Efficient Language Model Reasoning

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This field asks how language models can solve tasks such as math, coding, science questions, and multi-hop retrieval without spending unnecessary computation. Common approaches compress or prune chain-of-thought, stop generation when answers stabilize, and adapt reasoning budgets to task difficulty; others use reinforcement learning, distillation, search, parallel sampling, or smaller-model routing. Newer work also explores latent reasoning and memory or KV-cache management to reduce the cost of generating and retaining explicit thoughts. The central tension is that extra reasoning can help on difficult problems but may waste resources, introduce errors, or even hurt accuracy, so methods are judged by both quality and cost on benchmarks such as GSM8K, MATH, AIME, and GPQA.

Latest papers

373 papers89 papers in the last four weeks, up 218% on the four weeks before. 0.5% of all new papers.

Apr 7, 2026

ETR: Entropy Trend Reward for Efficient Chain-of-Thought Reasoning

Chain-of-thought (CoT) reasoning improves large language model performance on complex tasks, but often produces excessively long and inefficient reasoning traces. Existing methods shorten CoTs using length penalties or global entropy reduction, implicitly assuming that low uncertainty is desirable throughout reasoning. We show instead that reasoning efficiency is governed by the trajectory of uncertainty. CoTs with dominant downward entropy trends are substantially shorter. Motivated by this insight, we propose Entropy Trend Reward (ETR), a trajectory-aware objective that encourages progressive uncertainty reduction while allowing limited local exploration. We integrate ETR into Group Relative Policy Optimization (GRPO) and evaluate it across multiple reasoning models and challenging benchmarks. ETR consistently achieves a superior accuracy-efficiency tradeoff, improving DeepSeek-R1-Distill-7B by 9.9% in accuracy while reducing CoT length by 67% across four benchmarks. Code is available at https://github.com/Xuan1030/ETR

Xuan Xiong, Huan Liu, Li Gu +4

University of Toronto · McMaster University · Concordia University +1

Efficient Language Model Reasoning CoT Reasoning RL for Language Model Reasoning Reward Shaping

Apr 6, 2026

Not All Turns Are Equally Hard: Adaptive Thinking Budgets For Efficient Multi-Turn Reasoning in Agents

As LLM reasoning performance plateaus, improving inference-time compute efficiency is crucial to mitigate overthinking and long thinking traces even for simple queries. Prior approaches including length regularization, adaptive routing, and difficulty-based budget allocation primarily focus on single-turn settings and fail to address the sequential dependencies inherent in multi-turn reasoning. In this work, we formulate multi-turn reasoning as a sequential compute allocation problem and model it as a multi-objective Markov Decision Process. We propose TAB: Turn-Adaptive Budgets, a budget allocation policy trained via Group Relative Policy Optimization (GRPO) that learns to maximize task accuracy while respecting global per-problem token constraints. Consequently, TAB takes as input the conversation history and learns to adaptively allocate smaller budgets to easier turns and save appropriate number of tokens for the crucial harder reasoning steps. Our experiments on diverse agentic benchmarks demonstrate that TAB achieves a superior accuracy-cost tradeoff saving up to 35% tokens and reducing latency up to 30% while maintaining accuracy over static and off-the-shelf LLM budget baselines. Further, for systems where a plan of all turns is available apriori, we propose TAB All-SubQ, a budget allocation policy that budgets tokens based on the conversation history and entire plan saving up to 40% tokens over baselines.

Neharika Jali, Anupam Nayak, Gauri Joshi

Carnegie Mellon University

Multi-Turn Language Model Reasoning Efficient Language Model Reasoning Inference-Time Compute Allocation LLM Inference Scheduling RL for Language Model Reasoning

Apr 6, 2026

Early Stopping for Large Reasoning Models via Confidence Dynamics

Large reasoning models rely on long chain-of-thought generation to solve complex problems, but extended reasoning often incurs substantial computational cost and can even degrade performance due to overthinking. A key challenge is determining when the model should stop reasoning and produce the final answer. In this work, we study the confidence of intermediate answers during reasoning and observe two characteristic behaviors: correct reasoning trajectories often reach high-confidence answers early, while incorrect rollouts tend to produce long, unproductive reasoning traces and exhibit less reliable confidence dynamics. Motivated by these observations, we propose CoDE-Stop (Confidence Dynamics Early Stop), an early stopping method that leverages the dynamics of intermediate answer confidence to decide when to terminate reasoning, requiring no additional training and easily integrating into existing models. We evaluate CoDE-Stop on diverse reasoning and science benchmarks across multiple models. Compared to prior early stopping methods, it achieves a more favorable accuracy-compute tradeoff and reduces total token usage by 25-50% compared to standard full-length reasoning. In addition, we provide analyses of confidence dynamics during reasoning, offering insights into how confidence changes in both correct and incorrect trajectories.

Parsa Hosseini, Sumit Nawathe, Mahdi Salmani +2

University of Maryland · University of Southern California

Early Stopping for Language Model Reasoning Early Stopping Efficient Language Model Reasoning Large Reasoning Models Overthinking in Language Models Confidence Estimation in Language Models

Apr 6, 2026

QED-Nano: Teaching a Tiny Model to Prove Hard Theorems

Proprietary AI systems have recently demonstrated impressive capabilities on complex proof-based problems, with gold-level performance reported at the 2025 International Mathematical Olympiad (IMO). However, the training pipelines behind these systems remain largely undisclosed, and their reliance on large "internal" models and scaffolds makes them expensive to run, difficult to reproduce, and hard to study or improve upon. This raises a central question: can small, open models also be trained to achieve competitive reasoning performance on difficult Olympiad-level math? In this paper, we answer this question by building QED-Nano, a 4B model post-trained for Olympiad-level proofs. Our training recipe has three stages: (1) supervised fine-tuning to imbue good proof-writing styles by distilling from DeepSeek-Math-V2, (2) reinforcement learning (RL) with rubric-based rewards, and (3) expanding RL with a reasoning cache, which decomposes long proofs into iterative summarize-and-refine cycles and enables stronger test-time reasoning. QED-Nano surpasses the proof-generation performance of much larger open models, including Nomos-1 and GPT-OSS-120B, and approaches the performance of proprietary models like Gemini 3 Pro, at a fraction of the inference cost. To support further research on open mathematical reasoning, we release the full QED-Nano pipeline, including the QED-Nano and QED-Nano-SFT models, the FineProofs-SFT and FineProofs-RL datasets, and the training and evaluation code.

LM-Provers, Yuxiao Qu, Amrith Setlur +6

CMU · Hugging Face · ETH Zurich +1

Mathematical Reasoning LLM Mathematical Reasoning Efficient Language Model Reasoning Automated Theorem Proving RL for Language Model Reasoning

Apr 5, 2026

Profile-Then-Reason: Bounded Semantic Complexity for Tool-Augmented Language Agents

Large language model agents that use external tools are often implemented through reactive execution, in which reasoning is repeatedly recomputed after each observation, increasing latency and sensitivity to error propagation. This work introduces Profile--Then--Reason (PTR), a bounded execution framework for structured tool-augmented reasoning, in which a language model first synthesizes an explicit workflow, deterministic or guarded operators execute that workflow, a verifier evaluates the resulting trace, and repair is invoked only when the original workflow is no longer reliable. A mathematical formulation is developed in which the full pipeline is expressed as a composition of profile, routing, execution, verification, repair, and reasoning operators; under bounded repair, the number of language-model calls is restricted to two in the nominal case and three in the worst case. Experiments against a ReAct baseline on six benchmarks and four language models show that PTR achieves the pairwise exact-match advantage in 16 of 24 configurations. The results indicate that PTR is particularly effective on retrieval-centered and decomposition-heavy tasks, whereas reactive execution remains preferable when success depends on substantial online adaptation.

Paulo Akira F. Enabe

Escola Politénica, University of São Paulo

Tool-Using Language Agents LLM Agents LLM Agent Workflow Optimization Efficient Language Model Reasoning LLM Agent Reliability

Apr 4, 2026

LightThinker++: From Reasoning Compression to Memory Management

Large language models (LLMs) excel at complex reasoning, yet their efficiency is limited by the surging cognitive overhead of long thought traces. In this paper, we propose LightThinker, a method that enables LLMs to dynamically compress intermediate thoughts into compact semantic representations. However, static compression often struggles with complex reasoning where the irreversible loss of intermediate details can lead to logical bottlenecks. To address this, we evolve the framework into LightThinker++, introducing Explicit Adaptive Memory Management. This paradigm shifts to behavioral-level management by incorporating explicit memory primitives, supported by a specialized trajectory synthesis pipeline to train purposeful memory scheduling. Extensive experiments demonstrate the framework's versatility across three dimensions. (1) LightThinker reduces peak token usage by 70% and inference time by 26% with minimal accuracy loss. (2) In standard reasoning, LightThinker++ slashes peak token usage by 69.9% while yielding a +2.42% accuracy gain under the same context budget for maximum performance. (3) Most notably, in long-horizon agentic tasks, it maintains a stable footprint beyond 80 rounds (a 60%-70% reduction), achieving an average performance gain of 14.8% across different complex scenarios. Overall, our work provides a scalable direction for sustaining deep LLM reasoning over extended horizons with minimal overhead.

Yuqi Zhu, Jintian Zhang, Zhenjie Wan +7

Zhejiang University · Ant Group

Memory Management for LLM Agents Efficient Language Model Reasoning CoT Compression LLM Inference Acceleration Agent Memory Management Memory-Augmented Language Model Agents

Apr 3, 2026

NeuReasoner: Towards Explainable, Controllable, and Unified Reasoning via Mixture-of-Neurons

Large Reasoning Models (LRMs) have recently achieved remarkable success in complex reasoning tasks. However, closer scrutiny reveals persistent failure modes compromising performance and cost: I) Intra-step level, marked by calculation or derivation errors; II) Inter-step level, involving oscillation and stagnation; and III) Instance level, causing maladaptive over-thinking. Existing endeavors target isolated levels without unification, while their black-box nature and reliance on RL hinder explainability and controllability. To bridge these gaps, we conduct an in-depth white-box analysis, identifying key neurons (Mixture of Neurons, MoN) and their fluctuation patterns associated with distinct failures. Building upon these insights, we propose NeuReasoner, an explainable, controllable, and unified reasoning framework driven by MoN. Technically, NeuReasoner integrates lightweight MLPs for failure detection with a special token-triggered self-correction mechanism learned via SFT. During inference, special tokens are inserted upon failure detection to actuate controllable remedial behaviors. Extensive evaluations across six benchmarks, six backbone models (8B~70B) against nine competitive baselines, demonstrate that NeuReasoner achieves performance gains of up to 27.0% while reducing token consumption by 19.6% ~ 63.3%.

Haonan Dong, Kehan Jiang, Haoran Ye +3

State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University · School of Software and Microelectronics, Peking University

Large Reasoning Models Efficient Language Model Reasoning LLM Self-Correction LLM Interpretability

Apr 3, 2026

FoE: Forest of Errors Makes the First Solution the Best in Large Reasoning Models

Recent Large Reasoning Models (LRMs) like DeepSeek-R1 have demonstrated remarkable success in complex reasoning tasks, exhibiting human-like patterns in exploring multiple alternative solutions. Upon closer inspection, however, we uncover a surprising phenomenon: The First is The Best, where alternative solutions are not merely suboptimal but potentially detrimental. This observation challenges widely accepted test-time scaling laws, leading us to hypothesize that errors within the reasoning path scale concurrently with test time. Through comprehensive empirical analysis, we characterize errors as a forest-structured Forest of Errors (FoE) and conclude that FoE makes the First the Best, which is underpinned by rigorous theoretical analysis. Leveraging these insights, we propose RED, a self-guided efficient reasoning framework comprising two components: I) Refining First, which suppresses FoE growth in the first solution; and II) Discarding Subs, which prunes subsequent FoE via dual-consistency. Extensive experiments across five benchmarks and six backbone models demonstrate that RED outperforms eight competitive baselines, achieving performance gains of up to 19.0% while reducing token consumption by 37.7% ~ 70.4%. Moreover, comparative experiments on FoE metrics shed light on how RED achieves effectiveness.

Kehan Jiang, Haonan Dong, Zhaolu Kang +2

School of Software and Microelectronics, Peking University · State Key Laboratory of General Artificial Intelligence, School of Intelligence Science and Technology, Peking University

Efficient Language Model Reasoning Large Reasoning Models Test-Time Scaling Reasoning Consistency in Language Models

Apr 3, 2026

Evaluating the Formal Reasoning Capabilities of Large Language Models through Chomsky Hierarchy

The formal reasoning capabilities of LLMs are crucial for advancing automated software engineering. However, existing benchmarks for LLMs lack systematic evaluation based on computation and complexity, leaving a critical gap in understanding their formal reasoning capabilities. Therefore, it is still unknown whether SOTA LLMs can grasp the structured, hierarchical complexity of formal languages as defined by Computation Theory. To address this, we introduce ChomskyBench, a benchmark for systematically evaluating LLMs through the lens of Chomsky Hierarchy. Unlike prior work that uses vectorized classification for neural networks, ChomskyBench is the first to combine full Chomsky Hierarchy coverage, process-trace evaluation via natural language, and deterministic symbolic verifiability. ChomskyBench is composed of a comprehensive suite of language recognition and generation tasks designed to test capabilities at each level. Extensive experiments indicate a clear performance stratification that correlates with the hierarchy's levels of complexity. Our analysis reveals a direct relationship where increasing task difficulty substantially impacts both inference length and performance. Furthermore, we find that while larger models and advanced inference methods offer notable relative gains, they face severe efficiency barriers: achieving practical reliability would require prohibitive computational costs, revealing that current limitations stem from inefficiency rather than absolute capability bounds. A time complexity analysis further indicates that LLMs are significantly less efficient than traditional algorithmic programs for these formal tasks. These results delineate the practical limits of current LLMs, highlight the indispensability of traditional software tools, and provide insights to guide the development of future LLMs with more powerful formal reasoning capabilities.

Yihong Dong, Jianha Xiao, Xue Jiang +7

Peking University, China · Wuhan University, China

LLM Evaluation Efficient Language Model Reasoning LLM Inference Efficiency

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

Brief Is Better: Non-Monotonic Chain-of-Thought Budget Effects in Function-Calling Language Agents

How much should a language agent think before taking action? Chain-of-thought (CoT) reasoning is widely assumed to improve agent performance, but the relationship between reasoning length and accuracy in structured tool-use settings remains poorly understood. We present a systematic study of CoT budget effects on function-calling agents, sweeping six token budgets (0--512) across 200 tasks from the Berkeley Function Calling Leaderboard v3 Multiple benchmark. Our central finding is a striking non-monotonic pattern on Qwen2.5-1.5B-Instruct: brief reasoning (32 tokens) dramatically improves accuracy by 45% relative over direct answers, from 44.0% to 64.0%, while extended reasoning (256 tokens) degrades performance well below the no-CoT baseline, to 25.0% (McNemar p < 0.001). A three-way error decomposition reveals the mechanism. At d = 0, 30.5% of tasks fail because the model selects the wrong function from the candidate set; brief CoT reduces this to 1.5%, effectively acting as a function-routing step, while long CoT reverses the gain, yielding 28.0% wrong selections and 18.0% hallucinated functions at d = 256. Oracle analysis shows that 88.6% of solvable tasks require at most 32 reasoning tokens, with an average of 27.6 tokens, and a finer-grained sweep indicates that the true optimum lies at 8--16 tokens. Motivated by this routing effect, we propose Function-Routing CoT (FR-CoT), a structured brief-CoT method that templates the reasoning phase as "Function: [name] / Key args: [...]," forcing commitment to a valid function name at the start of reasoning. FR-CoT achieves accuracy statistically equivalent to free-form d = 32 CoT while reducing function hallucination to 0.0%, providing a structural reliability guarantee without budget tuning.

Xuan Qi

IIIS, Tsinghua University

Efficient Language Model Reasoning LLM Agent Reliability

Apr 2, 2026

Apriel-Reasoner: RL Post-Training for General-Purpose and Efficient Reasoning

Building general-purpose reasoning models using reinforcement learning with verifiable rewards (RLVR) across diverse domains has been widely adopted by frontier open-weight models. However, their training recipes and domain mixtures are often not disclosed. Joint optimization across domains poses significant challenges: domains vary widely in rollout length, problem difficulty, and sample efficiency. Further, models with long chain-of-thought traces increase inference cost and latency, making efficiency critical for practical deployment. We present Apriel-Reasoner, trained with a reproducible multi-domain RL post-training recipe on Apriel-Base, a 15B-parameter open-weight LLM, across five domains using public datasets: mathematics, code generation, instruction following, logical puzzles, and function calling. We introduce adaptive domain sampling that preserves target completed-rollout ratios despite heterogeneous rollout dynamics, and a difficulty-aware length penalty that, at no additional training overhead, encourages longer reasoning for difficult problems and shorter traces for easy ones. Trained with a strict 16K-token output budget, Apriel-Reasoner remains effective at a 32K output budget and improves over Apriel-Base on AIME 2025, GPQA, MMLU-Pro, and LiveCodeBench while producing 30-50% shorter reasoning traces. Among the evaluated open-weight models of similar scale, it improves the accuracy-token tradeoff using a fully public-data recipe.

Rafael Pardinas, Ehsan Kamalloo, David Vazquez +1

ServiceNow AI Research

LLM Inference Efficiency RL for Language Model Reasoning Efficient Language Model Reasoning Reinforcement Learning with Verifiable Rewards RL Post-Training Large Reasoning Models

Apr 2, 2026

On the Role of Reasoning Patterns in the Generalization Discrepancy of Long Chain-of-Thought Supervised Fine-Tuning

Supervised Fine-Tuning (SFT) on long Chain-of-Thought (CoT) trajectories has become a pivotal phase in building large reasoning models. However, how CoT trajectories from different sources influence the generalization performance of models remains an open question. In this paper, we conduct a comparative study using two sources of verified CoT trajectories generated by two competing models, DeepSeek-R1-0528 and gpt-oss-120b, with their problem sets controlled to be identical. Despite their comparable performance, we uncover a striking paradox: lower training loss does not translate to better generalization. SFT on DeepSeek-R1-0528 data achieves remarkably lower training loss, yet exhibits significantly worse generalization performance on reasoning benchmarks compared to those trained on gpt-oss-120b. To understand this paradox, we perform a multi-faceted analysis probing token-level SFT loss and step-level reasoning behaviors. Our analysis reveals a difference in reasoning patterns. gpt-oss-120b exhibits highly convergent and deductive trajectories, whereas DeepSeek-R1-0528 favors a divergent and branch-heavy exploration pattern. Consequently, models trained with DeepSeek-R1 data inherit inefficient exploration behaviors, often getting trapped in redundant exploratory branches that hinder them from reaching correct solutions. Building upon this insight, we propose a simple yet effective remedy of filtering out frequently branching trajectories to improve the generalization of SFT. Experiments show that training on selected DeepSeek-R1-0528 subsets surprisingly improves reasoning performance by up to 5.1% on AIME25, 5.5% on BeyondAIME, and on average 3.6% on five benchmarks.

Zhaoyi Li, Xiangyu Xi, Zhengyu Chen +6

University of Science and Technology of China · Meituan LongCat Team · City University of Hong Kong +1

Supervised Fine-Tuning Efficient Language Model Reasoning Overthinking in Language Models

Apr 2, 2026

ThinknCheck: Grounded Claim Verification with Compact, Reasoning-Driven, and Interpretable Models

We present ThinknCheck, a 1B-parameter verifier for grounded claim verification that first produces a short, structured rationale and then a binary verdict. We construct LLMAggreFact-Think, a 24.1k reasoning-augmented training set derived from LLMAggreFact, and fine-tune a 4-bit Gemma3 model to follow this format. On LLMAggreFact, ThinknCheck attains 78.1 balanced accuracy (BAcc), surpassing MiniCheck-7B (77.4) with 7x fewer parameters; removing the reasoning step reduces BAcc to 57.5. On SciFact, ThinknCheck reaches 64.7 BAcc, a +14.7 absolute gain over MiniCheck-7B. By contrast, zero-shot chain-of-thought on the base Gemma3-1B harms accuracy relative to direct answers, and preference optimization with a simple format+accuracy reward underperforms supervised reasoning. To probe the latter, we introduce GSMClaims and a domain-specialized variant, ThinknCheck-Science, which improves across benchmarks, including 61.0% accuracy on GSMClaims. Overall, explicit, supervised reasoning enables compact verifiers that are competitive while remaining resource-efficient and interpretable.

Delip Rao, Feijiang Han, Chris Callison-Burch

University of Pennsylvania, Philadelphia, PA, USA

Claim Verification LLM Answer Verification Automated Fact-Checking Efficient Language Model Reasoning

Apr 1, 2026

Adaptive Stopping for Multi-Turn LLM Reasoning

Large Language Models (LLMs) increasingly rely on multi-turn reasoning and interaction, such as adaptive retrieval-augmented generation (RAG) and ReAct-style agents, to answer difficult questions. These methods improve accuracy by iteratively retrieving information, reasoning, or acting, but introduce a key challenge: When should the model stop? Existing approaches rely on heuristic stopping rules or fixed turn budgets and provide no formal guarantees that the final prediction still contains the correct answer. This limitation is particularly problematic in high-stakes domains such as finance and healthcare, where unnecessary turns increase cost and latency, while stopping too early risks incorrect decisions. Conformal prediction (CP) provides formal coverage guarantees, but existing LLM-CP methods only apply to a single model output and cannot handle multi-turn pipelines with adaptive stopping. To address this gap, we propose Multi-Turn Language Models with Conformal Prediction (MiCP), the first CP framework for multi-turn reasoning. MiCP allocates different error budgets across turns, enabling the model to stop early while maintaining an overall coverage guarantee. We demonstrate MiCP on adaptive RAG and ReAct, where it achieves the target coverage on both single-hop and multi-hop question answering benchmarks while reducing the number of turns, inference cost, and prediction set size. We further introduce a new metric that jointly evaluates coverage validity and answering efficiency.

Xiaofan Zhou, Huy Nguyen, Bo Yu +2

Department of Computer Science, University of Illinois Chicago, Chicago, IL 60607, USA · Data science, Augustana College, Rock Island, IL 61201, USA · Department of Civil and Environmental Engineering, University of Utah, Salt Lake City, UT 84112, USA

Multi-Turn Language Model Reasoning Efficient Language Model Reasoning Conformal Prediction

Apr 1, 2026

Online Reasoning Calibration: Test-Time Training Enables Generalizable Conformal LLM Reasoning

While test-time scaling has enabled large language models to solve highly difficult tasks, state-of-the-art results come at exorbitant compute costs. These inefficiencies can be attributed to the miscalibration of post-trained language models, and the lack of calibration in popular sampling techniques. Here, we present Online Reasoning Calibration (ORCA), a framework for calibrating the sampling process that draws upon conformal prediction and test-time training. Specifically, we introduce a meta-learning procedure that updates the calibration module for each input. This allows us to provide valid confidence estimates under distributional shift, e.g. in thought patterns that occur across different stages of reasoning, or in prompt distributions between model development and deployment. ORCA not only provides theoretical guarantees on conformal risks, but also empirically shows higher efficiency and generalization across different reasoning tasks. At risk level

δ=0.1

, ORCA improves Qwen2.5-32B efficiency on in-distribution tasks with savings up to 47.5% with supervised labels and 40.7% with self-consistency labels. Under zero-shot out-of-domain settings, it improves MATH-500 savings from 24.8% of the static calibration baseline to 67.0% while maintaining a low empirical error rate, and the same trend holds across model families and downstream benchmarks. Our code is publicly available at https://github.com/wzekai99/ORCA.

Cai Zhou, Zekai Wang, Menghua Wu +6

Department of Electrical Engineering and Computer Science (MIT EECS) · Computer Science and Artificial Intelligence Laboratory (MIT CSAIL) · Laboratory for Information and Decision Systems (MIT LIDS) +1

Conformal Prediction for Language Models Language Model Calibration Confidence Estimation in Language Models Efficient Language Model Reasoning Conformal Prediction Test-Time Training

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

Think Anywhere in Code Generation

Recent advances in reasoning Large Language Models (LLMs) have primarily relied on upfront thinking, where reasoning occurs before final answer. However, this approach suffers from critical limitations in code generation, where upfront thinking is often insufficient as problems' full complexity only reveals itself during code implementation. Moreover, it cannot adaptively allocate reasoning effort throughout the code generation process where difficulty varies significantly. In this paper, we propose Think-Anywhere, a novel reasoning mechanism that enables LLMs to invoke thinking on-demand at any token position during code generation. We achieve Think-Anywhere by first teaching LLMs to imitate the reasoning patterns through cold-start training, then leveraging outcome-based RL rewards to drive the model's autonomous exploration of when and where to invoke reasoning. Extensive experiments on four mainstream code generation benchmarks (i.e., LeetCode, LiveCodeBench, HumanEval, and MBPP) show that Think-Anywhere achieves state-of-the-art performance over both existing reasoning methods and recent post-training approaches, while demonstrating consistent generalization across diverse LLMs. Our analysis further reveals that Think-Anywhere enables the model to adaptively invoke reasoning at high-entropy positions, providing enhanced interpretability.

Xue Jiang, Tianyu Zhang, Ge Li +8

School of Computer Science, Peking University · Tongyi Lab, Alibaba Group

LLM Code Generation Efficient Language Model Reasoning

Mar 30, 2026

CoT2-Meta: Budgeted Metacognitive Control for Test-Time Reasoning

Recent test-time reasoning methods improve performance by generating more candidate chains or searching over larger reasoning trees, but they typically lack explicit control over when to expand, what to prune, how to repair, and when to abstain. We introduce CoT2-Meta, a training-free metacognitive reasoning framework that combines object-level chain-of-thought generation with meta-level control over partial reasoning trajectories. The framework integrates four components: strategy-conditioned thought generation, tree-structured search, an online process oracle for step-level reasoning evaluation, and a meta-controller that allocates computation through expansion, pruning, repair, stopping, and fallback decisions. Under matched inference budgets, CoT2-Meta consistently outperforms strong single-path, sampling-based, and search-based baselines, including ReST-MCTS. On the default backbone, it achieves 92.8 EM on MATH, 90.4 accuracy on GPQA, 98.65 EM on GSM8K, 75.8 accuracy on BBEH, 85.6 accuracy on MMMU-Pro, and 48.8 accuracy on HLE, with gains over the strongest non-CoT2-Meta baseline of +3.6, +5.2, +1.15, +2.0, +4.3, and +4.3 points, respectively. Beyond these core results, the framework remains effective across a broader 15-benchmark suite spanning knowledge and QA, multi-hop reasoning, coding, and out-of-distribution evaluation. Additional analyses show better compute scaling, improved calibration, stronger selective prediction, targeted repair behavior, and consistent gains across backbone families. These results suggest that explicit metacognitive control is a practical design principle for reliable and compute-efficient test-time reasoning systems.

Siyuan Ma, Bo Gao, Zikai Xiao +6

Nanyang Technological University · Carnegie Mellon University · Zhejiang University +5

Efficient Language Model Reasoning Metacognition in Language Models Inference-Time Search Inference-Time Compute Allocation

Mar 29, 2026

Avoiding Overthinking and Underthinking: Curriculum-Aware Budget Scheduling for LLMs

Scaling test-time compute via extended reasoning has become a key paradigm for improving the capabilities of large language models (LLMs). However, existing approaches optimize reasoning under fixed or uniformly sampled token budgets, ignoring the fundamental mismatch between problem difficulty and allocated compute. This leads to overthinking on easy problems and underthinking on hard ones, resulting in suboptimal token efficiency across diverse reasoning scenarios. In this paper, we propose Budget-Adaptive Curriculum Reasoning (BCAE), a unified framework that jointly optimizes reasoning quality and token efficiency through three synergistic components: (1) a budget-conditioned unified policy that embeds the token budget as a continuous conditioning signal, eliminating the need for decoupled thinking and summarization strategies; (2) a curriculum-aware budget scheduler that adaptively shifts the training budget distribution from easy to hard problems based on real-time learning progress; and (3) a truncation-aware dense reward mechanism that provides fine-grained credit assignment at intermediate reasoning steps via process-level verification. We further introduce Budget-Conditioned Advantage Estimation (BCAE), a novel variance reduction technique that conditions the advantage baseline on the sampled budget, yielding more stable policy gradients. Experiments on mathematical reasoning benchmarks (MATH, GSM8K, AIME, and Minerva Math) demonstrate that BACR consistently outperforms other strong baselines across all token budgets, achieving up to 8.3% accuracy improvement under tight budgets while reducing average token consumption by 34% compared to unconstrained reasoning.

Amirul Rahman, Aisha Karim, Kenji Nakamura +1

University of Malaya

Efficient Language Model Reasoning Inference-Time Compute Allocation Overthinking in Language Models RL for Language Model Reasoning Numerical Reasoning in Language Models

Mar 25, 2026

Reaching Beyond the Mode: RL for Distributional Reasoning in Language Models

Given a question, a language model (LM) implicitly encodes a distribution over possible answers. In practice, post-training procedures for LMs often collapse this distribution onto a single dominant mode. While this is generally not a problem for benchmark-style evaluations that assume one correct answer, many real-world tasks inherently involve multiple valid answers or irreducible uncertainty. Examples include medical diagnosis, ambiguous question answering, and settings with incomplete information. In these cases, we would like LMs to generate multiple plausible hypotheses, ideally with confidence estimates for each one, and without computationally intensive repeated sampling to generate non-modal answers. This paper describes a multi-answer reinforcement learning approach for training LMs to perform distributional reasoning over multiple answers during inference. We modify the RL objective to enable models to explicitly generate multiple candidate answers in a single forward pass, internalizing aspects of inference-time search into the model's generative process. Across question-answering, medical diagnostic, and coding benchmarks, we observe improved diversity, coverage, and set-level calibration scores compared to single answer trained baselines. Models trained with our approach require fewer tokens to generate multiple answers than competing approaches. On coding tasks, they are also substantially more accurate. These results position multi-answer RL as a principled and compute-efficient alternative to inference-time scaling procedures such as best-of-k. Code and more information can be found at https://multi-answer-rl.github.io/.

Isha Puri, Mehul Damani, Idan Shenfeld +3

Massachusetts Institute of Technology

RL for Language Model Reasoning Efficient Language Model Reasoning

Mar 24, 2026

Caterpillar of Thoughts: The Optimal Test-Time Algorithm for Large Language Models

Large language models (LLMs) can often produce substantially better outputs when allowed to use additional test-time computation, such as sampling, chain of thought, backtracking, or revising partial solutions. Despite the growing empirical success of such techniques, there is limited theoretical understanding of how inference time computation should be structured, or what constitutes an optimal use of a fixed computation budget. We model test-time computation as an algorithm interacting with a Markov chain: at any point, the algorithm may resume generation from any previously observed state. That is, unlike standard Markov chains where the states are drawn passively, we allow the algorithm to backtrack to any previously observed state of the Markov chain at any time. Many of the existing test-time algorithms, such as Chain-of-Thought (CoT) (Wei et al., 2023), Tree-of-Thoughts (ToT) (Yao et al., 2023), or Best-of-

k

(Brown et al., 2024) could be seen as specific algorithms in this model. We prove that while backtracking can reduce the number of generations exponentially, a very limited form of backtracking is theoretically sufficient. Namely, we show that the optimal algorithm always generates a caterpillar tree. That is, if we remove the leaves of the state tree generated by the optimal algorithm, we obtain a path. Motivated by our characterization of the optimal algorithm, we present Caterpillar of Thoughts (CaT), a new test-time computation algorithm, reducing the number of token/state generations. Our empirical evaluation shows that CaT, compared to ToT, achieves a better success rate while also reducing the number of token generations.

Amir Azarmehr, Soheil Behnezhad, Alma Ghafari

Northeastern University

Inference-Time Optimization Efficient Language Model Reasoning Test-Time Scaling LLM Inference Acceleration

Mar 23, 2026

ROM: Real-time Overthinking Mitigation via Streaming Detection and Intervention

Large reasoning models (LRMs) often suffer from overthinking, continuing with redundant verification and repeated attempts even after reaching a correct solution. This wastes computation and can overturn an initially correct answer. We show that the transition from productive to redundant reasoning is decodable from late-layer hidden states. These representations separate the two phases around first-correct-solution boundaries beyond what position and lexical controls explain, and distinguish correct from incorrect solution endings. Building on this finding, we propose ROM (Real-time Overthinking Mitigation), which uses a lightweight streaming detector (0.07--0.25% of backbone parameters) to monitor a frozen LRM and intervene at well-formed reasoning boundaries without answer extraction or probe decoding. Counterfactual Self-Correction (CSC) augments detector training with wrong

\rightarrow

correct trajectories to preserve useful self-correction. Heads are trained separately for each backbone using shared MATH500 supervision and transfer zero-shot to four unseen benchmarks. Evaluated against ten baselines across five backbones from three families and five benchmarks, ROM

_{\text{CSC}}

reduces response length by 28--77% (45% on average), with significant reductions in all 25 settings and accuracy matching or exceeding vanilla decoding in 22. Measurements on two backbones further show 20--70% lower end-to-end latency with less than 0.5% detector overhead per decoding step. Code is available at https://github.com/SaFo-Lab/ROM.

Xinyan Wang, Xiaogeng Liu, Ming Pei +1

University of Wisconsin–Madison · Johns Hopkins University

Early Stopping for Language Model Reasoning Overthinking in Language Models Efficient Language Model Reasoning Large Reasoning Models LLM Inference Acceleration

Mar 23, 2026

Data-Free Layer-Adaptive Merging via Fisher Information for Long-to-Short Reasoning LLMs

Model merging has emerged as a practical approach to combine capabilities of specialized large language models (LLMs) without additional training. In the Long-to-Short (L2S) scenario, merging a base model with a long-chain-of-thought reasoning model aims to preserve reasoning accuracy while reducing output length. Existing methods rely on Task Arithmetic and its variants, which implicitly assume that model outputs vary linearly with the merging coefficient -- an assumption we show is systematically violated in L2S settings. We provide the first theoretical justification for layer-adaptive merging: we prove that merging error is bounded by a term proportional to the per-layer Hessian norm (Proposition~1), and establish that the Fisher Information Matrix (FIM) is a principled, computable proxy for this bound via the Fisher-Hessian equivalence at local optima. Building on this theory, we propose FIM-Merging, which computes diagonal FIM using only random token inputs (no domain-specific calibration data required) and uses it to assign per-layer merging coefficients. On the 7B L2S benchmark, FIM-TIES achieves state-of-the-art performance on five out of six evaluation benchmarks, including a +6.2 point gain on MATH500 over ACM-TIES (90.2 vs.\ 84.0), while requiring no calibration data. On the 1.5B benchmark, FIM-TIES achieves an average accuracy of 47.3, surpassing the previous best ACM-TIES (43.3) by +3.9 points, while reducing average response length by 91.9% relative to the long-CoT model. Our framework also provides a unified theoretical explanation for why existing layer-adaptive methods such as ACM empirically outperform uniform merging.

Tian Xia

Language Model Merging Model Merging Efficient Language Model Reasoning CoT Compression

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

Mar 20, 2026

The $\mathbf{Y}$ -Combinator for LLMs: Solving Long-Context Rot with $λ$ -Calculus

LLMs are increasingly used as general-purpose reasoners, but long inputs remain bottlenecked by a fixed context window. Recursive Language Models (RLMs) address this by externalising the prompt and recursively solving subproblems. Yet existing RLMs depend on an open-ended read-eval-print loop (REPL) in which the model generates arbitrary control code, making execution difficult to verify, predict, and analyse. We introduce

λ

-RLM, a framework for long-context reasoning that replaces free-form recursive code generation with a typed functional runtime grounded in

λ

-calculus. It executes a compact library of pre-verified combinators and uses neural inference only on bounded leaf subproblems, turning recursive reasoning into a structured functional program with explicit control flow. We show that

λ

-RLM admits formal guarantees absent from standard RLMs, including termination, closed-form cost bounds, controlled accuracy scaling with recursion depth, and an optimal partition rule under a simple cost model. Empirically, across four long-context reasoning tasks and nine base models,

λ

-RLM outperforms standard RLM in 29 of 36 model-task comparisons, improves average accuracy by up to +21.9 points across model tiers, and reduces latency by up to 4.1x. These results show that typed symbolic control yields a more reliable and efficient foundation for long-context reasoning than open-ended recursive code generation. The complete implementation of

λ

-RLM, is open-sourced for the community at: https://github.com/lambda-calculus-LLM/lambda-RLM.

Amartya Roy, Rasul Tutunov, Xiaotong Ji +2

The School of Interdisciplinary Research, Indian Institute of Technology (IIT) Delhi, Robert Bosch GmbH, India · Huawei Noah’s Ark Lab · Huawei Noah’s Ark +1

Long-Context Reasoning in Language Models Long-Context Language Model Inference Efficient Language Model Reasoning Recursive Language Models

Mar 20, 2026

LoopRPT: Reinforcement Pre-Training for Looped Language Models

Looped language models (LoopLMs) perform iterative latent computation to refine internal representations, offering an alternative to explicit chain-of-thought (CoT) reasoning. However, existing reinforcement learning (RL) paradigms primarily target output tokens, creating a structural mismatch with looped architectures whose reasoning unfolds implicitly. In this work, we propose LoopRPT, a reinforcement pre-training framework tailored for LoopLMs. By reframing next-token prediction as a next-token reasoning task, LoopRPT assigns reinforcement signals directly to latent steps using an EMA teacher reference and noisy latent rollouts. This formulation enables RL to directly shape intermediate representations, compressing effective reasoning into fewer iterations. We instantiate LoopRPT on Ouro across multiple model scales. Results show that LoopRPT improves per-step representation quality and achieves Pareto dominance in accuracy-computation trade-offs. Large gains on hard tokens indicate that LoopRPT enhances early-stage reasoning rather than merely encouraging premature exits. Our findings highlight reinforcement pre-training as a principled paradigm for learning efficient latent reasoning in LoopLMs.

Guo Tang, Shixin Jiang, Heng Chang +7

Harbin Institute of Technology, Harbin, China · Tsinghua University, Beijing, China · The Hong Kong University of Science and Technology, Guangzhou, China

Efficient Language Model Reasoning Implicit Reasoning in Language Models RL for Language Models Recursive Language Models

Mar 20, 2026

HyEvo: Self-Evolving Hybrid Agentic Workflows for Efficient Reasoning

Although agentic workflows have demonstrated strong potential for solving complex tasks, existing automated generation methods remain inefficient and underperform, as they rely on predefined operator libraries and homogeneous LLM-only workflows in which all task-level computation is performed through probabilistic inference. To address these limitations, we propose HyEvo, an automated workflow-generation framework that leverages heterogeneous atomic synthesis. HyEvo integrates probabilistic LLM nodes for semantic reasoning with deterministic code nodes for rule-based execution, offloading predictable operations from LLM inference and reducing inference cost and execution latency. To efficiently navigate the hybrid search space, HyEvo employs an LLM-driven multi-island evolutionary strategy with a reflect-then-generate mechanism, iteratively refining both workflow topology and node logic via execution feedback. Comprehensive experiments show that HyEvo consistently outperforms existing methods across diverse reasoning and coding benchmarks, while reducing inference cost and execution latency by up to 19

\times

and 16

\times

, respectively, compared to the state-of-the-art open-source baseline.

Beibei Xu, Yutong Ye, Chuyun Shen +3

East China Normal University · Beihang University · Shanghai University of International Business and Economics +1

Agentic Workflows LLM Agent Workflow Optimization Efficient Language Model Reasoning LLM-Based Program Synthesis

Mar 20, 2026

TextReasoningBench: Does Reasoning Really Improve Text Classification in Large Language Models?

Eliciting explicit, step-by-step reasoning traces from large language models (LLMs) has emerged as a dominant paradigm for enhancing model capabilities. Although such reasoning strategies were originally designed for problems requiring explicit multi-step reasoning, they have increasingly been applied to a broad range of NLP tasks. This expansion implicitly assumes that deliberative reasoning uniformly benefits heterogeneous tasks. However, whether such reasoning mechanisms truly benefit classification tasks remains largely underexplored, especially considering their substantial token and time costs. To fill this gap, we introduce TextReasoningBench, a systematic benchmark designed to evaluate the effectiveness and efficiency of reasoning strategies for text classification with LLMs. We compare seven reasoning strategies, namely IO, CoT, SC-CoT, ToT, GoT, BoC, and long-CoT across ten LLMs on five text classification datasets. Beyond traditional metrics such as accuracy and macro-F1, we introduce two cost-aware evaluation metrics that quantify the performance gain per reasoning token and the efficiency of performance improvement relative to token cost growth. Experimental results reveal three notable findings: (1) Reasoning does not universally improve classification performance: while moderate strategies such as CoT and SC-CoT yield consistent but limited gains (typically +1% to +3% on big models), more complex methods (e.g., ToT and GoT) often fail to outperform simpler baselines and can even degrade performance, especially on small models; (2) Reasoning is often inefficient: many reasoning strategies increase token consumption by 10

\times

to 100

\times

(e.g., SC-CoT and ToT) while providing only marginal performance improvements.

Xinyu Guo, Yazhou Zhang, Jing Qin

School of Computer Science and Technology, Tianjin University, China · School of Nursing, The Hong Kong Polytechnic University, HongKong

Large Language Model-Based Text Classification LLM Evaluation Efficient Language Model Reasoning Text Classification

Mar 19, 2026

Balancing the Reasoning Load: Difficulty-Differentiated Policy Optimization with Length Redistribution for Efficient and Robust Reinforcement Learning

Large Reasoning Models (LRMs) have shown exceptional reasoning capabilities, but they also suffer from the issue of overthinking, often generating excessively long and redundant answers. For problems that exceed the model's capabilities, LRMs tend to exhibit the overconfidence phenomenon, generating overly short but incorrect answers, which may contribute to suboptimal performance. To address these issues, we propose Difficulty-Differentiated Policy Optimization (DDPO), an efficient reinforcement learning algorithm that optimizes simple and complex tasks separately based on the overconfidence phenomenon. Specifically, it reduces the output length for simple tasks without compromising accuracy, while for complex tasks, it expands the exploration space to improve performance. We further derive the theoretical conditions for maximizing expected accuracy, which require the length distribution to closely approximate the optimal length and be as concentrated as possible. Based on these conditions, we propose using the difficulty-level average as a well-founded reference for length optimization. Extensive experiments on both in-domain and out-of-domain benchmarks validate the superiority and effectiveness of DDPO. Compared to GRPO, DDPO reduces the average answer length by 12% while improving accuracy by 1.85% across multiple benchmarks, achieving a better trade-off between accuracy and length. The code is available at https://github.com/Yinan-Xia/DDPO.

Yinan Xia, Haotian Zhang, Huiming Wang

Tianjin University · Kuaishou Technology

RL for Language Model Reasoning Efficient Language Model Reasoning RL Post-Training Overthinking in Language Models