LLM Reasoning

LLM: Large Language Model

Follow this topic Ask about this topic

This field asks how language models can carry out multi-step inference across mathematics, coding, logic, science, and real-world tasks, and how to tell robust reasoning from pattern matching. Common approaches include chain-of-thought prompting, self-consistency and tree search at inference time, tool use and symbolic verification, and post-training with supervised traces, reinforcement learning from verifiable rewards, or process feedback. Researchers are also exploring latent and recurrent computation to reduce reliance on long written traces, alongside benchmarks that test compositionality, robustness, and long-horizon execution. A central tension is that more computation can improve accuracy but raise cost, while plausible explanations and correct final answers do not by themselves establish faithful, reliable reasoning.

Latest papers

931 papers105 papers in the last four weeks, up 27% on the four weeks before. 0.6% of all new papers.

Apr 2, 2026

Compositional Neuro-Symbolic Reasoning

We study structured abstraction-based reasoning for the Abstraction and Reasoning Corpus (ARC) and compare its generalization to test-time approaches. Purely neural architectures lack reliable combinatorial generalization, while strictly symbolic systems struggle with perceptual grounding. We therefore propose a neuro-symbolic architecture that extracts object-level structure from grids, uses neural priors to propose candidate transformations from a fixed domain-specific language (DSL) of atomic patterns, and filters hypotheses using cross-example consistency. Instantiated as a compositional reasoning framework based on unit patterns inspired by human visual abstraction, the system augments large language models (LLMs) with object representations and transformation proposals. On ARC-AGI-2, it improves base LLM performance from 16% to 24.4% on the public evaluation set, and to 30.8% when combined with ARC Lang Solver via a meta-classifier. These results demonstrate that separating perception, neural-guided transformation proposal, and symbolic consistency filtering improves generalization without task-specific finetuning or reinforcement learning, while reducing reliance on brute-force search and sampling-based test-time scaling. We open-source the ARC-AGI-2 Reasoner code (https://github.com/CoreThink-AI/arc-agi-2-reasoner).

Anugyan Das, Omkar Ghugarkar, Vishvesh Bhat +1

CoreThink AI · Stanford University

Neuro-Symbolic Reasoning Visual Reasoning LLM Reasoning Program Synthesis

Apr 2, 2026

Batched Contextual Reinforcement: A Task-Scaling Law for Efficient Reasoning

Large Language Models employing Chain-of-Thought reasoning achieve strong performance but suffer from excessive token consumption that inflates inference costs. Existing efficiency methods such as explicit length penalties, difficulty estimators, or multi-stage curricula either degrade reasoning quality or require complex training pipelines. We introduce Batched Contextual Reinforcement, a minimalist, single-stage training paradigm that unlocks efficient reasoning through a simple structural modification: training the model to solve N problems simultaneously within a shared context window, rewarded purely by per-instance accuracy. This formulation creates an implicit token budget that yields several key findings: (1) We identify a novel task-scaling law: as the number of concurrent problems N increases during inference, per-problem token usage decreases monotonically while accuracy degrades far more gracefully than baselines, establishing N as a controllable throughput dimension. (2) BCR challenges the traditional accuracy-efficiency trade-off by demonstrating a "free lunch" phenomenon at standard single-problem inference. Across both 1.5B and 4B model families, BCR reduces token usage by 15.8% to 62.6% while consistently maintaining or improving accuracy across five major mathematical benchmarks. (3) Qualitative analyses reveal emergent self-regulated efficiency, where models autonomously eliminate redundant metacognitive loops without explicit length supervision. (4) Crucially, we empirically demonstrate that implicit budget constraints successfully circumvent the adversarial gradients and catastrophic optimization collapse inherent to explicit length penalties, offering a highly stable, constraint-based alternative for length control. These results prove BCR practical, showing simple structural incentives unlock latent high-density reasoning in LLMs.

Bangji Yang, Hongbo Ma, Jiajun Fan +1

University of Illinois Urbana-Champaign · Tsinghua University

Efficient Language Model Reasoning Efficient Language Model Inference LLM Reasoning RL for Language Model Reasoning

Apr 2, 2026

How LLMs Might Think

Do large language models (LLMs) think? Daniel Stoljar and Zhihe Vincent Zhang have recently developed an argument from rationality for the claim that LLMs do not think. We contend, however, that the argument from rationality not only falters, but leaves open an intriguing possibility: that LLMs engage only in arational, associative forms of thinking, and have purely associative minds. Our positive claim is that if LLMs think at all, they likely think precisely in this manner.

Joseph Gottlieb, Ethan Kemp, Matthew Trager

Dept. of Philosophy, Texas Tech University · Dept. of Philosophy, New York University · Dept. of History and Philosophy of Science, University of Pittsburgh, Matthew Trager

Apr 2, 2026

Answering the Wrong Question: Reasoning Trace Inversion for Abstention in LLMs

For Large Language Models (LLMs) to be reliably deployed, models must effectively know when not to answer: abstain. Reasoning models, in particular, have gained attention for impressive performance on complex tasks. However, reasoning models have been shown to have worse abstention abilities. Taking the vulnerabilities of reasoning models into account, we propose our Query Misalignment Framework. Hallucinations resulting in failed abstention can be reinterpreted as LLMs answering the wrong question (rather than answering a question incorrectly). Based on this framework, we develop a new class of state-of-the-art abstention methods called Trace Inversion. First, we generate the reasoning trace of a model. Based on only the trace, we then reconstruct the most likely query that the model responded to. Finally, we compare the initial query with the reconstructed query. Low similarity score between the initial query and reconstructed query suggests that the model likely answered the question incorrectly and is flagged to abstain. Extensive experiments demonstrate that Trace Inversion effectively boosts abstention performance in four frontier LLMs across nine abstention QA datasets, beating competitive baselines in 33 out of 36 settings.

Abinitha Gourabathina, Inkit Padhi, Manish Nagireddy +2

MIT · IBM Research · MIT-IBM Watson AI Lab

LLM Abstention LLM Hallucination Mitigation LLM Reasoning

Apr 2, 2026

Reliable Control-Point Selection for Steering Reasoning in Large Language Models

Steering vectors offer a training-free mechanism for controlling reasoning behaviors in large language models, but constructing effective vectors requires identifying genuine behavioral signals in the model's hidden states. For behaviors that can be toggled via prompts, this is straightforward. However, many reasoning behaviors -- such as self-reflection -- emerge spontaneously and resist prompt-level control. Current methods detect these behaviors through keyword matching in chain-of-thought traces, implicitly assuming that every detected boundary encodes a genuine behavioral signal. We show that this assumption is overwhelmingly wrong: across 541 keyword-detected boundaries, 93.3% are behaviorally unstable, failing to reproduce the detected behavior under re-generation from the same prefix. We develop a probabilistic model that formalizes intrinsic reasoning behaviors as stochastic events with context-dependent trigger probabilities, and show that unstable boundaries dilute the steering signal. Guided by this analysis, we propose stability filtering, which retains only boundaries where the model consistently reproduces the target behavior. Combined with a content-subspace projection that removes residual question-specific noise, our method achieves 0.784 accuracy on MATH-500 (+5.0 over the strongest baseline). The resulting steering vectors transfer across models in the same architecture family without re-extraction, improving Nemotron-Research-Reasoning-1.5B (+5.0) and DeepScaleR-1.5B-Preview (+6.0). Code is available at https://github.com/zhmzm/stability-steering.

Haomin Zhuang, Hojun Yoo, Xiaonan Luo +2

University of Notre Dame

Language Model Steering Activation Steering LLM Reasoning Implicit Reasoning in Language Models

Apr 2, 2026

Human-Guided Reasoning with Large Language Models for Vietnamese Speech Emotion Recognition

Vietnamese Speech Emotion Recognition (SER) remains challenging due to ambiguous acoustic patterns and the lack of reliable annotated data, especially in real-world conditions where emotional boundaries are not clearly separable. To address this problem, this paper proposes a human-machine collaborative framework that integrates human knowledge into the learning process rather than relying solely on data-driven models. The proposed framework is centered around LLM-based reasoning, where acoustic feature-based models are used to provide auxiliary signals such as confidence and feature-level evidence. A confidence-based routing mechanism is introduced to distinguish between easy and ambiguous samples, allowing uncertain cases to be delegated to LLMs for deeper reasoning guided by structured rules derived from human annotation behavior. In addition, an iterative refinement strategy is employed to continuously improve system performance through error analysis and rule updates. Experiments are conducted on a Vietnamese speech dataset of 2,764 samples across three emotion classes (calm, angry, panic), with high inter-annotator agreement (Fleiss Kappa = 0.8574), ensuring reliable ground truth. The proposed method achieves strong performance, reaching up to 86.59% accuracy and Macro F1 around 0.85-0.86, demonstrating its effectiveness in handling ambiguous and hard-to-classify cases. Overall, this work highlights the importance of combining data-driven models with human reasoning, providing a robust and model-agnostic approach for speech emotion recognition in low-resource settings.

Truc Nguyen, Then Tran, Binh Truong +1

University of Information Technology, Ho Chi Minh City, Vietnam · Vietnam National University Ho Chi Minh City, Ho Chi Minh City, Vietnam

Speech Emotion Recognition Human-in-the-Loop AI Low-Resource Language Processing LLM Reasoning

Apr 2, 2026

Fragile Reasoning: A Mechanistic Analysis of LLM Sensitivity to Meaning-Preserving Perturbations

Large language models demonstrate strong performance on mathematical reasoning benchmarks, yet remain surprisingly fragile to meaning-preserving surface perturbations. We systematically evaluate three open-weight LLMs, Mistral-7B, Llama-3-8B, and Qwen2.5-7B, on 677 GSM8K problems paired with semantically equivalent variants generated through name substitution and number format paraphrasing. All three models exhibit substantial answer-flip rates (28.8%-45.1%), with number paraphrasing consistently more disruptive than name swaps. To trace the mechanistic basis of these failures, we introduce the Mechanistic Perturbation Diagnostics (MPD) framework, combining logit lens analysis, activation patching, component ablation, and the Cascading Amplification Index (CAI) into a unified diagnostic pipeline. CAI, a novel metric quantifying layer-wise divergence amplification, outperforms first divergence layer as a failure predictor for two of three architectures (AUC up to 0.679). Logit lens reveals that flipped samples diverge from correct predictions at significantly earlier layers than stable samples. Activation patching reveals a stark architectural divide in failure localizability: Llama-3 failures are recoverable by patching at specific layers (43/60 samples), while Mistral and Qwen failures are broadly distributed (3/60 and 0/60). Based on these diagnostic signals, we propose a mechanistic failure taxonomy (localized, distributed, and entangled) and validate it through targeted repair experiments: steering vectors and layer fine-tuning recover 12.2% of localized failures (Llama-3) but only 7.2% of entangled (Qwen) and 5.2% of distributed (Mistral) failures.

Shou-Tzu Han, Rodrigue Rizk, KC Santosh

Department of Computer Science, University of South Dakota

Language Model Robustness LLM Reasoning Adversarial Robustness of Language Models LLM Interpretability Causal Interventions in Language Models

Apr 2, 2026

ThinkTwice: Jointly Optimizing Large Language Models for Reasoning and Self-Refinement

We introduce ThinkTwice, a simple two-phase framework that jointly optimizes LLMs to solve reasoning problems and refine the answers, based on Group Relative Policy Optimization (GRPO). In each pair of training steps, ThinkTwice first optimizes the model on solving reasoning problems, then optimizes it on refining its own solutions to the same problems, using the same binary correctness reward in both phases without correctness signals or critique annotations. Across five mathematical reasoning benchmarks and two model families including Qwen3-4B and Olmo3-7B, ThinkTwice substantially improves both reasoning and refinement performance over competitive online policy optimization baselines. Specifically, on Qwen3-4B, ThinkTwice outperforms GRPO on AIME by 5 percentage points before refinement and by 11.5 points after one self-refinement step, measured by pass@4. Analysis of the training dynamics of ThinkTwice reveals an implicit rectify-then-fortify curriculum: refinement predominantly corrects errors early in training and naturally shifts toward preserving already-correct solutions as the model improves, yielding a more rectified reward signal. Our work establishes joint training of reasoning and self-refinement as a principled and effective methodology for RLVR.

Difan Jiao, Qianfeng Wen, Blair Yang +2

Department of Computer Science, University of Toronto · Coolwei AI Lab

RL for Language Model Reasoning LLM Reasoning LLM Self-Refinement Reinforcement Learning with Verifiable Rewards

Apr 1, 2026

Procedural Knowledge at Scale Improves Reasoning

Test-time scaling has emerged as an effective way to improve language models on challenging reasoning tasks. However, most existing methods treat each problem in isolation and do not systematically reuse knowledge from prior reasoning trajectories. In particular, they underutilize procedural knowledge: how to reframe a problem, choose an approach, and verify or backtrack when needed. We introduce Reasoning Memory, a retrieval-augmented generation (RAG) framework for reasoning models that explicitly retrieves and reuses procedural knowledge at scale. Starting from existing corpora of step-by-step reasoning trajectories, we decompose each trajectory into self-contained subquestion-subroutine pairs, yielding a datastore of 32 million compact procedural knowledge entries. At inference time, a lightweight in-thought prompt lets the model verbalize the core subquestion, retrieve relevant subroutines within its reasoning trace, and reason under diverse retrieved subroutines as implicit procedural priors. Across six math, science, and coding benchmarks, Reasoning Memory consistently outperforms RAG with document, trajectory, and template knowledge, as well as a compute-matched test-time scaling baseline. With a higher inference budget, averaged across models and tasks, it improves over no retrieval by 19.5% and over the compute-matched baseline by 8.9%. Ablation studies show that these gains come from two key factors: the broad procedural coverage of the source trajectories and our decomposition and retrieval design, which together enable effective extraction and reuse of procedural knowledge. Our experiment code is available at https://github.com/facebookresearch/reasoning-memory.

Di Wu, Devendra Singh Sachan, Wen-tau Yih +1

University of California, Los Angeles · Meta FAIR

Retrieval-Augmented Reasoning LLM Reasoning Knowledge Augmentation for Language Models Structured Reasoning in Language Models Memory-Augmented Language Models

Apr 1, 2026

Reasoning Shift: How Context Silently Shortens LLM Reasoning

Large language models (LLMs) exhibiting test-time scaling behavior, such as extended reasoning traces and self-verification, have demonstrated remarkable performance on complex, long-term reasoning tasks. However, the robustness of these reasoning behaviors remains underexplored. To investigate this, we conduct a systematic evaluation of multiple reasoning models across three scenarios: (1) problems augmented with lengthy, irrelevant context; (2) multi-turn conversational settings with independent tasks; and (3) problems presented as a subtask within a complex task. We observe an interesting phenomenon: reasoning models tend to produce much shorter reasoning traces (up to 74%) for the same problem under different context conditions compared to the traces produced when the problem is presented in isolation. A finer-grained analysis reveals that this compression is associated with a decrease in self-verification and uncertainty management behaviors, such as double-checking. Importantly, we show that even when additional self-checks are forced, their efficiency depends not only on the content of the reasoning traces, but also on the presence of redundant context. We hope our findings draw additional attention to both the robustness of reasoning models and the problem of context management for LLMs.

Gleb Rodionov, Roman Garipov, George Yakushev

Yandex · HSE University

Language Model Robustness LLM Context Management LLM Reasoning Large Reasoning Models

Mar 31, 2026

Hierarchical Chain-of-Thought: Enhancing LLM Reasoning Performance and Efficiency

Chain-of-Thought (CoT) prompting has significantly improved the reasoning capabilities of large language models (LLMs). However, conventional CoT often relies on unstructured, flat reasoning chains that suffer from redundancy and suboptimal performance. In this work, we introduce Hierarchical Chain-of-Thought (Hi-CoT), a structured reasoning paradigm specifically designed to address the challenges of complex, multi-step reasoning. Hi-CoT decomposes the reasoning process into hierarchical substeps by alternating between instructional planning and step-by-step execution. This decomposition enables LLMs to better manage long reasoning horizons and maintain logical coherence. Extensive evaluations across diverse LLMs and mathematical reasoning benchmarks show that Hi-CoT consistently improves average accuracy by 6.2% (up to 61.4% on certain models and tasks) while reducing reasoning trace length by 13.9% compared to CoT. We further show that accuracy and efficiency are maximized when models strictly adhere to the hierarchical structure. Our code is available at https://github.com/XingshuaiHuang/Hi-CoT.

Xingshuai Huang, Derek Li, Bahareh Nikpour +1

Huawei Technologies Canada, Canada · Huawei Noah’s Ark Lab, Canada

CoT Reasoning LLM Reasoning Efficient Language Model Reasoning

Mar 31, 2026

Bethe Ansatz with a Large Language Model

We explore the capability of a Large Language Model (LLM) to perform specific computations in mathematical physics: the task is to compute the coordinate Bethe Ansatz solution of selected integrable spin chain models. We select three integrable Hamiltonians for which the solutions were unpublished; two of the Hamiltonians are actually new. We observed that the LLM semi-autonomously solved the task in all cases, with a few mistakes along the way. These were corrected after the human researchers spotted them. The results of the LLM were checked against exact diagonalization (performed by separate programs), and the derivations were also checked by the authors. The Bethe Ansatz solutions are interesting in themselves. Our second model manifestly breaks left-right invariance, but it is PT-symmetric, therefore its solution could be interesting for applications in Generalized Hydrodynamics. And our third model is solved by a special form of the nested Bethe Ansatz, where the model is interacting, but the nesting level has a free fermionic structure lacking

U(1)

-invariance. This structure appears to be unique and it was found by the LLM. We used ChatGPT 5.2 Pro and 5.4 Pro by OpenAI.

Balázs Pozsgay, István Vona

MTA-ELTE “Momentum” Integrable Quantum Dynamics Research Group, ELTE Eötvös Loránd University, Budapest, Hungary · Holographic Quantum Field Theory Research Group, HUN-REN Wigner Research Centre for Physics, Budapest, Hungary

Quantum Many-Body Physics Large Language Model-Guided Scientific Discovery LLM Reasoning

Mar 31, 2026

Learning to Generate Formally Verifiable Step-by-Step Logic Reasoning via Structured Formal Intermediaries

Large language models (LLMs) have recently demonstrated impressive performance on complex, multi-step reasoning tasks, especially when post-trained with outcome-rewarded reinforcement learning Guo et al. 2025. However, it has been observed that outcome rewards often overlook flawed intermediate steps, leading to unreliable reasoning steps even when final answers are correct. To address this unreliable reasoning, we propose PRoSFI (Process Reward over Structured Formal Intermediates), a novel reward method that enhances reasoning reliability without compromising accuracy. Instead of generating formal proofs directly, which is rarely accomplishable for a modest-sized (7B) model, the model outputs structured intermediate steps aligned with its natural language reasoning. Each step is then verified by a formal prover. Only fully validated reasoning chains receive high rewards. The integration of formal verification guides the model towards generating step-by-step machine-checkable proofs, thereby yielding more credible final answers. PRoSFI offers a simple and effective approach to training trustworthy reasoning models.

Luoxin Chen, Yichi Zhou, Huishuai Zhang

Wangxuan Institue of Computer Technology, Peking University. · ByteDance.

LLM Reasoning LLM Reliability Reinforcement Learning with Verifiable Rewards Process Reward Models

Mar 30, 2026

ERPO: Token-Level Entropy-Regulated Policy Optimization for Large Reasoning Models

Reinforcement learning from verifiable rewards has significantly advanced the reasoning capabilities of large language models. However, Group Relative Policy Optimization (GRPO) typically assigns a uniform, sequence-level advantage to all tokens, thereby overlooking the intrinsic information heterogeneity along reasoning chains. We show that this coarse-grained credit assignment leads to premature entropy collapse and encourages the model to generate redundant, low-quality reasoning paths. Through systematic empirical analysis, we identify Critical Decision Pivots (CDPs): transient high-entropy states where the policy's trajectory is most sensitive to perturbations. These pivots represent the "forks in the road" where effective multi-path exploration is most crucial yet often suppressed by uniform advantage signals. Building on these insights, we propose Entropy-Regulated Policy Optimization (ERPO), which transitions the optimization focus from coarse sequences to fine-grained token dynamics. ERPO introduces three synergistic components: (i) Entropy-aware Gating, which adaptively amplifies exploration at CDPs to facilitate diverse path discovery; (ii) Bucket-based Implicit Normalization, which mitigates difficulty bias by aligning token progress windows; and (iii) Result-anchored Advantage Synthesis, which re-weights token-level signals via outcome-driven anchors. Extensive experiments on competitive mathematical benchmarks demonstrate that ERPO significantly outperforms GRPO. Notably, ERPO not only boosts reasoning accuracy but also yields significantly more concise and robust derivation paths, while achieving performance comparable to large models with orders of magnitude more parameters.

Song Yu, Li Li, Wenwen Zhao +1

School of Computer and Information Science, Southwest University, Chongqing, 400715, China

RL for Language Model Reasoning RL for Language Models LLM Reasoning Large Reasoning Models

Mar 29, 2026

Model Capability Dominates: Inference-Time Optimization Lessons from AIMO 3

Majority voting over multiple LLM attempts improves mathematical reasoning, but correlated errors limit the effective sample size. A natural fix is to assign different reasoning strategies to different voters. The approach, Diverse Prompt Mixer, is tested on the AIMO 3 competition: 3 models, 23+ experiments, 50 IMO-level problems, one H100 80 GB, 5-hour limit. Every prompt-level intervention fails. High-temperature sampling already decorrelates errors; weaker strategies reduce accuracy more than they reduce correlation. Across an 8-point capability gap at equal N=8 and every optimization tested, model capability dominates. The gap between the best majority-vote score (42/50) and pass@20 (~45.5) is selection loss, not prompt loss. A verifier-based selector could close it. Prompt engineering cannot.

Natapong Nitarach

LLM Reasoning LLM Prompting Language Model Ensembles Test-Time Scaling Self-Consistency Decoding

Mar 28, 2026

Rethinking Easy-to-Hard: Limits of Curriculum Learning in Post-Training for Deductive Reasoning

Curriculum learning (CL), motivated by the intuition that learning in increasing order of difficulty should ease generalization, is commonly adopted both in pre-training and post-training of large language models (LLMs). The intuition of CL is particularly compelling for compositional reasoning, where complex problems are built from elementary inference rules; however, the actual impact of CL on such tasks remains largely underexplored. We present a systematic empirical study of CL for post-training of LLMs, using synthetic arithmetic and logical benchmarks where difficulty is characterized by reasoning complexity rather than surface-level proxies. Surprisingly, across multiple model families and curriculum schedules, we find no robust advantage in difficulty-based sequencing over standard random sampling in either accuracy or response length. These findings persist across both supervised fine-tuning (SFT) and reinforcement learning (RL) methods. Our study suggests that, in the context of deductive reasoning, the specific ordering of training examples plays a negligible role in achieving compositional generalization, challenging the practical utility of curriculum-based post-training.

Maximilian Mordig, Andreas Opedal, Weiyang Liu +1

Max Planck Institute for Intelligent Systems, Tübingen · ETH Zürich · The Chinese University of Hong Kong

Curriculum Learning Language Model Post-Training LLM Reasoning

Mar 26, 2026

SafeMath: Safe Solutions for Unsafe Math Word Problems

Recent research points toward LLMs being manipulated through adversarial and seemingly benign inputs, resulting in harmful, biased, or policy-violating outputs. In this paper, we study an underexplored issue concerning harmful and toxic mathematical word problems. We show that math questions, particularly those framed as natural language narratives, can serve as a subtle medium for propagating biased, unethical, or psychologically harmful content, with heightened risks in educational settings involving children. To support a systematic study of this phenomenon, we introduce ToxicGSM, a dataset of 1.9k arithmetic problems in which harmful or sensitive context is embedded while preserving mathematically well-defined reasoning tasks. Using this dataset, we audit the behaviour of existing LLMs and analyse the trade-offs between safety enforcement and mathematical correctness. We further propose SafeMath -- a safety alignment technique that reduces harmful outputs while maintaining, and in some cases improving, mathematical reasoning performance. Our results highlight the importance of disentangling linguistic harm from math reasoning and demonstrate that effective safety alignment need not come at the cost of accuracy.

Sagnik Basu, Subhrajit Mitra, Aman Juneja +3

1Indian Institute of Technology Kharagpur · 2Cisco Systems · 3National University of Singapore

LLM Safety Alignment LLM Safety Evaluation LLM Reasoning

Mar 25, 2026

Why Does Self-Distillation (Sometimes) Degrade the Reasoning Capability of LLMs?

Self-distillation has emerged as an effective post-training paradigm for LLMs, often improving performance while shortening reasoning traces. However, in mathematical reasoning, we find that it can reduce response length while degrading performance. We trace this degradation to the suppression of epistemic verbalization - the model's expression of uncertainty during reasoning. Through controlled experiments varying conditioning context richness and task coverage, we show that conditioning the teacher on rich information suppresses uncertainty expression, enabling rapid in-domain optimization with limited task coverage but harming OOD performance, where unseen problems benefit from expressing uncertainty and adjusting accordingly. Across Qwen3-1.7B/8B, DeepSeek-Distill-Qwen-7B, and Olmo3-7B-Instruct, we observe performance drops of up to 40%. Our findings highlight that exposing appropriate levels of uncertainty is crucial for robust reasoning and underscore the importance of optimizing reasoning behavior beyond merely reinforcing correct answer traces.

Jeonghye Kim, Xufang Luo, Minbeom Kim +5

Microsoft Research · KAIST · SK hynix +1

Self-Distillation Language Model Distillation LLM Reasoning Language Model Robustness

Mar 25, 2026

Thinking with Tables: Enhancing Multi-Modal Tabular Understanding via Neuro-Symbolic Reasoning

Multimodal Large Language Models (MLLMs) have demonstrated remarkable reasoning capabilities across modalities such as images and text. However, tabular data, despite being a critical real-world modality, remains relatively underexplored in multimodal learning. In this paper, we focus on the task of Tabular-Vision Multi-Modal Understanding (TVMU) and identify three core challenges: (1) high structural variability and data incompleteness in tables, (2) implicit and complex feature dependencies, and (3) significant heterogeneity in problem-solving pipelines across downstream tasks. To address these issues, we propose Thinking with Tables (TWT). TWT employs a program-aided code-based neuro-symbolic reasoning mechanism that facilitates key operations, such as information extraction and element modeling, by interacting with external environments. We evaluate TWT on eight representative datasets. Experimental results demonstrate that TWT consistently outperforms existing baselines by an average of 10% in accuracy, achieving performance comparable to, or even surpassing, proprietary commercial SOTA LLMs on TVMU tasks. Models and codes are available at https://github.com/kunyang-YU/Thinking-with-Tables

Kun-Yang Yu, Zhi Zhou, Shi-Yu Tian +6

State Key Laboratory of Novel Software Technology, Nanjing University, China · School of Artificial Intelligence, Nanjing University, China · School of Intelligence Science and Technology, Nanjing University, China

Multimodal Understanding Multimodal Large Language Models Multimodal Reasoning LLM Reasoning Neuro-Symbolic Reasoning

Mar 25, 2026

HDPO: Hybrid Distillation Policy Optimization via Privileged Self-Distillation

Large language models trained with reinforcement learning (RL) for mathematical reasoning face a fundamental challenge: on problems the model cannot solve at all - "cliff" prompts - the RL gradient vanishes entirely, preventing any learning signal from reaching these failure modes. We introduce Hybrid Distillation Policy Optimization (HDPO), which augments standard RL with privileged self-distillation targeting cliff prompts. On each training step, HDPO identifies prompts where all rollouts fail, generates privileged rollouts by providing the model with ground-truth information, filters for correct solutions, and distills the teacher's token-level distribution into the student. Because teacher and student share the same weights - differing only in their input - the realizability gap is provably bounded, unlike cross-model distillation. We prove that R=1 filtered privileged generation recovers the optimal KL-regularized RL policy in the hard-threshold limit. Experiments on OpenMathInstruct-2 with Qwen2.5-Math-1.5B-Instruct show that HDPO consistently improves coverage metrics (pass@4 by +0.8-1.1%, pass@8 by +0.4-1.7%) while maintaining greedy accuracy, with the distillation weight lambda providing direct control over the exploration-exploitation tradeoff.

Ken Ding

NVIDIA

RL for Language Model Reasoning LLM Reasoning On-Policy Distillation Self-Distillation

Mar 24, 2026

Off-Policy Value-Based Reinforcement Learning for Large Language Models

Improving data utilization efficiency is critical for scaling reinforcement learning (RL) for long-horizon tasks where generating trajectories is expensive. However, the dominant RL methods for LLMs are largely on-policy: they update each batch of data only once, discard it, and then collect fresh samples, resulting in poor sample efficiency. In this work, we explore an alternative value-based RL framework for LLMs that naturally enables off-policy learning. We propose ReVal, a Bellman-update-based method that combines stepwise signals capturing internal consistency with trajectory-level signals derived from outcome verification. ReVal naturally supports replay-buffer-based training, allowing efficient reuse of past trajectories. Experiments on standard mathematical reasoning benchmarks show that ReVal not only converges faster but also outperforms GRPO in final performance. On DeepSeek-R1-Distill-1.5B, ReVal improves training efficiency and achieves improvement of 2.7% in AIME24 and 4.5% in out-of-domain benchmark GPQA over GRPO. These results suggest that value-based RL is a practical alternative to policy-based methods for LLM training.

Peng-Yuan Wang, Ziniu Li, Tian Xu +8

National Key Laboratory for Novel Software Technology & School of Artificial Intelligence, Nanjing University, China · The Chinese University of Hong Kong, Shenzhen · Shenzhen Research Institute of Big Data +1

Reinforcement Learning RL for Language Model Reasoning Off-Policy RL RL Fine-Tuning LLM Reasoning

Mar 24, 2026

LogicDiff: Logic-Guided Denoising Improves Zero-Shot Reasoning in Masked Diffusion Language Models

Masked diffusion language models (MDLMs) generate text by iteratively unmasking tokens from a fully masked sequence. Their standard confidence-based unmasking strategy systematically defers high-entropy logical connective tokens, degrading reasoning performance. We introduce LogicDiff, an inference-time method that replaces confidence-based unmasking with logic-role-guided unmasking. A lightweight classification head (4.2M parameters, 0.05% of the base model) predicts the logical role of each masked position (premise, connective, derived step, conclusion, or filler) from the base model's hidden states with 98.4% accuracy, and a dependency-ordered scheduler unmasks tokens in logical order. In zero-shot settings, LogicDiff improves LLaDA-8B-Instruct accuracy from 22.0% to 60.7% on GSM8K (+38.7 percentage points) and from 23.6% to 29.2% on MATH-500 (+5.6 pp), with less than 6% speed overhead. However, with 8-shot chain-of-thought prompting, the baseline reaches approximately 70% and LogicDiff provides no additional improvement. Analysis reveals that few-shot prompting implicitly resolves the same ordering problem that LogicDiff explicitly addresses, and that fixed role-based ordering can cause premature commitment to numerical values before sufficient context is available. Our results characterize the Flexibility Trap as primarily a zero-shot phenomenon and identify context-adaptive ordering as a key direction for future work.

Shaik Aman

Independent Researcher, Nellore, Andhra Pradesh, India

Masked Diffusion Models Diffusion Language Model Decoding LLM Reasoning

Mar 24, 2026

PRISM: A Dual View of LLM Reasoning through Semantic Flow and Latent Computation

Large language models (LLMs) solve complex problems by generating multi-step reasoning traces. Yet these traces are typically analyzed from only one of two perspectives: the sequence of tokens across different reasoning steps in the generated text, or the hidden-state vectors across model layers within one step. We introduce PRISM (Probabilistic Reasoning Inspection through Semantic and Implicit Modeling), a framework and diagnostic tool for jointly analyzing both levels, providing a unified view of how reasoning evolves across steps and layers. Across multiple reasoning models and benchmarks, PRISM uncovers systematic patterns in the reasoning process, showing that failed trajectories are more likely to become trapped in unproductive verification loops and further diverge into distinct modes such as overthinking and premature commitment, which behave differently once a candidate answer is reached. It further reveals how prompting reshapes reasoning behavior beyond aggregate accuracy by altering both semantic transitions and internal computational patterns. By modeling reasoning trajectories as structured processes, PRISM makes these behaviors observable and analyzable rather than relying solely on final-task accuracy. Taken together, these insights position PRISM as a practical tool for analyzing and diagnosing reasoning processes in LLMs.

Ruidi Chang, Jiawei Zhou, Hanjie Chen

Rice University · Stony Brook University

LLM Reasoning LLM Interpretability Overthinking in Language Models

Mar 24, 2026

Explanation Generation for Contradiction Reconciliation with LLMs

Existing NLP work commonly treats contradictions as errors to be resolved by choosing which statements to accept or discard. Yet a key aspect of human reasoning in social and professional settings is the ability to hypothesize explanations that reconcile contradictions. For example, "Cassie hates coffee" and "She buys coffee everyday" appear contradictory, but are in fact compatible if Cassie was assigned the daily chore of buying coffee for all her coworkers. Despite advances in the reasoning capabilities of large language models (LLMs), their ability to hypothesize such explanations remains largely unexplored. To address this gap, we introduce the task of reconciliatory explanation generation, where models must generate explanations that effectively render contradictory statements compatible. We propose a novel method of reusing natural language inference (NLI) datasets, and introduce quality metrics that enable scalable automatic evaluation. Experiments with 13 LLMs in thinking and non-thinking modes reveal models' limited success in this task, with longer reasoning chains negatively associated with explanation success. As a proof of concept, we further adapt our introduced task and metrics for reinforcement-learning training, finding that trained models exhibit improved accuracy in non-thinking mode on two narrative reasoning benchmarks (True Detective and MuSR). Our findings highlight reconciliatory explanation generation as a challenge in LLM reasoning and motivate further work to investigate its potential for improving model capabilities.

Jason Chan, Zhixue Zhao, Robert Gaizauskas

University of Sheffield, UK

LLM Reasoning Reasoning Consistency in Language Models

Mar 23, 2026

Thinking Deeper, Not Longer: Memory-Efficient Test-Time Reasoning with Depth-Recurrent Transformers for Compositional Generalization

Standard Transformers have a fixed computational depth, limiting their ability to generalize to tasks that require variable-depth reasoning. The usual remedy, Chain-of-Thought (CoT), spends tokens to reason, inflating the key--value cache and making latency grow with the step count, so memory becomes the limiting cost when reasoning is served over large query batches. We study a depth-recurrent Transformer that decouples computational depth from parameter count by iterating a shared-weight block, so that each added reasoning step costs flat memory and linear latency, with no token generation. Three ingredients keep the recurrence stable for 20+ thinking steps: a silent thinking objective that supervises only the final output, LayerScale initialization, and an identity-biased gate that opens a gradient highway across steps. We characterize it on three compositional domains with decreasing structural bias: graph reachability (adjacency masking), nested boolean logic (relative positioning), and unstructured relational text (no positional cue). We find a computational frontier: accuracy climbs once the thinking-step count meets the task's complexity, reaching near-perfect performance on the two structured tasks and a lower plateau on unstructured text. How it climbs depends on the structural bias---abruptly from chance on the graph task, gradually on the other two. Depth recurrence extrapolates beyond the training range: it succeeds on the graph task where fixed-depth models barely extrapolate, and on the two sequence tasks comes within two points of fixed-depth Transformers that use

4

--

6.4\times

more parameters. On the graph task, whose adjacency mask makes propagation depth verifiable, intermediate per-step supervision---a standard recipe for deep iterative models---consistently harms this extrapolation. We release the code for reproducibility.

Hung-Hsuan Chen

Computer Science and Information Engineering National Central University Taoyuan, Taiwan

Efficient Transformer Inference Recurrent Transformers Structured Reasoning Algorithmic Reasoning Compositional Generalization LLM Reasoning

Mar 22, 2026

Beyond Memorization: Distinguishing Between Pattern-Based and Epistemic Reasoning in LLMs Using Epistemic Puzzles

Epistemic reasoning requires agents to infer the state of the world from partial observations and information about other agents' knowledge. Prior work evaluating LLMs on epistemic puzzles often frames failures as memorization rather than reasoning. We argue that this dichotomy is too coarse for newer models: memorization is a limiting case of pattern-based reasoning, where a model matches a task to a familiar template and applies the corresponding solution. We introduce a two-dimensional benchmark over Dynamic Epistemic Logic (DEL) puzzles, separating narrative familiarity from inference complexity, which allows us to distinguish pattern-based from epistemic reasoning. We find that models are substantially more robust to surface form changes than prior work suggested, yet consistently struggle in asymmetric settings where familiar patterns no longer apply and success requires tracking fragmented epistemic states. Code, datasets, and evaluation results are available at https://github.com/adigabay84/del-puzzles-benchmark.

Adi Gabay, Gabriel Stanovsky, Liat Peterfreund

School of Computer Science and Engineering The Hebrew University of Jerusalem

Epistemic Logic LLM Reasoning

Mar 22, 2026

Enhancing reasoning accuracy in large language models during inference time

Large Language Models (LLMs) often exhibit strong linguistic abilities while remaining unreliable on multi-step reasoning tasks, particularly when deployed without additional training or fine-tuning. In this work, we study inference-time techniques to improve the reasoning accuracy of LLMs. We systematically evaluate three classes of inference-time strategies: (i) self-consistency via stochastic decoding, where the model is sampled multiple times using controlled temperature and nucleus sampling and the most frequent final answer is selected; (ii) dual-model reasoning agreement, where outputs from two independent models are compared and only consistent reasoning traces are trusted; and (iii) self-reflection, where the model critiques and revises its own reasoning. Across all evaluated methods, we employ Chain-of-Thought (CoT) [1] prompting to elicit explicit intermediate reasoning steps before generating final answers. In this work, we provide a controlled comparative evaluation across three inference-time strategies under identical prompting and verification settings. Our experiments on LLM [2] show that self-consistency with nucleus sampling and controlled temperature value yields the substantial gains, achieving a 9% to 15% absolute improvement in accuracy over greedy single-pass decoding, well-suited for low-risk domains, offering meaningful gains with minimal overhead. The dual-model approach provides additional confirmation for model reasoning steps thus more appropriate for moderate-risk domains, where higher reliability justifies additional compute. Self-reflection offers only marginal improvements, suggesting limited effectiveness for smaller non-reasoning models at inference time.

Vinay Sharma, Manish Jain

LLM Inference LLM Reasoning Inference-Time Guidance Self-Consistency Decoding

Mar 22, 2026

ORACLE: Optimizing Reasoning Abilities of Large Language Models via Constraint-Led Synthetic Data Elicitation

Training large language models (LLMs) with synthetic reasoning data has become a popular approach to enhancing their reasoning capabilities, while a key factor influencing the effectiveness of this paradigm is the quality of the generated multi-step reasoning data. To generate high-quality reasoning data, many recent methods generate synthetic reasoning paths and filter them based on final answer correctness, often overlooking flaws in intermediate reasoning steps. To enhance the verification of intermediate reasoning steps, prior work primarily resorts to code execution or symbolic reasoning engines. However, code-based validation is restricted to code or mathematical tasks, and reasoning engines require a well-structured and complete context. As a result, existing methods fail to function effectively in natural language reasoning tasks that involve ambiguous or incomplete contexts. In these tasks, synthetic data still lack reliable checks for verifying each reasoning step. To address this challenge, we introduce ORACLE, a structured data generation framework inspired by syllogistic reasoning. ORACLE integrates the generative strengths of LLMs with symbolic supervision: the LLM produces step-wise reasoning contexts, while a symbolic reasoning engine verifies the validity of each intermediate step. By employing a unified prompting template to elicit modular reasoning chains, ORACLE enables fine-grained, step-level validation, facilitating the construction of high-quality multi-step reasoning data. Across six logical, factual, and commonsense reasoning benchmarks, our ORACLE consistently outperforms strong baselines on multiple models.

Zhuojie Yang, Wentao Wan, Keze Wang

School of Computer Science and Engineering, Sun Yat-sen University

Synthetic Data Generation for Language Models LLM Reasoning Reasoning Verification

Mar 21, 2026

Mitigating Shortcut Reasoning in Language Models: A Gradient-Aware Training Approach

Large language models exhibit strong reasoning capabilities, yet often rely on shortcuts such as surface pattern matching and answer memorization rather than genuine logical inference. We propose Shortcut-Aware Reasoning Training (SART), a gradient-aware framework that detects and mitigates shortcut-promoting samples via ShortcutScore and gradient surgery. Our method identifies shortcut signals through gradient misalignment with validation objectives and answer-token concentration, and modifies training dynamics accordingly. Experiments on controlled reasoning benchmarks show that SART achieves +16.5% accuracy and +40.2% robustness over the strongest baseline, significantly improving generalization under distribution shifts. Code is available at: https://github.com/fuyanjie/short-cut-aware-data-centric-reasoning.

Hongyu Cao, Kunpeng Liu, Dongjie Wang +1

Arizona State University · Clemson University · University of Kansas

Shortcut Learning in Language Models LLM Reasoning Language Model Robustness

Mar 21, 2026

Reasoning Topology Matters: Network-of-Thought for Complex Reasoning Tasks

Existing prompting paradigms structure LLM reasoning in limited topologies: Chain-of-Thought (CoT) produces linear traces, while Tree-of-Thought (ToT) performs branching search. Yet complex reasoning often requires merging intermediate results, revisiting hypotheses, and integrating evidence from multiple sources. We propose Network-of-Thought (NoT), a framework that models reasoning as a directed graph with typed nodes and edges, guided by a heuristic-based controller policy. Across four benchmarks (GSM8K, Game of 24, HotpotQA, ProofWriter) and three models (GPT-4o-mini, Llama-3.3-70B-Instruct, Qwen2.5-72B-Instruct), we investigate when network topology outperforms chain or tree structures, whether LLM-generated heuristics can guide graph-based reasoning search, and the computation-accuracy tradeoff across topologies, evaluating each method on accuracy, topology simplicity, and token efficiency. Our results show that CoT remains effective for sequential tasks with GPT-4o-mini (89.5% on GSM8K), while NoT surpasses ToT on multi-hop reasoning (91.0% vs.\ 88.0% on HotpotQA with LLM-as-Judge). With 72B open-source models, NoT achieves the highest accuracy on GSM8K (91.5%), and Qwen2.5-72B achieves the best multi-hop QA result overall (91.7% on HotpotQA). Self-generated controller heuristics outperform fixed and random strategies on logical reasoning, with uncertainty-only weighting achieving 57.0% on ProofWriter. We also find that evaluation methodology significantly impacts method rankings: string-match underestimates all methods on open-ended QA, with the largest gap for NoT, a pattern consistent across all three models (14--18 percentage point gap on HotpotQA).

Fan Huang

Indiana University Bloomington

LLM Reasoning LLM Reasoning with Graphs Efficient Language Model Reasoning Multi-Hop Reasoning