# CoT-UQ: Improving Response-wise Uncertainty Quantification in LLMs with Chain-of-Thought

arXiv: https://arxiv.org/abs/2502.17214 · HTML: https://mlsanity.com/paper/2502.17214/

## Key facts

- Cited by 23 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 27 of its 34 references that are in the map.
- First posted on arXiv 24 Feb 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, 27 of 27)

- [Training language models to follow instructions with human feedback](https://mlsanity.com/paper/2203.02155/) (2022)
- [LLaMA: Open and Efficient Foundation Language Models](https://mlsanity.com/paper/2302.13971/) (2023)
- [Training Verifiers to Solve Math Word Problems](https://mlsanity.com/paper/2110.14168/) (2021)
- [DeepSeekMath: Pushing the Limits of Mathematical Reasoning in Open Language Models](https://mlsanity.com/paper/2402.03300/) (2024)
- [PaLM: Scaling Language Modeling with Pathways](https://mlsanity.com/paper/2204.02311/) (2022)
- [Large Language Models are Zero-Shot Reasoners](https://mlsanity.com/paper/2205.11916/) (2022)
- [HotpotQA: A Dataset for Diverse, Explainable Multi-hop Question Answering](https://mlsanity.com/paper/1809.09600/) (2018)
- [Language Models (Mostly) Know What They Know](https://mlsanity.com/paper/2207.05221/) (2022)
- [Constructing A Multi-hop QA Dataset for Comprehensive Evaluation of Reasoning Steps](https://mlsanity.com/paper/2011.01060/) (2020)
- [Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs](https://mlsanity.com/paper/2306.13063/) (2023)
- [Are NLP Models really able to Solve Simple Math Word Problems?](https://mlsanity.com/paper/2103.07191/) (2021)
- [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)
- [Teaching Models to Express Their Uncertainty in Words](https://mlsanity.com/paper/2205.14334/) (2022)
- [Selection-Inference: Exploiting Large Language Models for Interpretable Logical Reasoning](https://mlsanity.com/paper/2205.09712/) (2022)
- [A Diverse Corpus for Evaluating and Developing English Math Word Problem Solvers](https://mlsanity.com/paper/2106.15772/) (2021)
- [Towards Revealing the Mystery behind Chain of Thought: A Theoretical Perspective](https://mlsanity.com/paper/2305.15408/) (2023)
- [LLMs Know More Than They Show: On the Intrinsic Representation of LLM Hallucinations](https://mlsanity.com/paper/2410.02707/) (2024)
- [Large Language Model Guided Tree-of-Thought](https://mlsanity.com/paper/2305.08291/) (2023)
- [Fine-tuning Language Models for Factuality](https://mlsanity.com/paper/2311.08401/) (2023)
- [A Stitch in Time Saves Nine: Detecting and Mitigating Hallucinations of LLMs by Validating Low-Confidence Generation](https://mlsanity.com/paper/2307.03987/) (2023)
- [SelfCheck: Using LLMs to Zero-Shot Check Their Own Step-by-Step Reasoning](https://mlsanity.com/paper/2308.00436/) (2023)
- [Language Model Cascades: Token-level uncertainty and beyond](https://mlsanity.com/paper/2404.10136/) (2024)
- [GTBench: Uncovering the Strategic Reasoning Limitations of LLMs via Game-Theoretic Evaluations](https://mlsanity.com/paper/2402.12348/) (2024)
- [Uncertainty Quantification with Pre-trained Language Models: A Large-Scale Empirical Analysis](https://mlsanity.com/paper/2210.04714/) (2022)
- [MARS: Meaning-Aware Response Scoring for Uncertainty Estimation in Generative LLMs](https://mlsanity.com/paper/2402.11756/) (2024)
- [ERA-CoT: Improving Chain-of-Thought through Entity Relationship Analysis](https://mlsanity.com/paper/2403.06932/) (2024)
- [Multiple Choice Questions: Reasoning Makes Large Language Models (LLMs) More Self-Confident, Especially When They are Wrong](https://mlsanity.com/paper/2501.09775/) (2025)

## Built on by (most cited first, 23 of 23)

- [Uncertainty Quantification and Confidence Calibration in Large Language Models: A Survey](https://mlsanity.com/paper/2503.15850/) (2025)
- [Position: Uncertainty Quantification Needs Reassessment for Large-language Model Agents](https://mlsanity.com/paper/2505.22655/) (2025)
- [TokUR: Token-Level Uncertainty Estimation for Large Language Model Reasoning](https://mlsanity.com/paper/2505.11737/) (2025)
- [Confidence Estimation for LLMs in Multi-turn Interactions](https://mlsanity.com/paper/2601.02179/) (2026)
- [AgentForesight: Online Auditing for Early Failure Prediction in Multi-Agent Systems](https://mlsanity.com/paper/2605.08715/) (2026)
- [Dive into the Agent Matrix: A Realistic Evaluation of Self-Replication Risk in LLM Agents](https://mlsanity.com/paper/2509.25302/) (2025)
- [Uncertainty Quantification for Retrieval-Augmented Reasoning](https://mlsanity.com/paper/2510.11483/) (2025)
- [Let the Model Distribute Its Doubt: Confidence Estimation through Verbalized Probability Distribution](https://mlsanity.com/paper/2511.14275/) (2025)
- [Semantic Calibration Prevails Where Token Confidence Fails: Benchmarking Long-Form Scientific QA](https://mlsanity.com/paper/2602.00279/) (2026)
- [SELFDOUBT: Uncertainty Quantification for Reasoning LLMs via the Hedge-to-Verify Ratio](https://mlsanity.com/paper/2604.06389/) (2026)
- [Uncertainty Propagation in LLM-Based Systems](https://mlsanity.com/paper/2604.23505/) (2026)
- [Large Language Models Decide Early and Explain Later](https://mlsanity.com/paper/2604.22266/) (2026)
- [A Single Layer to Explain Them All:Understanding Massive Activations in Large Language Models](https://mlsanity.com/paper/2605.08504/) (2026)
- [Quantifying Consistency in LLM Logical Reasoning via Structural Uncertainty](https://mlsanity.com/paper/2606.17312/) (2026)
- [TableMind++: An Uncertainty-Aware Programmatic Agent for Tool-Augmented Table Reasoning](https://mlsanity.com/paper/2603.07528/) (2026)
- [ART: Attention Replacement Technique to Improve Factuality in LLMs](https://mlsanity.com/paper/2604.06393/) (2026)
- [Monitoring Web Agents Without Internal Signals: Observable Trajectories and Key-Step Supervision](https://mlsanity.com/paper/2609.02057/) (2026)
- [Quantifying and Understanding Uncertainty in Large Reasoning Models](https://mlsanity.com/paper/2604.13395/) (2026)
- [VERDI: Single-Call Confidence Estimation for Verification-Based LLM Judges via Decomposed Inference](https://mlsanity.com/paper/2605.11334/) (2026)
- [GUT: Quantifying and Optimizing the Reasoning Uncertainty of LLMs via Graph Complexity](https://mlsanity.com/paper/2609.05284/) (2026)
- [Uncertainty Quantification for LLM Agents: A Taxonomy, an Evaluation Protocol, and an Empirical Study](https://mlsanity.com/paper/2609.07395/) (2026)
- [Dream2Discern: Learning from Hard Latent Variants for Runtime Failure Prediction in Multi-Agent Systems](https://mlsanity.com/paper/2610.16071/) (2026)
- [Argument Graph Uncertainty: Quantifying Uncertainty from the Logical Structure of Reasoning Chains](https://mlsanity.com/paper/2610.20328/) (2026)

## Abstract (arXiv)

Large language models (LLMs) excel in many tasks but struggle to accurately quantify uncertainty in their generated responses. This limitation makes it challenging to detect misinformation and ensure reliable decision-making. Existing uncertainty quantification (UQ) methods for LLMs are primarily prompt-wise rather than response-wise, often requiring multiple response samples, which incurs high computational costs. Moreover, LLMs have been shown to be overconfident, particularly when using reasoning steps to derive their answers. In this work, we propose CoT-UQ, a response-wise UQ framework that integrates LLMs' inherent reasoning capabilities through Chain-of-Thought (CoT) into the UQ process. CoT-UQ captures critical information during inference by extracting keywords from each reasoning step and assessing their importance to the final answer. This key reasoning information is then aggregated to produce a final uncertainty estimate. We conduct extensive experiments based on Llama Family with model sizes varying from 8B to 13B across logical and mathematical reasoning tasks. Experimental results demonstrate that CoT-UQ significantly outperforms existing UQ methods, achieving an average improvement of 5.9% AUROC compared to current UQ methods. The code is available at: https://github.com/ZBox1005/CoT-UQ.