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

arXiv: https://arxiv.org/abs/2505.11737 · HTML: https://mlsanity.com/paper/2505.11737/

## 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.

## Placed in

- LLM reasoning / [Test-time compute and efficient thinking](https://mlsanity.com/lr/test-time-compute-and-efficient-thinking/)

## Builds on (most cited first, 30 of 69)

- [Attention Is All You Need](https://mlsanity.com/paper/1706.03762/) (2017)
- [Language Models are Few-Shot Learners](https://mlsanity.com/paper/2005.14165/) (2020)
- [The Llama 3 Herd of Models](https://mlsanity.com/paper/2407.21783/) (2024)
- [LoRA: Low-Rank Adaptation of Large Language Models](https://mlsanity.com/paper/2106.09685/) (2021)
- [Chain-of-Thought Prompting Elicits Reasoning in Large Language Models](https://mlsanity.com/paper/2201.11903/) (2022)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [Evaluating Large Language Models Trained on Code](https://mlsanity.com/paper/2107.03374/) (2021)
- [Direct Preference Optimization: Your Language Model is Secretly a Reward Model](https://mlsanity.com/paper/2305.18290/) (2023)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [Efficient Memory Management for Large Language Model Serving with PagedAttention](https://mlsanity.com/paper/2309.06180/) (2023)
- [Self-Consistency Improves Chain of Thought Reasoning in Language Models](https://mlsanity.com/paper/2203.11171/) (2022)
- [Dropout as a Bayesian Approximation: Representing Model Uncertainty in Deep Learning](https://mlsanity.com/paper/1506.02142/) (2015)
- [Simple and Scalable Predictive Uncertainty Estimation using Deep Ensembles](https://mlsanity.com/paper/1612.01474/) (2016)
- [Let's Verify Step by Step](https://mlsanity.com/paper/2305.20050/) (2023)
- [Tree of Thoughts: Deliberate Problem Solving with Large Language Models](https://mlsanity.com/paper/2305.10601/) (2023)
- [Scaling Instruction-Finetuned Language Models](https://mlsanity.com/paper/2210.11416/) (2022)
- [Sequence to Sequence Learning with Neural Networks](https://mlsanity.com/paper/1409.3215/) (2014)
- [Emergent Abilities of Large Language Models](https://mlsanity.com/paper/2206.07682/) (2022)
- [DeBERTa: Decoding-enhanced BERT with Disentangled Attention](https://mlsanity.com/paper/2006.03654/) (2020)
- [FActScore: Fine-grained Atomic Evaluation of Factual Precision in Long Form Text Generation](https://mlsanity.com/paper/2305.14251/) (2023)
- [Large Language Monkeys: Scaling Inference Compute with Repeated Sampling](https://mlsanity.com/paper/2407.21787/) (2024)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Solving math word problems with process- and outcome-based feedback](https://mlsanity.com/paper/2211.14275/) (2022)
- [Semantic Uncertainty: Linguistic Invariances for Uncertainty Estimation in Natural Language Generation](https://mlsanity.com/paper/2302.09664/) (2023)
- [Just Ask for Calibration: Strategies for Eliciting Calibrated Confidence Scores from Language Models Fine-Tuned with Human Feedback](https://mlsanity.com/paper/2305.14975/) (2023)
- [SelfCheckGPT: Zero-Resource Black-Box Hallucination Detection for Generative Large Language Models](https://mlsanity.com/paper/2303.08896/) (2023)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Language Agent Tree Search Unifies Reasoning Acting and Planning in Language Models](https://mlsanity.com/paper/2310.04406/) (2023)
- [Open-Reasoner-Zero: An Open Source Approach to Scaling Up Reinforcement Learning on the Base Model](https://mlsanity.com/paper/2503.24290/) (2025)
- [INSIDE: LLMs' Internal States Retain the Power of Hallucination Detection](https://mlsanity.com/paper/2402.03744/) (2024)

## Built on by (most cited first, 24 of 24)

- [Uncertainty Quantification in LLM Agents: Foundations, Emerging Challenges, and Opportunities](https://mlsanity.com/paper/2602.05073/) (2026)
- [Semantic Energy: Detecting LLM Hallucination Beyond Entropy](https://mlsanity.com/paper/2508.14496/) (2025)
- [Alignment and Safety in Large Language Models: Safety Mechanisms, Training Paradigms, and Emerging Challenges](https://mlsanity.com/paper/2507.19672/) (2025)
- [Geometric Uncertainty for Detecting and Correcting Hallucinations in LLMs](https://mlsanity.com/paper/2509.13813/) (2025)
- [SSR: Socratic Self-Refine for Large Language Model Reasoning](https://mlsanity.com/paper/2511.10621/) (2025)
- [BAS: A Decision-Theoretic Approach to Evaluating Large Language Model Confidence](https://mlsanity.com/paper/2604.03216/) (2026)
- [BrowseConf: Confidence-Guided Test-Time Scaling for Web Agents](https://mlsanity.com/paper/2510.23458/) (2025)
- [Schema for In-Context Learning](https://mlsanity.com/paper/2510.13905/) (2025)
- [The Alignment Tax: Response Homogenization in Aligned LLMs and Its Implications for Uncertainty Estimation](https://mlsanity.com/paper/2603.24124/) (2026)
- [Improving Semantic Uncertainty Quantification in LVLMs with Semantic Gaussian Processes](https://mlsanity.com/paper/2512.14177/) (2025)
- [Token-Guard: Towards Token-Level Hallucination Control via Self-Checking Decoding](https://mlsanity.com/paper/2601.21969/) (2026)
- [LookWise: Knowing When and Where to Look for Fine-Grained Visual Reasoning in Multimodal Large Language Models](https://mlsanity.com/paper/2603.00171/) (2026)
- [Beyond Majority Voting: Efficient Best-Of-N with Radial Consensus Score](https://mlsanity.com/paper/2604.12196/) (2026)
- [Towards Generation-Efficient Uncertainty Estimation in Large Language Models](https://mlsanity.com/paper/2605.06053/) (2026)
- [Aligning LLM Uncertainty with Human Disagreement in Subjectivity Analysis](https://mlsanity.com/paper/2605.10415/) (2026)
- [Scaling Reasoning Hop Exposes Weaknesses: Demystifying and Improving Hop Generalization in Large Language Models](https://mlsanity.com/paper/2601.21214/) (2026)
- [Efficient Epistemic Uncertainty Estimation for Large Language Models via Knowledge Distillation](https://mlsanity.com/paper/2602.01956/) (2026)
- [FERA: Uncertainty-Aware Federated Reasoning for Large Language Models](https://mlsanity.com/paper/2605.10082/) (2026)
- [Dual-Dimensional Consistency: Balancing Budget and Quality in Adaptive Inference-Time Scaling](https://mlsanity.com/paper/2605.15100/) (2026)
- [Intrinsic Selection and Particle Resampling for Inference-Time Scaling Beyond Domain Verifiability](https://mlsanity.com/paper/2606.08850/) (2026)
- [Leveraging Visual Signals for Robust Token-Level Uncertainty in Vision-Language Generation](https://mlsanity.com/paper/2605.27136/) (2026)
- [Localizing Input Uncertainty Quantification for Large Language Models via Shapley Values](https://mlsanity.com/paper/2605.28170/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [Semantic Uncertainty Quantification Needs Factual Equivalence](https://mlsanity.com/paper/2609.34967/) (2026)

## 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.