mlsanityData to 14 Oct 2026

MUR: Momentum Uncertainty guided Reasoning for Large Language Models

arXiv 2507.14958 ↗First posted 20 Jul 2025cs.CLcited by 17

On the map: LLM reasoning → Test-time compute and efficient thinking

Abstract (arXiv)

Large Language Models have achieved impressive performance on reasoning-intensive tasks, yet optimizing their reasoning efficiency remains an open challenge. While Test-Time Scaling (TTS) improves reasoning quality, it often leads to overthinking, wasting tokens on redundant computations. This work investigates how to efficiently and adaptively guide current model' test-time scaling without additional training. Inspired by the concept of momentum in physics, we propose Momentum Uncertainty-guided Reasoning (MUR), which dynamically allocates thinking budgets to critical reasoning steps by tracking and aggregating stepwise uncertainty over time. To support flexible inference-time control, we introduce gamma-control, a simple mechanism that tunes the reasoning budget via a single hyperparameter. We provide in-depth theoretical proof to support the superiority of MUR in terms of stability and biases. MUR is comprehensively evaluated against various TTS methods across four challenging benchmarks (MATH-500, AIME24, AIME25, and GPQA-diamond) using different sizes of recent Qwen3 models (1.7B, 4B, and 8B). Results demonstrate that MUR reduces computation by by over 45% on average while improving accuracy from 0.33 to 3.46%.

Key facts. Cited by 17 papers in the map (data through 14 Oct 2026). Placed in Test-time compute and efficient thinking, one of 17 directions in LLM reasoning. Builds on 48 of its 63 references that are in the map. First posted on arXiv 20 Jul 2025.

Builds on

48 of 63 references.

Closest ancestors · 11

Same direction, newest first

  1. 2025Think Only When You Need with Large Hybrid-Reasoning Models20 May
  2. 2025Dynamic Early Exit in Reasoning Models22 Apr
  3. 2025Genius: A Generalizable and Purely Unsupervised Self-Training Framework For Advanced Reasoning11 Apr
  4. 2025Dancing with Critiques: Enhancing LLM Reasoning with Stepwise Natural Language Self-Critique21 Mar
  5. 2025Stop Overthinking: A Survey on Efficient Reasoning for Large Language Models20 Mar
  6. 2025φ-Decoding: Adaptive Foresight Sampling for Balanced Inference-Time Exploration and Exploitation17 Mar
  7. 2025Sampling-Efficient Test-Time Scaling: Self-Estimating the Best-of-N Sampling in Early Decoding3 Mar
  8. 2025Towards Thinking-Optimal Scaling of Test-Time Compute for LLM Reasoning25 Feb
  9. 2025TokenSkip: Controllable Chain-of-Thought Compression in LLMs17 Feb
  10. 2024Do NOT Think That Much for 2+3=? On the Overthinking of o1-Like LLMs30 Dec
  11. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May

Other references · 37

  1. 2014Adam: A Method for Stochastic Optimizationcited by 37,240
  2. 2020Language Models are Few-Shot Learnerscited by 32,419
  3. 2024The Llama 3 Herd of Modelscited by 14,715
  4. 2025Qwen3 Technical Reportcited by 8,820
  5. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,944
  6. 2021Measuring Mathematical Problem Solving With the MATH Datasetcited by 5,371
  7. 2023Let's Verify Step by Stepcited by 3,789
  8. 2023GPQA: A Graduate-Level Google-Proof Q&A Benchmarkcited by 2,879
  9. 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 991
  10. 2023Math-Shepherd: Verify and Reinforce LLMs Step-by-step without Human Annotationscited by 928
  11. 2023Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generationcited by 819
  12. 2023Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedbackcited by 812
25 more
  1. 2023SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Modelscited by 810
  2. 2025LIMO: Less is More for Reasoningcited by 498
  3. 2024INSIDE: LLMs' Internal States Retain the Power of Hallucination Detectioncited by 323
  4. 2022Out-of-Distribution Detection and Selective Generation for Conditional Language Modelscited by 197
  5. 2024Kernel Language Entropy: Fine-grained Uncertainty Quantification for LLMs from Semantic Similaritiescited by 159
  6. 2025General-Reasoner: Advancing LLM Reasoning Across All Domainscited by 135
  7. 2023Quantifying Uncertainty in Answers from any Language Model and Enhancing their Trustworthinesscited by 122
  8. 2020An Improved Analysis of Stochastic Gradient Descent with Momentumcited by 119
  9. 2023Decomposing Uncertainty for Large Language Models through Input Clarification Ensemblingcited by 114
  10. 2025GenPRM: Scaling Test-Time Compute of Process Reward Models via Generative Reasoningcited by 97
  11. 2025A Survey of Uncertainty Estimation Methods on Large Language Modelscited by 62
  12. 2024SPUQ: Perturbation-Based Uncertainty Quantification for Large Language Modelscited by 56
  13. 2024Beyond Examples: High-level Automated Reasoning Paradigm in In-Context Learning via MCTScited by 54
  14. 2024Distinguishing the Knowable from the Unknowable with Language Modelscited by 47
  15. 2024Uncertainty in Language Models: Assessment through Rank-Calibrationcited by 41
  16. 2024Can Language Models Perform Robust Reasoning in Chain-of-thought Prompting with Noisy Rationales?cited by 41
  17. 2025Think When You Need: Self-Adaptive Chain-of-Thought Learningcited by 38
  18. 2025Z1: Efficient Test-time Scaling with Codecited by 35
  19. 2023Quantifying Uncertainty in Natural Language Explanations of Large Language Modelscited by 32
  20. 2025TemplateRL: Structured Template-Guided Reinforcement Learning for LLM Reasoningcited by 28
  21. 2024Non-myopic Generation of Language Models for Reasoning and Planningcited by 26
  22. 2024Resilience of Large Language Models for Noisy Instructionscited by 20
  23. 2025MARS: Multi-Agent Adaptive Reasoning with Socratic Guidance for Automated Prompt Optimizationcited by 15
  24. 2025Guiding Reasoning in Small Language Models with LLM Assistancecited by 14
  25. 2024On the Performance Analysis of Momentum Method: A Frequency Domain Perspectivecited by 8

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2025: 5; 2026: 12.

17 papers.

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  1. 2025Semantic-Space Exploration and Exploitation in RLVR for LLM Reasoningcited by 17
  2. 2025ReProbe: Efficient Test-Time Scaling of Multi-Step Reasoning by Probing Internal States of Large Language Modelscited by 10
  3. 2026Neural Chain-of-Thought Search: Searching the Optimal Reasoning Path to Enhance Large Language Modelscited by 8
  4. 2026Reliable Thinking with Imagescited by 5
  5. 2025Overthinking Reduction with Decoupled Rewards and Curriculum Data Schedulingcited by 4
  6. 2025Putting on the Thinking Hats: A Survey on Chain of Thought Fine-tuning from the Perspective of Human Reasoning Mechanismcited by 4
  7. 2026Draft-Thinking: Learning Efficient Reasoning in Long Chain-of-Thought LLMscited by 3
  8. 2026Learning Adaptive LLM Decodingcited by 3
  9. 2025Fast, Slow, and Tool-augmented Thinking for LLMs: A Reviewcited by 2
  10. 2026TRiMS: Real-Time Tracking of Minimal Sufficient Length for Efficient Reasoning via RLcited by 2
  11. 2026When Embedding-Based Defenses Fail: Rethinking Safety in LLM-Based Multi-Agent Systemscited by 2
  12. 2026MAXS: Meta-Adaptive Exploration with LLM Agentscited by 1
5 more
  1. 2026Test-time Scaling over Perception: Resolving the Grounding Paradox in Thinking with Imagescited by 1
  2. 2026Dual-Dimensional Consistency: Balancing Budget and Quality in Adaptive Inference-Time Scalingcited by 1
  3. 2026Towards Efficient and Robust Linguistic Emotion Diagnosis for Mental Health via Multi-Agent Instruction Refinementcited by 0
  4. 2026Uncertainty-Aware Budget Allocation for Adaptive Test-Time Reasoningcited by 0
  5. 2026ThinkBooster: A Unified Framework for Seamless Test-Time Scaling of LLM Reasoningcited by 0

Similar, not cited

Close in wording, no citation either way

  1. 2026Improving reasoning at inference time via uncertainty minimisation
  2. 2025ThreadWeaver: Adaptive Threading for Efficient Parallel Reasoning in Language Models
  3. 2025Certainty-Guided Reasoning in Large Language Models: A Dynamic Thinking Budget Approach
  4. 2025The Art of Scaling Test-Time Compute for Large Language Models
  5. 2025Less is More: Improving LLM Reasoning with Minimal Test-Time Intervention
  6. 2026Enhancing reasoning accuracy in large language models during inference time
  7. 2025Step-level Verifier-guided Hybrid Test-Time Scaling for Large Language Models
  8. 2025LIMOPro: Reasoning Refinement for Efficient and Effective Test-time Scaling