LLM Reasoning

LLM: Large Language Model

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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 11, 2026

Adapt to Thrive! Adaptive Power-Mean Policy Optimization for Improved LLM Reasoning

Reinforcement Learning with Verifiable Rewards (RLVR) is an essential paradigm that enhances the reasoning capabilities of Large Language Models (LLMs). However, existing methods typically rely on static policy optimization schemes that misalign with the model's evolving reasoning capabilities. To address this issue, we propose Adaptive Power-Mean Policy Optimization (APMPO), which comprises two main innovations: Power-Mean Policy Optimization (PMPO) and Feedback-Adaptive Clipping (FAC). Specifically, PMPO introduces a generalized power-mean objective. This enables the model to adaptively transition from the signal-amplifying behavior of the arithmetic mean to the consistency-enforcing behavior of the geometric mean. FAC adaptively adjusts clipping bounds based on real-time reward statistics to overcome the limitations of static mechanisms. Capitalizing on these innovations, APMPO improves learning dynamics and reasoning performance. Extensive experiments on nine datasets across three reasoning tasks showcase the superiority of APMPO over state-of-the-art RLVR-based baselines. For instance, APMPO boosts the average Pass@1 score on mathematical reasoning benchmarks by 3.0 points compared to GRPO when using Qwen2.5-3B-Instruct.

Yiming Huang, Zhenbo Shi, Shuzheng Gao +3

Harbin Institute of Technology, Shenzhen · The Chinese University of Hong Kong · Peng Cheng Laboratory

RL for Language Model Reasoning Policy Optimization LLM Reasoning Reinforcement Learning with Verifiable Rewards

Apr 11, 2026

Free Energy-Driven Reinforcement Learning with Adaptive Advantage Shaping for Unsupervised Reasoning in LLMs

Unsupervised reinforcement learning (RL) has emerged as a promising paradigm for enabling self-improvement in large language models (LLMs). However, existing unsupervised RL-based methods often lack the capacity to adapt to the model's evolving reasoning capabilities during training. Therefore, these methods can misdirect policy optimization in the absence of ground-truth supervision. To address this issue, we introduce FREIA, a novel RL-based algorithm built on two key innovations: (1) Free Energy-Driven Reward (FER) adapts rewards to balance consensus and exploration based on the Free Energy Principle. (2) Adaptive Advantage Shaping (AAS) adaptively adjusts learning signals based on the statistical characteristics of sampled rewards. Empirical evaluations on nine datasets across three reasoning tasks showcase that FREIA outperforms other unsupervised RL-based baselines. Notably, in mathematical reasoning tasks, FREIA surpasses other methods by an average of 0.5 to 3.5 points in Pass@1 using the DeepSeek-R1-Distill-Qwen-1.5B model.

Yiming Huang, Zhenbo Shi, Xin-Cheng Wen +4

Harbin Institute of Technology, Shenzhen · The Chinese University of Hong Kong · Peng Cheng Laboratory

Reinforcement Learning RL for Language Model Reasoning LLM Reasoning Reward Shaping

Apr 11, 2026

AI Achieves a Perfect LSAT Score

This paper reports the first documented instance of a language model achieving a perfect score on an officially disclosed Law School Admission Test (LSAT). Controlled experiments on eight reasoning models show that varying the prompt, shuffling answer choices, and sampling multiple responses have no meaningful effect as drivers of performance. Ablating the thinking phase that models generate before answering, however, lowers frontier accuracy by up to 8 percentage points, predominantly in logical reasoning. Distilled models produce full thinking traces in the same format yet plateau far below frontier performance. A pilot process reward model fine-tuned via QLoRA on official LSAT explanations narrows this gap through Best-of-5 selection, with gains again predominantly in logical reasoning. The gatekeeper of elite legal education since 1948, the LSAT has not merely been passed but answered without a single error by models that reason. The upper bound of the cognitive capacities it has tested is no longer exclusive to human cognition.

Bonmu Ku

LLM Reasoning LLM Evaluation CoT Reasoning Legal Reasoning Educational Assessment

Apr 10, 2026

Process Reward Agents for Steering Knowledge-Intensive Reasoning

Reasoning in knowledge-intensive domains remains challenging as intermediate steps are often not locally verifiable: unlike math or code, evaluating step correctness may require synthesizing clues across large external knowledge sources. As a result, subtle errors can propagate through reasoning traces, potentially never to be detected. Prior work has proposed process reward models (PRMs), including retrieval-augmented variants, but these methods operate post hoc, scoring completed trajectories, which prevents their integration into dynamic inference procedures. Here, we introduce Process Reward Agents (PRA), an inference-time method for providing domain-grounded, online, step-wise rewards to a frozen policy. In contrast to prior retrieval-augmented PRMs, PRA enables search-based decoding to rank and prune candidate trajectories at every generation step. Experiments on multiple medical reasoning benchmarks demonstrate that PRA consistently outperforms strong baselines, achieving 81.9% accuracy on MedQA with Qwen3-4B, a new state of the art at the 4B scale. Importantly, PRA generalizes to unseen frozen policy models ranging from 0.5B to 8B parameters, improving their accuracy by up to 25.7% without any policy model updates. More broadly, PRA suggests a paradigm in which frozen reasoners are decoupled from domain-specific reward modules, allowing the deployment of new backbones in complex domains without retraining.

Jiwoong Sohn, Tomasz Sternal, Kenneth Styppa +2

ETH Zürich, Switzerland · Heidelberg University, Germany

LLM Reasoning Process Reward Models Language Model Decoding Medical Reasoning

Apr 10, 2026

ASTRA: Adaptive Semantic Tree Reasoning Architecture for Complex Table Question Answering

Table serialization remains a critical bottleneck for Large Language Models (LLMs) in complex table question answering, hindered by challenges such as structural neglect, representation gaps, and reasoning opacity. Existing serialization methods fail to capture explicit hierarchies and lack schema flexibility, while current tree-based approaches suffer from limited semantic adaptability. To address these limitations, we propose ASTRA (Adaptive Semantic Tree Reasoning Architecture) including two main modules, AdaSTR and DuTR. First, we introduce AdaSTR, which leverages the global semantic awareness of LLMs to reconstruct tables into Logical Semantic Trees. This serialization explicitly models hierarchical dependencies and employs an adaptive mechanism to optimize construction strategies based on table scale. Second, building on this structure, we present DuTR, a dual-mode reasoning framework that integrates tree-search-based textual navigation for linguistic alignment and symbolic code execution for precise verification. Experiments on complex table benchmarks demonstrate that our method achieves state-of-the-art (SOTA) performance.

Xiaoke Guo, Songze Li, Zhiqiang Liu +4

Zhejiang University

Table QA LLM Reasoning

Apr 10, 2026

SPPO: Sequence-Level PPO for Long-Horizon Reasoning Tasks

Proximal Policy Optimization (PPO) is central to aligning Large Language Models (LLMs) in reasoning tasks with verifiable rewards. However, standard token-level PPO struggles in this setting due to the instability of temporal credit assignment over long Chain-of-Thought (CoT) horizons and the prohibitive memory cost of the value model. While critic-free alternatives like GRPO mitigate these issues, they incur significant computational overhead by requiring multiple samples for baseline estimation, severely limiting training throughput. In this paper, we introduce Sequence-Level PPO (SPPO), a scalable algorithm that harmonizes the sample efficiency of PPO with the stability of outcome-based updates. SPPO reformulates the reasoning process as a Sequence-Level Contextual Bandit problem, employing a decoupled scalar value function to derive low-variance advantage signals without multi-sampling. Extensive experiments on mathematical benchmarks demonstrate that SPPO significantly surpasses standard PPO and matches the performance of computation-heavy group-based methods, offering a resource-efficient framework for aligning reasoning LLMs.

Tianyi Wang, Yixia Li, Long Li +6

Southern University of Science and Technology · Beijing University of Posts and Telecommunications · INFLY TECH +3

RL for Language Model Reasoning Proximal Policy Optimization LLM Reasoning

Apr 9, 2026

SUPERNOVA: Eliciting General Reasoning in LLMs with Reinforcement Learning on Natural Instructions

Reinforcement Learning with Verifiable Rewards (RLVR) has substantially improved reasoning in formal domains such as mathematics and code, but extending these gains beyond STEM remains challenging. Extending RLVR beyond STEM is fundamentally constrained by the lack of high-quality verifiable training data. In this work, we introduce SUPERNOVA, a framework for curating RLVR data from natural instruction datasets, which are a rich source of expert-annotated data but are underexplored for RLVR training. Through 100+ controlled RL experiments, we systematically study how to utilize these dataset for RLVR and how data curation decisions affect downstream reasoning performance . In particular, we investigate three data designs: (a) source task selection, (b) task mixing, and (c) synthetic interventions. Our analysis reveals that source task selection has a significant impact on downstream reasoning performance. Moreover, selecting tasks based on their performance for individual target tasks outperforms strategies based on overall average performance and synthetic interventions do not improve reasoning. Guided by these insights, we construct SUPERNOVA, a high-quality RLVR dataset of 25K instances curated from natural instruction datasets. We show that training Qwen3-0.6B on SUPERNOVA outperforms the base Qwen3-0.6B, yielding a relative gain of 64.4pp on BigBench Extra Hard (BBEH), a challenging benchmark comprising 23 complex reasoning tasks. Importantly, we find that gains from SUPERNOVA generalize to unseen benchmarks, larger model scales, and newer model families. Overall, our findings provide practical insights for curating human-annotated resources to extend RLVR to general reasoning. Models, Data, Code at https://github.com/asuvarna31/supernova.

Ashima Suvarna, Kendrick Phan, Mehrab Beikzadeh +2

University of California, Los Angeles

RL for Language Model Reasoning LLM Reasoning Reinforcement Learning with Verifiable Rewards

Apr 9, 2026

When to Trust Tools? Adaptive Tool Trust Calibration For Tool-Integrated Math Reasoning

Large reasoning models (LRMs) have achieved strong performance enhancement through scaling test time computation, but due to the inherent limitations of the underlying language models, they still have shortcomings in tasks that require precise computation and extensive knowledge reserves. Tool-Integrated Reasoning (TIR) has emerged as a promising paradigm that incorporates tool call and execution within the reasoning trajectory. Although recent works have released some powerful open-source TIR models, our analysis reveals that these models still suffer from critical deficiencies. We find that when the reasoning of the model conflicts with the tool results, the model tends to believe in its own reasoning. And there are cases where the tool results are correct but are ignored by the model, resulting in incorrect answers, which we define as "Tool Ignored''. This indicates that the model does not know when to trust or ignore the tool. To overcome these limitations, We introduce Adaptive Tool Trust Calibration (ATTC), a novel framework that guides the model to adaptively choose to trust or ignore the tool results based on the confidence score of generated code blocks. The experimental results from various open-source TIR models of different sizes and across multiple datasets demonstrate that ATTC effectively reduces the "Tool Ignored" issue, resulting in a performance increase of 4.1% to 7.5%.

Ruotao Xu, Yixin Ji, Yu Luo +5

School of Computer Science and Technology, Soochow University · Department of Foundation Model, 2012 Labs, Huawei · Harbin Institute of Technology, Shenzhen (HITSZ)

Tool-Integrated Reasoning LLM Reasoning Large Reasoning Models

Apr 8, 2026

Multi-Turn Reasoning LLMs for Task Offloading in Mobile Edge Computing

Emerging computation-intensive applications impose stringent latency requirements on resource-constrained mobile devices. Mobile Edge Computing (MEC) addresses this challenge through task offloading. However, designing effective policies remains difficult due to dynamic task arrivals, time-varying channels, and the spatio-temporal coupling of server queues. Conventional heuristics lack adaptability, while Deep Reinforcement Learning (DRL) suffers from limited generalization and architectural rigidity, requiring retraining when network topology changes. Although Large Language Models (LLMs) offer semantic reasoning capabilities, standard Supervised Fine-Tuning (SFT) yields myopic policies that greedily minimize immediate latency without accounting for long-term system evolution. To address these limitations, we propose COMLLM, a generative framework that enables foresighted decision-making in MEC systems. COMLLM integrates Group Relative Policy Optimization (GRPO) with a Look-Ahead Collaborative Simulation (LACS) mechanism, which performs multi-step Monte Carlo rollouts while jointly modeling server queue dynamics. By incorporating these rollouts into the reward design, the framework captures the long-term impact of current decisions on future system states. Experimental results demonstrate that COMLLM achieves near-optimal latency and improved load-balancing fairness. Notably, it exhibits zero-shot topological scalability, allowing a model trained on small-scale networks to generalize to larger, unseen topologies without retraining, outperforming SFT, DRL, and heuristic baselines.

Ning Yang, Chuangxin Cheng, Haijun Zhang

Institute of Automation, Chinese Academy of Sciences, Beijing, 100190, China · School of Mechano-Electronic Engineering, Xidian University, Xi’an, 710071, China · School of Computer and Communication Engineering, University of Science and Technology Beijing, Beijing, 100083, China

Edge Computing LLM Reasoning RL for LLM Agents

Apr 8, 2026

STRIDE-ED: A Strategy-Grounded Stepwise Reasoning Framework for Empathetic Dialogue Systems

Empathetic dialogue requires not only recognizing a user's emotional state but also making strategy-aware, context-sensitive decisions throughout response generation. However, the lack of a comprehensive empathy strategy framework, explicit task-aligned multi-stage reasoning, and high-quality strategy-aware data fundamentally limits existing approaches, preventing them from effectively modeling empathetic dialogue as a complex, multi-stage cognitive and decision-making process. To address these challenges, we propose STRIDE-ED, a STRategy-grounded, Interpretable, and DEep reasoning framework that models Empathetic Dialogue through structured, strategy-conditioned reasoning. To support effective learning, we develop a strategy-aware data refinement pipeline integrating LLM-based annotation, multi-model consistency-weighted evaluation, and dynamic sampling to construct high-quality training data aligned with empathetic strategies. Furthermore, we adopt a two-stage training paradigm that combines supervised fine-tuning with multi-objective reinforcement learning to better align model behaviors with target emotions, empathetic strategies, and response formats. Extensive experiments demonstrate that STRIDE-ED generalizes across diverse open-source LLMs and consistently outperforms existing methods on both automatic metrics and human evaluations. Our data and code are publicly available at https://github.com/jicoder-nwpu/STRIDE-ED.

Hongru Ji, Yuyin Fan, Meng Zhao +3

School of Artificial Intelligence, OPtics and ElectroNics (iOPEN), Northwestern Polytechnical University, China · School of Artificial Intelligence and Big Data, Henan University of Technology, China · School of Computer Science, Northwestern Polytechnical University, China

Emotion-Aware Dialogue Generation LLM Reasoning

Apr 8, 2026

GCoT-Decoding: Unlocking Deep Reasoning Paths for Universal Question Answering

Chain-of-Thought reasoning can enhance large language models, but it requires manually designed prompts to guide the model. Recently proposed CoT-decoding enables the model to generate CoT-style reasoning paths without prompts, but it is only applicable to problems with fixed answer sets. To address this limitation, we propose a general decoding strategy GCoT-decoding that extends applicability to a broader range of question-answering tasks. GCoT-decoding employs a two-stage branching method combining Fibonacci sampling and heuristic error backtracking to generate candidate decoding paths. It then splits each path into a reasoning span and an answer span to accurately compute path confidence, and finally aggregates semantically similar paths to identify a consensus answer, replacing traditional majority voting. We conduct extensive experiments on six datasets covering both fixed and free QA tasks. Our method not only maintains strong performance on fixed QA but also achieves significant improvements on free QA, demonstrating its generality.

Guanran Luo, Wentao Qiu, Zhongquan Jian +2

School of Informatics, Xiamen University

LLM Reasoning Language Model Decoding

Apr 8, 2026

Reasoning Fails Where Step Flow Breaks

Large reasoning models (LRMs) that generate long chains of thought now perform well on multi-step math, science, and coding tasks. However, their behavior is still unstable and hard to interpret, and existing analysis tools struggle with such long, structured reasoning traces. We introduce Step-Saliency, which pools attention--gradient scores into step-to-step maps along the question--thinking--summary trajectory. Across several models, Step-Saliency reveals two recurring information-flow failures: Shallow Lock-in, where shallow layers over-focus on the current step and barely use earlier context, and Deep Decay, where deep layers gradually lose saliency on the thinking segment and the summary increasingly attends to itself and the last few steps. Motivated by these patterns, we propose StepFlow, a saliency-inspired test-time intervention that adjusts shallow saliency patterns measured by Step-Saliency via Odds-Equal Bridge and adds a small step-level residual in deep layers via Step Momentum Injection. StepFlow improves accuracy on math, science, and coding tasks across multiple LRMs without retraining, indicating that repairing information flow can recover part of their missing reasoning performance.

Xiaoyu Xu, Yulan Pan, Xiaosong Yuan +4

Shanghai Jiao Tong University · Fuzhou University · Jilin University

LLM Reasoning Large Reasoning Models Inference-Time Intervention LLM Interpretability

Apr 8, 2026

SHAPE: Stage-aware Hierarchical Advantage via Potential Estimation for LLM Reasoning

Process supervision has emerged as a promising approach for enhancing LLM reasoning, yet existing methods fail to distinguish meaningful progress from mere verbosity, leading to limited reasoning capabilities and unresolved token inefficiency. To address this, we propose Stage-aware Hierarchical Advantage via Potential Estimation (SHAPE), a framework that formalizes reasoning as a trajectory through a state space of empirical solvability. SHAPE introduces a hierarchical credit assignment mechanism: at the segment level, it employs a stage-aware advantage function to prioritize efficient breakthroughs in low-potential states; at the token level, it utilizes entropy-driven redistribution to sharpen execution signals. Extensive experiments in math reasoning across three base models and five benchmarks demonstrate that SHAPE achieves an average accuracy gain of 3% with 30% reduced token consumption.

Zhengyang Ai, Zikang Shan, Xiaodong Ai +3

Huawei Taylor Lab · Center for Data Science, Peking University · Shanghai University of Finance and Economics

LLM Reasoning Efficient Language Model Reasoning Process Supervision RL for Language Model Reasoning

Apr 7, 2026

SELFDOUBT: Uncertainty Quantification for Reasoning LLMs via the Hedge-to-Verify Ratio

Uncertainty estimation for reasoning language models remains difficult to deploy in practice: sampling-based methods are computationally expensive, while common single-pass proxies such as verbalized confidence or trace length are often inconsistent across models. This problem is compounded for proprietary reasoning APIs that expose neither logits nor intermediate token probabilities, leaving practitioners with no reliable uncertainty signal at inference time. We propose SELFDOUBT, a single-pass uncertainty framework that resolves this impasse by extracting behavioral signals directly from the reasoning trace itself. Our key signal, the Hedge-to-Verify Ratio (HVR), detects whether a reasoning trace contains uncertainty markers and, if so, whether they are offset by explicit selfchecking behavior. Unlike methods that require multiple sampled traces or model internals, SELFDOUBT operates on a single observed reasoning trajectory, making it suitable for latency- and cost-constrained deployment over any proprietary API. We evaluate SELFDOUBT across seven models and three multi-step reasoning benchmarks (BBH, GPQA-Diamond, and MMLU-Pro). Most notably, traces containing no hedging markers are correct 96% of the time, revealing an emergent high-precision confidence gate at zero additional cost. For the remaining cases, the full SELFDOUBT score significantly outperforms sampling-based semantic entropy at 10x lower inference cost. A deployment cascade combining both stages attains 90% accuracy at 71% coverage without any task-specific labels. These results establish SELFDOUBT as a scalable, production-ready foundation for uncertainty estimation over proprietary reasoning models.

Satwik Pandey, Suresh Raghu, Shashwat Pandey

Independent Researcher · Zillow Group

LLM Uncertainty Estimation Confidence Estimation in Language Models Confidence Estimation LLM Reasoning

Apr 7, 2026

The Master Key Hypothesis: Unlocking Cross-Model Capability Transfer via Linear Subspace Alignment

We investigate whether post-trained capabilities can be transferred across models without retraining, with a focus on transfer across different model scales. We propose the Master Key Hypothesis, which states that model capabilities correspond to directions in a low-dimensional latent subspace that induce specific behaviors and are transferable across models through linear alignment. Based on this hypothesis, we introduce UNLOCK, a training-free and label-free framework that extracts a capability direction by contrasting activations between capability-present and capability-absent Source variants, aligns it with a Target model through a low-rank linear transformation, and applies it at inference time to elicit the behavior. Experiments on reasoning behaviors, including Chain-of-Thought (CoT) and mathematical reasoning, demonstrate substantial improvements across model scales without training. For example, transferring CoT reasoning from Qwen1.5-14B to Qwen1.5-7B yields an accuracy gain of 12.1% on MATH, and transferring a mathematical reasoning direction from Qwen3-4B-Base to Qwen3-14B-Base improves AGIEval Math accuracy from 61.1% to 71.3%, surpassing the 67.8% achieved by the 14B post-trained model. Our analysis shows that the success of transfer depends on the capabilities learned during pre-training, and that our intervention amplifies latent capabilities by sharpening the output distribution toward successful reasoning trajectories.

Rishab Balasubramanian, Pin-Jie Lin, Rituraj Sharma +6

Virginia Tech · Amazon · UNC Chapel Hill

Transfer Learning Activation Steering Representation Alignment LLM Reasoning

Apr 7, 2026

LLM Reasoning as Trajectories: Step-Specific Representation Geometry and Correctness Signals

This work characterizes large language models' chain-of-thought generation as a structured trajectory through representation space. We show that mathematical reasoning traverses functionally ordered, step-specific subspaces that become increasingly separable with layer depth. This structure already exists in base models, while reasoning training primarily accelerates convergence toward termination-related subspaces rather than introducing new representational organization. While early reasoning steps follow similar trajectories, correct and incorrect solutions diverge systematically at late stages. This late-stage divergence enables mid-reasoning prediction of final-answer correctness with ROC-AUC up to 0.87. Furthermore, we introduce trajectory-based steering, an inference-time intervention framework that enables reasoning correction and length control based on derived ideal trajectories. Together, these results establish reasoning trajectories as a geometric lens for interpreting, predicting, and controlling LLM reasoning behavior.

Lihao Sun, Hang Dong, Bo Qiao +3

Microsoft

LLM Reasoning Representation Geometry in Language Models Language Model Steering

Apr 7, 2026

Towards Effective In-context Cross-domain Knowledge Transfer via Domain-invariant-neurons-based Retrieval

Large language models (LLMs) have made notable progress in logical reasoning, yet still fall short of human-level performance. Current boosting strategies rely on expert-crafted in-domain demonstrations, limiting their applicability in expertise-scarce domains, such as specialized mathematical reasoning, formal logic, or legal analysis. In this work, we demonstrate the feasibility of leveraging cross-domain demonstrating examples to boost the LLMs' reasoning performance. Despite substantial domain differences, many reusable implicit logical structures are shared across domains. In order to effectively retrieve cross-domain examples for unseen domains under investigation, in this work, we further propose an effective retrieval method, called domain-invariant neurons-based retrieval (DIN-Retrieval). Concisely, DIN-Retrieval first summarizes a hidden representation that is universal across different domains. Then, during the inference stage, we use the DIN vector to retrieve structurally compatible cross-domain demonstrations for the in-context learning. Experimental results in multiple settings for the transfer of mathematical and logical reasoning demonstrate that our method achieves an average improvement of 1.8 over the state-of-the-art methods \footnote{Our implementation is available at https://github.com/Leon221220/DIN-Retrieval}.

Jianzhi Yan, Zhiming Li, Le Liu +6

Harbin Institute of Technology, Shenzhen, China · Pengcheng Laboratory, Shenzhen, China

Cross-Domain Transfer Learning Retrieval-Augmented ICL LLM Reasoning Invariant Representation Learning

Apr 6, 2026

$π^2$ : Structure-Originated Reasoning Data Improves Long-Context Reasoning Ability of Large Language Models

We study a QA curation pipeline for improving long-context complex reasoning in large language models (LLMs). Our approach,

π^2

, constructs high-quality reasoning data through rigorous QA curation: 1) extracting and expanding tables from Wikipedia, 2) from the collected tables together with relevant metadata, generating complex reasoning questions whose answers are automatically determined and validated through dual-path code execution, 3) finally, back-translating chain-of-thoughts solutions grounded in realistic context. Supervised fine-tuning with gpt-oss-20b and Qwen3-4B-Instruct-2507 on

π^2

yields consistent improvements across four long-context reasoning benchmarks and our alike

π^2

-Bench, with average absolute accuracy gains of +6.25% and +3.37% respectively. Through deeper analyses, we observe that reasoning style contributes little, while faithful reasoning patterns discovered by back translation and grounded realistic long context, as

π^2

is designed for, are crucial for the improvement. Our code, data, and models are fully open-source at https://github.com/vtpss/pi-squared.

Quyet V. Do, Thinh Pham, Nguyen Nguyen +3

Virginia Tech, VA 24061, USA

Long-Context Reasoning in Language Models LLM Reasoning Synthetic Data Generation for Language Models

Apr 6, 2026

Are Latent Reasoning Models Easily Interpretable?

Latent reasoning models (LRMs) have attracted significant research interest due to their low inference cost (relative to explicit reasoning models) and theoretical ability to explore multiple reasoning paths in parallel. However, these benefits come at the cost of reduced interpretability: LRMs are difficult to monitor because they do not reason in natural language. This paper presents an investigation into LRM interpretability by examining two state-of-the-art LRMs. First, we find that latent reasoning tokens are often unnecessary for LRMs' predictions; on logical reasoning datasets, LRMs can almost always produce the same final answers without using latent reasoning at all. This underutilization of reasoning tokens may partially explain why LRMs do not consistently outperform explicit reasoning methods and raises doubts about the stated role of these tokens in prior work. Second, we demonstrate that when latent reasoning tokens are necessary for performance, we can decode gold reasoning traces up to 65-93% of the time for correctly predicted instances. This suggests LRMs often implement the expected solution rather than an uninterpretable reasoning process. Finally, we present a method to decode a verified natural language reasoning trace from latent tokens without knowing a gold reasoning trace a priori, demonstrating that it is possible to find a verified trace for a majority of correct predictions but only a minority of incorrect predictions. Our findings highlight that current LRMs largely encode interpretable processes, and interpretability itself can be a signal of prediction correctness.

Connor Dilgren, Sarah Wiegreffe

Department of Computer Science, University of Maryland, College Park, MD, USA

Implicit Reasoning in Language Models LLM Reasoning LLM Interpretability

Apr 6, 2026

Cog-DRIFT: Exploration on Adaptively Reformulated Instances Enables Learning from Hard Reasoning Problems

Reinforcement learning from verifiable rewards (RLVR) has improved the reasoning abilities of LLMs, yet a fundamental limitation remains: models cannot learn from problems that are too difficult to solve under their current policy, as these yield no meaningful reward signal. We propose a simple yet effective solution based on task reformulation. We transform challenging open-ended problems into cognitively simpler variants -- such as multiple-choice and cloze formats -- that preserve the original answer while reducing the effective search space and providing denser learning signals. These reformulations span a spectrum from discriminative to generative tasks, which we exploit to bootstrap learning: models first learn from structured, easier formats, and this knowledge transfers back to improve performance on the original open-ended problems. Building on this insight, we introduce Cog-DRIFT, a framework that constructs reformulated variants and organizes them into an adaptive curriculum based on difficulty. Training progresses from easier to harder formats, enabling the model to learn from problems that previously yielded zero signal under standard RL post-training. Cog-DRIFT not only improves on the originally unsolvable hard problems (absolute +10.11% for Qwen and +8.64% for Llama) but also generalizes well to other held-out datasets. Across 2 models and 6 reasoning benchmarks, our method consistently outperforms standard GRPO and strong guided-exploration baselines. On average, Cog-DRIFT shows +4.72% (Qwen) and +3.23% (Llama) improvements over the second-best baseline. We further show that Cog-DRIFT improves pass@k at test time, and the curriculum improves sample efficiency. Overall, our results highlight task reformulation and curriculum learning as an effective paradigm for overcoming the exploration barrier in LLM post-training.

Justin Chih-Yao Chen, Archiki Prasad, Zaid Khan +4

UNC Chapel Hill

RL for Language Model Reasoning LLM Reasoning Reinforcement Learning with Verifiable Rewards Curriculum RL

Apr 5, 2026

Position: Logical Soundness is not a Reliable Criterion for Neurosymbolic Fact-Checking with LLMs

As large language models (LLMs) are increasing integrated into fact-checking pipelines, formal logic is often proposed as a rigorous means by which to mitigate bias, errors and hallucinations in these models' outputs. For example, some neurosymbolic systems verify claims by using LLMs to translate natural language into logical formulae and then checking whether the proposed claims are logically sound, i.e. whether they can be validly derived from premises that are verified to be true. We argue that such approaches structurally fail to detect misleading claims due to systematic divergences between conclusions that are logically sound and inferences that humans typically make and accept. Drawing on studies in cognitive science and pragmatics, we present a typology of cases in which logically sound conclusions systematically elicit human inferences that are unsupported by the underlying premises. Consequently, we advocate for a complementary approach: leveraging human-like reasoning tendencies of LLMs as a feature rather than a bug, and using these models to validate the outputs of formal components in neurosymbolic systems against potentially misleading conclusions.

Jason Chan, Robert Gaizauskas, Zhixue Zhao

School of Computer Science, University of Sheffield, United Kingdom

Automated Fact-Checking Neuro-Symbolic Reasoning LLM Reasoning Pragmatic Reasoning in Language Models

Apr 5, 2026

Can LLMs Learn to Reason Robustly under Noisy Supervision?

Reinforcement Learning with Verifiable Rewards (RLVR) effectively trains reasoning models that rely on abundant perfect labels, but its vulnerability to unavoidable noisy labels due to expert scarcity remains critically underexplored. In this work, we take the first step toward a systematic analysis of noisy label mechanisms in RLVR. In contrast to supervised classification, most RLVR algorithms incorporate a rollout-based condition: a label's influence on training is contingent on whether the current policy can generate rollouts that realize it, a property that naturally extends to noisy labels. Based on this observation, we distinguish two types of noise: inactive noisy labels, which reduce data efficiency, and active noisy labels, which are reinforced and risk skewing the model toward incorrect distributions. From experiments on training with noisy samples, we identify an Early Correctness Coherence phenomenon: although noisy samples begin to lag behind in later stages, accuracy on both clean and noisy samples increases similarly in early training. Motivated by this dynamic, we propose Online Label Refinement (OLR), which progressively corrects potentially noisy labels with majority-voted answers when two conditions hold: a positive slope in the majority answer's rollout pass rate and stable historical consistency across updates, enabling gradual self-correction as the policy improves. We evaluate OLR on six in-distribution mathematical reasoning benchmarks (AIME24/25, AMC, MATH-500, Minerva, and Olympiad) and three out-of-distribution tasks (ARC-c, GPQA-diamond, and MMLU-pro). Across noise ratios from 0.1 to 0.9, OLR consistently improves robustness under both inactive and active noisy-label settings, achieving average gains of 3.6% to 3.9% on in-distribution benchmarks and 3.3% to 4.6% on out-of-distribution evaluations.

Shenzhi Yang, Guangcheng Zhu, Bowen Song +7

Zhejiang University · Ant Group · University of Wisconsin-Madison

LLM Reasoning Noisy-Label Learning Reinforcement Learning with Verifiable Rewards Learning with Noisy Labels

Apr 4, 2026

When Models Know More Than They Say: Probing Analogical Reasoning in LLMs

Analogical reasoning is a core cognitive faculty essential for narrative understanding. While LLMs perform well when surface and structural cues align, they struggle in cases where an analogy is not apparent on the surface but requires latent information, suggesting limitations in abstraction and generalisation. In this paper we compare a model's probed representations with its prompted performance at detecting narrative analogies, revealing an asymmetry: for rhetorical analogies, probing significantly outperforms prompting in open-source models, while for narrative analogies, they achieve a similar (low) performance. This suggests that the relationship between internal representations and prompted behavior is task-dependent and may reflect limitations in how prompting accesses available information.

Hope McGovern, Caroline Craig, Thomas Lippincott +1

Cambridge University · Northeastern University · Athenahealth +1

Analogical Reasoning for Language Models LLM Reasoning Language Model Probing LLM Prompting

Apr 4, 2026

TableVision: A Large-Scale Benchmark for Spatially Grounded Reasoning over Complex Hierarchical Tables

Structured tables are essential for conveying high-density information in professional domains such as finance, healthcare, and scientific research. Despite the progress in Multimodal Large Language Models (MLLMs), reasoning performance remains limited for complex tables with hierarchical layouts. In this paper, we identify a critical Perception Bottleneck through quantitative analysis. We find that as task complexity scales, the number of involved discrete visual regions increases disproportionately. This processing density leads to an internal "Perceptual Overload," where MLLMs struggle to maintain accurate spatial attention during implicit generation. To address this bottleneck, we introduce TableVision, a large-scale, trajectory-aware benchmark designed for spatially grounded reasoning. TableVision stratifies tabular tasks into three cognitive levels (Perception, Reasoning, and Analysis) across 13 sub-categories. By utilizing a rendering-based deterministic grounding pipeline, the dataset explicitly couples multi-step logical deductions with pixel-perfect spatial ground truths, comprising 6,799 high-fidelity reasoning trajectories. Our empirical results, supported by diagnostic probing, demonstrate that explicit spatial constraints significantly recover the reasoning potential of MLLMs. Furthermore, our two-stage decoupled framework achieves a robust 12.3% overall accuracy improvement on the test set. TableVision provides a rigorous testbed and a fresh perspective on the synergy between perception and logic in document understanding.

Xiaoyu Chen, Lu Dai, Hanqing Wang +6

The Hong Kong University of Science and Technology (Guangzhou) · The Hong Kong University of Science and Technology · The Chinese University of Hong Kong +1

Table Reasoning Spatial Reasoning Benchmarks VLM Reasoning Visually Grounded Reasoning LLM Reasoning

Apr 3, 2026

Vocabulary Dropout for Curriculum Diversity in LLM Co-Evolution

Co-evolutionary self-play, where one language model generates problems and another solves them, promises curriculum learning without human supervision. The promise breaks down early in practice. The proposer converges to a narrow distribution of problems that satisfy the reward function, and the collapsed curriculum teaches the solver little, stalling the loop. We introduce vocabulary dropout, a lightweight intervention that randomly masks the proposer's output logits during both policy training and curriculum generation. The mask is hard and non-stationary, so the proposer cannot lock into fixed token sequences. Training Qwen3-4B and Qwen3-8B on mathematical reasoning via R-Zero, vocabulary dropout sustains proposer diversity throughout training across lexical, semantic, and functional measures, and improves the solver by an average of +4.4 points at 8B with the largest gains on competition-level benchmarks. Explicit action-space constraints, filling the structural role that game rules fill in classical self-play, can keep co-evolution in language productive. Vocabulary dropout is one simple way to impose them.

Jacob Dineen, Aswin RRV, Zhikun Xu +1

Arizona State University

Curriculum RL RL for Language Model Reasoning LLM Reasoning

Apr 3, 2026

TABQAWORLD: Optimizing Multimodal Reasoning for Multi-Turn Table Question Answering

Multimodal reasoning has emerged as a powerful framework for enhancing reasoning capabilities of reasoning models. While multi-turn table reasoning methods have improved reasoning accuracy through tool use and reward modeling, they rely on fixed text serialization for table state readouts. This introduces representation errors in table encoding that significantly accumulate over multiple turns. Such accumulation is alleviated by tabular grounding methods in the expense of inference compute and cost, rendering real world deployment impractical. To address this, we introduce TABQAWORLD, a table reasoning framework that jointly optimizes tabular action through representation and estimation. For representation, TABQAWORLD employs an action-conditioned multimodal selection policy, which dynamically switches between visual and textual representations to maximize table state readout reliability. For estimation, TABQAWORLD optimizes stepwise reasoning trajectory through table metadata including dimension, data types and key values, safely planning trajectory and compressing low-complexity actions to reduce conversation turns and latency. Designed as a training-free framework, empirical evaluations show that TABQAWORLD achieves state-of-the-art performance with 4.87% accuracy improvements over baselines, with 5.42% accuracy gain and 33.35% inference latency reduction over static settings, establishing a new standard for reliable and efficient table reasoning.

Tung Sum Thomas Kwok, Xinyu Wang, Xiaofeng Lin +7

University of California, Los Angeles · SimpleWay · McGill University +2

Table Reasoning Table QA LLM Reasoning Efficient Multimodal Inference Multimodal Reasoning

Apr 3, 2026

R2-Write: Reflection and Revision for Open-Ended Writing with Deep Reasoning

While deep reasoning with long chain-of-thought has dramatically improved large language models in verifiable domains like mathematics, its effectiveness for open-ended tasks such as writing remains unexplored. In this paper, we conduct a systematic investigation revealing that existing mainstream reasoning models achieve limited gains on open-ended writing tasks. Our further analysis shows that these models lack deep reflection and revision patterns in open-ended writing, resulting in substantially smaller improvements compared to mathematical reasoning tasks. To address this limitation, we introduce R2-Write: an automated framework that synthesizes high-quality thinking trajectories enriched with explicit reflection and revision patterns through iterative writer-judge interaction. To prevent redundant reflections, we design a process reward mechanism that supervises reflection quality during reinforcement learning, improving both performance and token efficiency. Extensive experiments across multiple creative writing and deep-research benchmarks demonstrate significant improvements, validating that explicitly incorporating reflection and revision patterns unlocks deep reasoning capabilities for open-ended writing tasks.

Wanlong Liu, Bo Zhang, Chenliang Li +4

Tongyi Lab, Alibaba Group · Tsinghua University, Beijing, China

Open-Ended Generation LLM Reasoning LLM Self-Refinement RL for Language Model Reasoning

Apr 3, 2026

DeltaLogic: Minimal Premise Edits Reveal Belief-Revision Failures in Logical Reasoning Models

Reasoning benchmarks typically evaluate whether a model derives the correct answer from a fixed premise set, but they under-measure a closely related capability that matters in dynamic environments: belief revision under minimal evidence change. We introduce DeltaLogic, a benchmark transformation protocol that converts natural-language reasoning examples into short revision episodes. Each episode first asks for an initial conclusion under premises P, then applies a minimal edit δ(P), and finally asks whether the previous conclusion should remain stable or be revised. We instantiate DeltaLogic from FOLIO and ProofWriter and evaluate small causal language models with constrained label scoring. On a completed 30-episode Qwen evaluation subset, stronger initial reasoning still does not imply stronger revision behavior: Qwen3-1.7B reaches 0.667 initial accuracy but only 0.467 revision accuracy, with inertia rising to 0.600 on episodes where the gold label should change, while Qwen3-0.6B collapses into near universal abstention. There, Qwen3-4B preserves the same inertial failure pattern (0.650 initial, 0.450 revised, 0.600 inertia), whereas Phi-4-mini-instruct is substantially stronger (0.950 initial, 0.850 revised) but still exhibits non-trivial abstention and control instability. These results suggest that logical competence under fixed premises does not imply disciplined belief revision after local evidence edits. DeltaLogic therefore targets a distinct and practically important reasoning capability that complements existing logical inference and belief-updating benchmarks.

Amit Dhanda

Amazon

LLM Reasoning Belief Updating in LLMs Reasoning Consistency in Language Models Knowledge Conflicts in Language Models

Apr 3, 2026

Trivial Vocabulary Bans Improve LLM Reasoning More Than Deep Linguistic Constraints

A previous study reported that E-Prime (English without the verb "to be") selectively altered reasoning in language models, with cross-model correlations suggesting a structural signature tied to which vocabulary was removed. I designed a replication with active controls to test the proposed mechanism: cognitive restructuring through specific vocabulary-cognition mappings. The experiment tested five conditions (unconstrained control, E-Prime, No-Have, elaborated metacognitive prompt, neutral filler-word ban) across six models and seven reasoning tasks (N=15,600 trials, 11,919 after compliance filtering). Every prediction from the cognitive restructuring hypothesis was disconfirmed. All four treatments outperformed the control (83.0%), including both active controls predicted to show null effects. The neutral filler-word ban, banning words like "very" and "just" with no role in logical inference, produced the largest improvement (+6.7 pp), while E-Prime produced the smallest (+3.7 pp). The four conditions ranked in perfect inverse order of theoretical depth. The cross-model correlation signature did not replicate (mean r=0.005). These results are consistent with a simpler mechanism: any constraint that forces a model off its default generation path acts as an output regularizer, improving reasoning by disrupting fluent but shallow response patterns. The shallowest constraints work best because they impose monitoring load with minimal conceptual disruption. I present these findings as a case study in discovery through disconfirmation.

Rodney Jehu-Appiah

Apr 2, 2026

Do We Need Frontier Models to Verify Mathematical Proofs?

Advances in training, post-training, and inference-time methods have enabled frontier reasoning models to win gold medals in math competitions and settle challenging open problems. Gaining trust in the responses of these models requires that natural language proofs be checked for errors. LLM judges are increasingly being adopted to meet the growing demand for evaluating such proofs. While verification is considered easier than generation, what model capability does reliable verification actually require? We systematically evaluate four open-source and two frontier LLMs on datasets of human-graded natural language proofs of competition-level problems. We consider two key metrics: verifier accuracy and self-consistency (the rate of agreement across repeated judgments on the same proof). We observe that smaller open-source models are only up to ~10% behind frontier models in accuracy but they are up to ~25% more inconsistent. Furthermore, we see that verifier accuracy is sensitive to prompt choice across all models. We then demonstrate that the smaller models, in fact, do possess the mathematical capabilities to verify proofs at the level of frontier models, but they struggle to reliably elicit these capabilities with general judging prompts. Through an LLM-guided prompt search, we synthesize an ensemble of specialized prompts that overcome the specific failure modes of smaller models, boosting their performance by up to 9.1% in accuracy and 15.9% in self-consistency. These gains are realized across models and datasets, allowing models like Qwen3.5-35B to perform on par with frontier models such as Gemini 3.1 Pro for proof verification.

Aaditya Naik, Guruprerana Shabadi, Rajeev Alur +1

University of Pennsylvania, U.S.A.

LLM Input Optimization Reasoning Verification LLM Reasoning LLM Evaluation LLM Prompting Self-Consistency in Language Models