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

[2505.11737] TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning Skip to main content Search Submit Donate Log in Search arXiv Press Enter to search · Advanced search Computer Science > Machine Learning arXiv:2505.11737 (cs) [Submitted on 16 May 2025 ( v1 ), last revised 11 Apr 2026 (this version, v4)] Title: TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning Authors: Tunyu Zhang , Haizhou Shi , Yibin Wang , Hengyi Wang , Xiaoxiao He , Zhuowei Li , Haoxian Chen , Ligong Han , Kai Xu , Huan Zhang , Dimitris Metaxas , Hao Wang View a PDF of the paper titled TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning, by Tunyu Zhang and 11 other authors View PDF HTML (experimental) Abstract: 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. Comments: Accepted to International Conference on Learning Representations (ICLR) 2026 Subjects: Machine Learning (cs.LG) ; Artificial Intelligence (cs.AI); Computation and Language (cs.CL) Cite as: arXiv:2505.11737 [cs.LG] (or arXiv:2505.11737v4 [cs.LG] for this version) https://doi.org/10.48550/arXiv.2505.11737 Focus to learn more arXiv-issued DOI via DataCite Submission history From: Tunyu Zhang [ view email ] [v1] Fri, 16 May 2025 22:47:32 UTC (650 KB) [v2] Thu, 4 Sep 2025 21:49:52 UTC (708 KB) [v3] Thu, 25 Sep 2025 21:44:35 UTC (767 KB) [v4] Sat, 11 Apr 2026 18:08:02 UTC (759 KB) Full-text links: Access Paper: View a PDF of the paper titled TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning, by Tunyu Zhang and 11 other authors View PDF HTML (experimental) TeX Source view license Current browse context: cs.LG < prev | next > new | recent | 2025-05 Change to browse by: cs cs.AI cs.CL References & Citations NASA ADS Google Scholar Semantic Scholar export BibTeX citation Loading... BibTeX formatted citation × loading... Data provided by: Bookmark Bibliographic Tools Bibliographic and Citation Tools Bibliographic Explorer Toggle Bibliographic Explorer ( What is the Explorer? ) Connected Papers Toggle Connected Papers ( What is Connected Papers? ) Litmaps Toggle Litmaps ( What is Litmaps? ) scite.ai Toggle scite Smart Citations ( What are Smart Citations? ) Code, Data, Media Code, Data and Media Associated with this Article alphaXiv Toggle alphaXiv ( What is alphaXiv? ) Links to Code Toggle CatalyzeX Code Finder for Papers ( What is CatalyzeX? ) DagsHub Toggle DagsHub ( What is DagsHub? ) GotitPub Toggle Gotit.pub ( What is GotitPub? ) Huggingface Toggle Hugging Face ( What is Huggingface? ) ScienceCast Toggle ScienceCast ( What is ScienceCast? ) Demos Demos Replicate Toggle Replicate ( What is Replicate? ) Spaces Toggle Hugging Face Spaces ( What is Spaces? ) Spaces Toggle TXYZ.AI ( What is TXYZ.AI? ) Related Papers Recommenders and Search Tools Link to Influence Flower Influence Flower ( What are Influence Flowers? ) Core recommender toggle CORE Recommender ( What is CORE? ) IArxiv recommender toggle IArxiv Recommender ( What is IArxiv? ) Author Venue Institution Topic About arXivLabs arXivLabs: experimental projects with community collaborators arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website. Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them. Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs . Which authors of this paper are endorsers? | Disable MathJax ( What is MathJax? ) We gratefully acknowledge support from our major funders , member institutions , , and all contributors. About · Help · Contact · Subscribe · Copyright · Privacy · Accessibility · Operational Status (opens in new tab) Major funding support from

Related documents

• Pinocchio: Fast Uncertainty Estimates for Black-Box Language Models#1062665
• Pinocchio: Fast Uncertainty Estimates for Black-Box Language Models#1028739
• BiG-SURE - Bipartite Graph for Semantic Uncertainty and Reliability Estimation of LLMs#820695
• Choosing the Right Language Mode at Inference Time for Multilingual Reliability#927921
• CounterBench: Evaluating and Improving Counterfactual Reasoning in Large Language Models#139128