Adaptive Unique Residual Allocation), a spectral regularization framework that enforces Spectral Independence between reasoning and safety. By explicitly estimating the null space of the alignment manifold and constraining reasoning updates to its orthogonal complement, AURA enables models to improve logical reasoning without compromising safety. Empirically, AURA recovers 23.0% of the lost performance while preserving greater than 0.98 cosine fidelity to the safe state, demonstrating that reasoning and alignment can be effectively decoupled through geometric regularization.

Akash Das, Ishan Roy

Fidelity Investments

LLM Safety Alignment LLM Safety LLM Reasoning

Oct 1, 2026cs.CL

ReHoPER: Receding-Horizon Planning for Enhanced Reasoning

We propose ReHoPER, an inference-only, zero-shot method that improves large language models' reasoning by generating and answering intermediate questions along multiple paths before the final answer. It iteratively plans a horizon of candidate intermediate questions, selects one to answer, and replans from the updated history. ReHoPER is task-agnostic, using the same generic instructions across datasets and models without labeled data or task-specific prompt design. Across multiple datasets, including iLLC, a new controlled benchmark for compositional reasoning, ReHoPER outperforms strong baselines, with the largest gains in the most compositional settings. Our implementation and the iLLC generator are publicly available to support future work.

Saeed Ahmadnia, Cornelia Caragea

Department of Computer Science University of Illinois Chicago

Compositional Reasoning Sequential Decision Making LLM Reasoning

Sep 30, 2026cs.CL

Reason in Style: Discovering and Controlling Style in Language Models

Language models learn content and style jointly, making stylistic variation in their outputs difficult to identify and control. We study whether recurring styles in model responses can be discovered without supervision and explicitly controlled. We design an algorithm that learns to separate representations of content and style from language models' outputs and validate its effectiveness on math questions in a controlled setting. By applying this method to over 100K verified traces from nine distinct teacher models, we discover six recurring yet imbalanced styles. We then fine-tune smaller student models to follow these styles when explicitly conditioned on them, using importance weighting to balance the contribution of the styles represented in the corpus. This approach improves Pass@

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over standard fine-tuning on the same data across six math reasoning benchmarks, demonstrating that we can diversify the style of answers effectively. We confirm that this also results in strong correspondence between requested and realized styles. We find that style affects correctness: the probability of solving a problem depends on the style we condition on, and different problems benefit from different styles. In summary, our results show that stylistic variation in model-generated data can be discovered in an unsupervised way, and made explicit, providing a source of both control and improved reasoning performance.

Ioana Marinescu, Eric Karl Oermann, Kyunghyun Cho

NYU · NYU & NYU Langone Health

Unsupervised Learning Language Model Steering Representation Disentanglement LLM Reasoning

Sep 30, 2026cs.LG

Exploring More, Reasoning Better: Stepwise Risk-Sensitive GRPO for Diffusion Language Models

Diffusion large language models (dLLMs) generate text by denoising a sequence or successive blocks, allowing several tokens to be revealed in parallel. Reinforcement learning with verifiable rewards (RLVR) reuses terminal feedback across these decisions, even as their conditioning context changes. We propose stepwise risk-sensitive GRPO (StepRS-GRPO), which varies the risk coefficient of the group-advantage transformation across denoising states while retaining the underlying trainer. For binary rewards, we show that this transformation is exactly a prompt- and state-dependent rescaling of centered outcome advantages. A capability-based calibration suggests a coefficient scale, while endpoint and interpolation ablations guide schedule selection. Across multiple dLLM backbones and mathematical reasoning benchmarks, StepRS-GRPO improves both pass@1 accuracy and pass@k coverage over centered GRPO, while increasing answer diversity. In our ablation studies, mass-matched controls support the contributions of state allocation and schedule direction, and the gains persist after matching the root mean square (RMS) of the advantages to that of centered GRPO. Reasoning-trace diagnostics further show that the diversity gains from StepRS-GRPO extend beyond final-answer strings.

Yue YU, Bowen Zuo, David Crandall +2

Indiana University · University of California, Riverside

RL for Language Model Reasoning Group Relative Policy Optimization Risk-Sensitive RL RL for Diffusion Models Diffusion Language Models LLM Reasoning

Sep 30, 2026cs.LG

Random Recursive Models

Recursive models create computational depth through parameter reuse, offering a parameter-efficient alternative to increasing model size. However, most recursive models repeatedly apply one learned transformation or a prescribed sequence of transformations, restricting computation to a fixed layer order. We introduce the Random Recursive Model (RRM), which maintains a pool of

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learned layers and performs

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recursive steps by sampling one layer independently with replacement for each example and step. This enables flexible layer reuse while retaining the parameter efficiency of recurrence. We evaluate RRM on challenging reasoning tasks, where it matches or exceeds the baselines, often with 50-75 % fewer parameters. RRM can vary its depth at inference, including beyond that seen during training, without retraining or adding parameters, improving tasks that benefit from deeper iterative computation. RRM also supports Monte Carlo inference and probabilistic test-time scaling, both of which improve performance without retraining. These insights may open new directions in neural network architecture design.

Jama Hussein Mohamud, Mirco Ravanelli

Mila – Quebec AI Institute · Université de Montréal · Concordia University

Efficient Neural Network Inference LLM Reasoning Recursive Language Models

Sep 30, 2026cs.LG

Semifactual Credit-Augmented Policy Optimization

Reinforcement learning with verifiable rewards (RLVR) has improved the reasoning capabilities of large language models (LLMs), yet their predictions remain sensitive to task-irrelevant prompt features. We investigate this sensitivity through semifactual prompt interventions that preserve the underlying problem and its answer. Our analysis reveals substantial variation in token-level sensitivity and shows that suppressing high-drift token candidates during decoding improves reasoning accuracy without updating model weights. These findings highlight a limitation of Group Relative Policy Optimization (GRPO), which assigns the same outcome-derived advantage to every response token and may reinforce potential spurious dependence alongside useful reasoning. Motivated by this observation, we introduce Semifactual Credit-Augmented Policy Optimization (SCAPO), a causally inspired variant of GRPO that incorporates semifactual stability into token-level credit assignment. SCAPO measures token probability drift for fixed responses under semifactual interventions and uses normalized stability scores to reduce advantages for relatively unstable tokens during early training, while granting no additional credit for stability alone. On Qwen3-4B-Base and Qwen3-1.7B-Base, SCAPO improves AIME 2024-2026 accuracy over GRPO by 5.63 and 4.17 percentage points, respectively. At both model scales, SCAPO achieves the best results on most evaluated mathematics benchmarks and all evaluated out-of-distribution benchmarks among the compared methods. These results suggest that semifactual stability provides an effective training signal for improving reasoning and generalization through finer-grained credit assignment in RLVR. The code is available at https://github.com/DtYXs/SCAPO.

Junshu Pan, Zhizhang Fu, Shulin Huang +5

Zhejiang University · Westlake University · Shanghai Innovation Institute +1

Prompt Sensitivity RL for Language Model Reasoning Credit Assignment in RL Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Causal Interventions in Language Models+1

Sep 30, 2026cs.CL

When a Kindergartener Solves Calculus: Measuring Capability Leakage in Role-Prompted Reasoning Models

We investigate the problem of role-capability leakage (RCL), in which a role-prompted reasoning model generates convincing in-role text while continuing to exhibit capabilities on benchmarks that exceed those implied by the assigned role. For example, when a model is prompted to assume the role of a kindergarten student, one might expect its performance on a mathematics benchmark to reflect kindergarten-level ability rather than expert-level proficiency in solving calculus problems. We introduce RoleCapBench, a curriculum-grounded benchmark for evaluating RCL across six educational roles and four assessment levels spanning elementary school through A-level, and use it to evaluate three open-weight reasoning models. We find that although the models can generate stylistically convincing in-role responses, they consistently fail to align their underlying capabilities with their assigned roles. Naive role prompting yields strong role-voice scores of 1.218--1.389 while retaining above-role accuracy of 0.811--0.898. RCL persists across a range of prompting conditions, including prompts that explicitly instruct the model to match the role's capability level. To mitigate this problem, we propose Injection, an inference-time intervention that combines explicit, role-specific capability guidelines with a guiding prefilled response prefix. Injection improves role-capability alignment across models, reducing above-role accuracy by up to 0.562 while preserving in-role accuracy with a marginal drop of less than 0.058 across most models. All artifacts, including scripts and evaluation data, will be released upon acceptance.

Pakhapoom Sarapat, Saksorn Ruangtanusak, Kunat Pipatanakul +1

SCB DataX · Nanyang Technological University

Large Language Model-Based Role-Play Simulation LLM Security LLM Reasoning Large Reasoning Models

Sep 30, 2026cs.AI

OverForge: Reasoning Through Strategies and Tactics Helps Cooperative Lifelong Adaptation

Cooperative language-model agents must coordinate over long horizons and adapt to changing environments and to partners with unfamiliar conventions, yet existing agents map observations to actions without separating persistent coordination strategies from their tactical execution. We introduce OverForge, a training-free hierarchical architecture that separates strategic reasoning over roles and divisions of labour from tactical reasoning over actions within each agent's private, partner-conditioned world model. A metacognitive Prefrontal Cortex Module couples the two levels by forming strategy-action branches, imagining their consequences with a forward model, and committing when confident. In OvercookedV2, OverForge delivers 7 soups in a connected kitchen versus 3 for each flat LLM baseline, retains agreed roles, and adopts roles proposed by unfamiliar partners. Ablations and a fixed-strategy probe show that persistent strategies guide tactical adaptation while each reasoning level contributes to coordination. Memory restarts show that cross-episode partner knowledge supports task performance and partner prediction, linking the hierarchy to continual adaptation.

Oana Madalina Fron, Ojas Shirekar, Chirag Raman

Tapri Lab, Department of Pattern Recognition and Bioinformatics, Delft University of Technology, Delft, The Netherlands

Continual Learning for LLM Agents Multi-Agent LLM Systems Multi-Agent Coordination Long-Horizon LLM Agents LLM Reasoning

Sep 30, 2026cs.LG

Self-Repulsive Sampling for Diffusion Language Models

Sampling several responses and voting over their answers can improve a language model's accuracy, but repeated answers limit the benefit of additional samples. Raising temperature increases diversity at a potential cost to per-sample accuracy. We introduce Self-Repulsion (SR), a sampler for masked diffusion language models that uses peer commitments to diversify the pool. At each penalized denoising step, each path lowers a token's logit according to how many peers have committed that token at the same position. Paths share a batched forward pass and then commit in sequence, so later paths observe choices made earlier in the same step. This coupling requires no training or additional forward or backward pass and can produce distinct paths even at temperature zero. When all paths commit a position together from identical logits, the update exactly maximizes total logit minus a convex duplication cost. On LLaDA-8B-Instruct with ten paths and 128 denoising steps, deterministic SR reaches 80.38% plurality accuracy on GSM8K, compared with 70.17% for the unpenalized greedy decoder. At temperature 0.6 and matched model-evaluation budgets, the count penalty improves over self-consistency by 2.06 percentage points in blocks of 32 and 14.50 under pure diffusion. Experiments on GSM8K, MATH and TruthfulQA show that voting gains arise mainly from higher coverage of correct answers, with gains that vary by benchmark and decoding regime.

Michael Helcig, Martin Jaggi

ETH Zürich · EPFL

Diffusion Language Model Decoding Diverse Text Generation Diffusion Language Models Self-Consistency in Language Models LLM Reasoning

Sep 30, 2026cs.AI

Can Computation from Earlier Problems Help LLMs Solve New Ones?

Large language models often solve independent problems in the same conversation. Can computation from earlier problems help them solve new ones? To answer this question, we first conduct preliminary experiments showing that retained history can raise or lower later-turn accuracy, even within the same domain. To understand these effects, we use controlled replay to isolate internal state changes specific to each problem-history pairing. Across different histories, these changes preserve similar relationships among current problems. To improve reasoning under retained history, we introduce STAIR (Stale-Token Attention for Inter-query Reuse). STAIR captures keys and values from earlier response generation in a fixed bank. It learns to redirect current queries when they read this bank during prompt processing. The base model remains frozen; only 12,288 parameters are trained. Across three Qwen models and four benchmarks, STAIR improves average later-turn accuracy by up to 11.67 percentage points over the unmodified model with history.

Jipei He, Wenhui Tan, Xiaoyi Yu +4

Gaoling School of Artificial Intelligence, Renmin University of China, Beijing, China · University of Modena and Reggio Emilia, Italy

Memory-Augmented Language Models LLM Inference LLM Reasoning

Sep 30, 2026cs.LG

GRPO Training Dynamics for Small Language Models

Group Relative Policy Optimization (GRPO) has emerged as a memory-efficient reinforcement fine-tuning (RFT) technique for reasoning-intensive tasks. How- ever, GRPO training dynamics on small language models (SLMs) remain poorly understood, limiting its reliable adoption and reproducibility in open and resource- constrained environments. In this work, we present a systematic study of GRPO fine-tuning for SLMs ranging from 1.5B to 7B parameters under a practical single- node 8xA100 compute budget. Our study spans multiple model families and reasoning domains, including mathematics, coding, and multiple-choice question answering (MCQ) in science. Across these settings, we analyze how group size affects policy convergence, training stability, and downstream benchmark per- formance. We further characterize tensor-level update dynamics during GRPO training and investigate whether the choice of LoRA target modules and layers can improve the performance of GRPO-tuned models. While our initial GRPO-tuned models outperform their base counterparts on approximately 80% of mathematical benchmark evaluations, they demonstrate limited capability on MCQ and code reasoning tasks. Guided by our mechanistic evaluations, we refined our LoRA and reward-shaping configurations to improve performance in latter domains. These findings provide practical guidance for GRPO training for SLMs.

Rajat Ghosh, Vaishnavi Bhargava, Henry Wong +2

Nutanix

RL for Language Model Reasoning Group Relative Policy Optimization Small Language Models RL Fine-Tuning LLM Reasoning

Sep 29, 2026cs.LO

What Was Said, Not What Was 'Thought': Type-6 Logic for CoT Verification

We introduce Type-6 logic, a variant of dynamic epistemic logic augmented with two operators (uncertainty and recurrence), designed to model the inferential dynamics of contemporary large language model (LLM) chain-of-thought (CoT) reasoning. Type-6 accounts for common LLM reasoning pathologies such as unlicensed revision, enthymemes, loopbacks, and unverifiable/incorrect claims. We propose a verifier based on Type-6 logic that builds a graph out the trace, and checks it against Type-6's axioms and inference rules. We evaluate our framework on LLM-generated CoTs four splits spanning formal and informal reasoning. Our verifier detects structurally unsound reasoning steps that surface-level heuristics miss, and allows for easy visualisation of the model's reasoning process. In our corpus, our verifier shows that derived contradiction is the most common hard-fail category in CoT, and that only about 3% of the propositions of a trace have impact on the final derivation. Ablation studies show that other verification methods (LLMs-as-judges, other neurosymbolic approaches, etc.) cannot be considered interchangeable: for example, agreement between LLMs-as-judges and LINC is

κ\approx 0.034

, and this persists within a method across underlying models. Type-6, however, is the most agreed-with method amongst the ones we tested. We prove our verifier runs on average-case linear time; and release our logic specification and artefacts.

Adrian de Wynter

Microsoft and the University of York

LLM Answer Verification Dynamic Epistemic Logic LLM Reasoning

Sep 29, 2026cs.LG

Privy to the Foil: Recasting Value Estimation with a Self-Privileged Critic for RLVR

Assigning credit to intermediate steps remains a central challenge in training Large Language Models (LLMs) on multi-step reasoning tasks with sparse terminal rewards, and actor-critic methods such as PPO address this by learning value functions to construct token-level advantages. Their effectiveness, however, hinges on reliable value estimation, a difficult task requiring the critic to both assess progress toward a correct solution and anticipate an evolving policy's future behavior; errors in either can compromise credit assignment and destabilize online training. In this paper, we revisit the standard state-only formulation of value estimation and propose

π

PPO, a self-privileged actor-critic framework. By reusing verified same-prompt rollouts as contrastive evidence,

π

PPO helps the critic assess intermediate reasoning against successful and failed attempts, while preserving standard policy optimization and the deployment interface. Experiments show that

π

PPO consistently improves value-estimation quality by a substantial margin and outperforms representative actor-critic and critic-free RLVR baselines on challenging mathematical reasoning benchmarks, while remaining effective even when paired with substantially smaller asymmetric critics.

Kun Liang, Chenming Tang, Clive Bai +5

School of Computer Science, Peking University · National Key Laboratory for Multimedia Information Processing, Peking University · Foundation Model Department, Tencent

Value Function Estimation RL for Language Model Reasoning Credit Assignment in RL Step-Level Credit Assignment in RL Reinforcement Learning with Verifiable Rewards Actor-Critic Methods+1

Sep 29, 2026cs.AI

Solving Without Stopping: On-Policy Distillation at Small Scale

On-policy distillation, where a student learns from a stronger teacher's feedback on its own outputs, is a common way to pass reasoning to smaller models. We analyze what it transfers at small scale, distilling Qwen3-8B into Qwen3 4B, 1.7B and 0.6B students, in thinking mode (reason at length, then end the reasoning and answer) and, for comparison, in non-thinking mode (no separate reasoning phase). Long reasoning needs two abilities, solving a problem and knowing when it is solved, and we find that distillation transfers the first, but in thinking mode not the second. Solving improves at every size, up to two ceilings, which we measure comprehensively across both modes and all student sizes: a student's single attempt never exceeds what it could already reach in many attempts before training, and the smaller the student, the further it stays below the teacher. Stopping is where the modes part. In non-thinking mode every student keeps stopping; in thinking mode students stop ending their reasoning early in training, and the smaller the student, the less of this ability survives: the teacher signals a stop almost only where a student already ends its reasoning, so distillation teaches no new stops; it only keeps the student's existing stops that land on a right answer, and a weak student has few such stops. The smallest students often reach the right value but do not commit to it: they either rarely mark it or mark it and write past it. Together, these results describe how small students behave under on-policy distillation, and a diagnostic that separates answer marking, correctness and stopping.

Hongyang Li, Yiming Zhu, Xiao Li +3

University of Luxembourg · Seafill Open-Source Community · Universit´e Paris-Saclay

Reasoning Distillation Small Language Models On-Policy Distillation LLM Reasoning

Sep 29, 2026cs.CL

What Does Post-Training Change in Multilingual Reasoning?

Open-source reasoning models provide unequal access to reasoning capability across languages. When a model can solve a problem but cannot deliver a complete solution in the user's language, language becomes an access barrier rather than merely a source of performance variation. We audit Qwen3 checkpoints on competition-mathematics tasks in eleven languages. Across the ten non-English languages, only 15.4-17.9% of problems receive a correct, terminating solution with visible reasoning in the requested language in any of 16 samples, compared with 92.9% in English. To identify the source of this disparity, we evaluate thirteen endpoints from one model family, spanning released checkpoints, multilingual supervised fine-tuning (SFT) at two scales, controlled SFT ablations, and three reinforcement-learning (RL) reward formulations. We jointly track correctness, language adherence, termination, and delivery efficiency. The dominant bottleneck shifts across post-training stages. Released models often reason in English. Multilingual SFT restores target-language reasoning, but accuracy declines across multilingual, English-only, and single-language SFT runs, showing that this cost is not specific to multilingual mixing; non-English reasoning traces additionally become prone to non-terminating loops. RL restores termination in both arms at no cost in accuracy, but only the arm whose reward includes a language term delivers: rewarding correctness alone returns the model to English. Together, these stages establish a constructive post-training path from English-pivoted capability to multilingual reasoning that is reliably delivered.

Hongyang Li, Xiao Li, Caesar Wu +2

University of Luxembourg · Seafill Open-Source Community

Multilingual Language Model Evaluation Cross-Lingual Reasoning in Language Models RL for Language Model Reasoning Language Model Post-Training LLM Reasoning

Sep 29, 2026cs.LG

Beam Search as Test-Time Self-Distillation via Counterfactual Contexts

Self-Distillation Fine-Tuning (SDFT) enables a language model to act as its own teacher: by conditioning on a demonstration, the model produces an implicit reward via pointwise mutual information, which guides on-policy learning without external supervision. However, SDFT operates at training time: it requires gradient updates and access to expert demonstrations, making it inapplicable at inference. We propose test-time self-distillation, a decoding-time method that extracts a steering signal from the self-distillation framework without any parameter updates, reward models, or training data. Our key insight is that counterfactual contexts, i.e. fixed textual templates that hypothetically prime the model for excellent versus poor reasoning, can substitute for the demonstration. The log-odds ratio of a candidate answer under these two counterfactual conditions defines a new reward signal. We derive the optimal KL-regularized policy under this reward, which takes the form of a Gibbs reweighting of the base distribution. Crucially, this reweighting is global: it cannot be decomposed into independent per-token operations without ignoring future trajectory quality. We therefore approximate the target distribution via beam search. Experiments on mathematical reasoning (MATH500), code generation (HumanEval), and graduate-level science QA (GPQA) across multiple model scales show that test-time self-distillation improves over standard sampling, low temperature, beam search and power sampling baselines on average, demonstrating that the self-distillation principle can be operationalized at inference time.

Su Ee Tan, Xiaotong Ji, Rasul Tutunov +2

Huawei Noah’s Ark Lab · UCL Centre for AI

Language Model Distillation Self-Distillation Inference-Time Guidance LLM Reasoning