mlsanityData to 14 Oct 2026

TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning

arXiv 2505.11737 ↗First posted 16 May 2025cs.LG cs.AI cs.CLcited by 24

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

Abstract (arXiv)

While Large Language Models (LLMs) have demonstrated impressive capabilities, their output quality remains inconsistent across various application scenarios, making it difficult to identify trustworthy responses, especially in complex tasks requiring multi-step reasoning. In this paper, we propose a Token-level Uncertainty estimation framework for Reasoning (TokUR) that enables LLMs to self-assess and self-improve their responses in mathematical reasoning. Specifically, we introduce low-rank random weight perturbation during LLM decoding to generate predictive distributions for token-level uncertainty estimation, and we aggregate these uncertainty quantities to capture the semantic uncertainty of generated responses. Experiments on mathematical reasoning datasets of varying difficulty demonstrate that TokUR exhibits a strong correlation with answer correctness and model robustness, and the uncertainty signals produced by TokUR can be leveraged to enhance the model's reasoning performance at test time. These results highlight the effectiveness of TokUR as a principled and scalable approach for improving the reliability and interpretability of LLMs in challenging reasoning tasks.

Key facts. Cited by 24 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 69 of its 92 references that are in the map. First posted on arXiv 16 May 2025.

Builds on

69 of 92 references.

Closest ancestors · 7

Same direction, newest first

  1. 2025Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey20 Mar
  2. 2025Scalable Best-of-N Selection for Large Language Models via Self-Certainty25 Feb
  3. 2025CoT-UQ: Improving Response-wise Uncertainty Quantification in LLMs with Chain-of-Thought24 Feb
  4. 2025CER: Confidence Enhanced Reasoning in LLMs20 Feb
  5. 2025Rollout Roulette: A Probabilistic Inference Approach to Inference-Time Scaling of LLMs using Particle-Based Monte Carlo Methods3 Feb
  6. 2023Tree of Thoughts: Deliberate Problem Solving with Large Language Models17 May
  7. 2023Self-Evaluation Guided Beam Search for Reasoning1 May

Other references · 62

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  4. 2021LoRA: Low-Rank Adaptation of Large Language Modelscited by 14,380
  5. 2022Chain-of-Thought Prompting Elicits Reasoning in Large Language Modelscited by 12,459
  6. 2021Training Verifiers to Solve Math Word Problemscited by 10,109
  7. 2021Evaluating Large Language Models Trained on Codecited by 8,320
  8. 2023Direct Preference Optimization: Your Language Model is Secretly a Reward Modelcited by 8,065
  9. 2025DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learningcited by 6,330
  10. 2023Efficient Memory Management for Large Language Model Serving with PagedAttentioncited by 5,944
  11. 2022Self-Consistency Improves Chain of Thought Reasoning in Language Modelscited by 5,708
  12. 2015Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learningcited by 4,448
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  4. 2014Sequence to Sequence Learning with Neural Networkscited by 2,986
  5. 2022Emergent Abilities of Large Language Modelscited by 2,512
  6. 2020DeBERTa: Decoding-enhanced BERT with Disentangled Attentioncited by 2,181
  7. 2023FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generationcited by 1,282
  8. 2024Large Language Monkeys: Scaling Inference Compute with Repeated Samplingcited by 991
  9. 2023Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMscited by 974
  10. 2022Solving math word problems with process- and outcome-based feedbackcited by 901
  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
  13. 2023SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Modelscited by 810
  14. 2022Teaching Models to Express Their Uncertainty in Wordscited by 751
  15. 2023Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Modelscited by 574
  16. 2025Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Modelcited by 461
  17. 2024INSIDE: LLMs' Internal States Retain the Power of Hallucination Detectioncited by 323
  18. 2025rStar-Math: Small LLMs Can Master Math Reasoning with Self-Evolved Deep Thinkingcited by 313
  19. 2015Probabilistic Backpropagation for Scalable Learning of Bayesian Neural Networkscited by 295
  20. 2023Generating with Confidence: Uncertainty Quantification for Black-box Large Language Modelscited by 293
  21. 2024Semantic Entropy Probes: Robust and Cheap Hallucination Detection in LLMscited by 259
  22. 2024Continual Learning of Large Language Models: A Comprehensive Surveycited by 234
  23. 2017Beam Search Strategies for Neural Machine Translationcited by 232
  24. 2022Out-of-Distribution Detection and Selective Generation for Conditional Language Modelscited by 197
  25. 2023Shifting Attention to Relevance: Towards the Predictive Uncertainty Quantification of Free-Form Large Language Modelscited by 150
  26. 2018Correcting Length Bias in Neural Machine Translationcited by 120
  27. 2021Epistemic Neural Networkscited by 120
  28. 2024To Believe or Not to Believe Your LLMcited by 120
  29. 2023Bayesian Low-rank Adaptation for Large Language Modelscited by 115
  30. 2023Decomposing Uncertainty for Large Language Models through Input Clarification Ensemblingcited by 114
  31. 2024Benchmarking Uncertainty Quantification Methods for Large Language Models with LM-Polygraphcited by 105
  32. 2024Large Language Models Must Be Taught to Know What They Don't Knowcited by 100
  33. 2023Enhancing Uncertainty-Based Hallucination Detection with Stronger Focuscited by 99
  34. 2022Mutual Information Alleviates Hallucinations in Abstractive Summarizationcited by 68
  35. 2023LoRA ensembles for large language model fine-tuningcited by 67
  36. 2016Towards Bayesian Deep Learning: A Framework and Some Existing Methodscited by 58
  37. 2024BLoB: Bayesian Low-Rank Adaptation by Backpropagation for Large Language Modelscited by 50
  38. 2024Uncertainty Quantification for In-Context Learning of Large Language Modelscited by 45

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Citing papers per year: 2025: 7; 2026: 17.

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  2. 2025Semantic Energy: Detecting LLM Hallucination Beyond Entropycited by 18
  3. 2025Alignment and Safety in Large Language Models: Safety Mechanisms, Training Paradigms, and Emerging Challengescited by 15
  4. 2025Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMscited by 13
  5. 2025SSR: Socratic Self-Refine for Large Language Model Reasoningcited by 7
  6. 2026BAS: A Decision-Theoretic Approach to Evaluating Large Language Model Confidencecited by 7
  7. 2025BrowseConf: Confidence-Guided Test-Time Scaling for Web Agentscited by 5
  8. 2025Schema for In-Context Learningcited by 4
  9. 2026The Alignment Tax: Response Homogenization in Aligned LLMs and Its Implications for Uncertainty Estimationcited by 4
  10. 2025Improving Semantic Uncertainty Quantification in LVLMs with Semantic Gaussian Processescited by 3
  11. 2026Token-Guard: Towards Token-Level Hallucination Control via Self-Checking Decodingcited by 2
  12. 2026LookWise: Knowing When and Where to Look for Fine-Grained Visual Reasoning in Multimodal Large Language Modelscited by 2
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  2. 2026Towards Generation-Efficient Uncertainty Estimation in Large Language Modelscited by 2
  3. 2026Aligning LLM Uncertainty with Human Disagreement in Subjectivity Analysiscited by 2
  4. 2026Scaling Reasoning Hop Exposes Weaknesses: Demystifying and Improving Hop Generalization in Large Language Modelscited by 1
  5. 2026Efficient Epistemic Uncertainty Estimation for Large Language Models via Knowledge Distillationcited by 1
  6. 2026FERA: Uncertainty-Aware Federated Reasoning for Large Language Modelscited by 1
  7. 2026Dual-Dimensional Consistency: Balancing Budget and Quality in Adaptive Inference-Time Scalingcited by 1
  8. 2026Intrinsic Selection and Particle Resampling for Inference-Time Scaling Beyond Domain Verifiabilitycited by 1
  9. 2026Leveraging Visual Signals for Robust Token-Level Uncertainty in Vision-Language Generationcited by 0
  10. 2026Localizing Input Uncertainty Quantification for Large Language Models via Shapley Valuescited by 0
  11. 2026Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Studycited by 0
  12. 2026Semantic Uncertainty Quantification Needs Factual Equivalencecited by 0

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  2. 2025ReliableMath: Benchmark of Reliable Mathematical Reasoning on Large Language Models
  3. 2025Revisiting Uncertainty Estimation and Calibration of Large Language Models
  4. 2026SELFDOUBT: Uncertainty Quantification for Reasoning LLMs via the Hedge-to-Verify Ratio
  5. 2026Embedding Perturbation may Better Reflect Intermediate-Step Uncertainty in LLM Reasoning
  6. 2025Reasoning Under Uncertainty: Exploring Probabilistic Reasoning Capabilities of LLMs
  7. 2026Thinking by Subtraction: Confidence-Driven Contrastive Decoding for LLM Reasoning
  8. 2026Improving Mathematical Reasoning Capabilities in Large Language Models via Reasoning Process Error Classification