C o T - UQ : Improving Response-wise Uncertainty Quantification in LLM s with Chain-of-Thought (2025)

Abstract: 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 leads to inefficiency. Moreover, LLMs have been shown to be overconfident, particularly when using reasoning steps to derive their answers. In this work, we introduce a novel approach to quantify response-wise uncertainty by integrating LLMs’ inherent reasoning capabilities through Chain-of-Thought (CoT) into the UQ process. Our CoT-UQ framework captures critical information during inference by extracting keywords from each reasoning step and assessing their importance to the final answer. The uncertainty scores of keywords are then aggregated based on their significance 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.

## introduction large language models (llms) have demonstrated groundbreaking capabilities across a variety of applications @xcite @xcite . particularly, prompting techniques like chain-of-thought (cot) @xcite have significantly enhanced llms reasoning capabilities, ranging from multiround conversation @xcite , logical reasoning @xcite and mathematical reasoning @xcite 2024; @xcite . however, llms often unpredictably hallucinate @xcite , i.e., making plausible but incorrect statements @xcite , limiting their deployment in safety-critical applications @xcite . to improve the reliability of llms, uncertainty quantification (uq) has emerged as a key strategy for determining when humans can trust llmgenerated outputs. however, existing uq methods for llms are primarily prompt-wise @xcite @xcite . that is, uncertainty is calculated at the prompt level rather than for each individual response. these methods require multiple response samples per prompt, leading to high computational costs and inference time. besides, some studies @xcite propose leveraging an llm's own ability to evaluate the uncertainty of its responses without relying on external knowledge. however, these approaches suffer from overconfidence issues, particularly when reasoning steps, such as chain-of-thought (cot), are used before deriving the final answer @xcite . overconfidence has been attributed to the model's inherent bias toward trusting its own outputs @xcite . to enable response-wise reliable uq, we propose utilizing llms' powerful reasoning capabilities in the uq process. our motivation comes from an intuitive insight: providing access to the reasoning path allows the model to use additional context for confidence calibration, leading to a more informed assessment of the final answer's uncertainty. as illustrated in figure 1 , while llms tend to be overconfident in their generated answers, and using cot can further amplify this issue, we hypothesize that incorporating key reasoning information into the uq process can effectively mitigate inflated confidence scores, resulting in better-calibrated uncertainty estimates. this naturally raises a critical research question: how can llms' reasoning steps be utilized to improve uncertainty estimation? to answer this question, we propose a new framework, namely, chain-of-thought enhanced uncertainty quantification (cot-uq). at a high level, cot-uq provides response-wise uncertainty by integrating reasoning steps from cot into the uq process. specifically, as illustrated in figure 2 , cot-uq leverages the llm's reasoning process to extract keywords from each inference step and assess their importance in determining the final answer. by incorporating this critical information, cot-uq achieves better-calibrated uncertainty estimation, either by aggregating token probabilities of extracted keywords or by integrating the reasoning path into the self-evaluation process. we conducted extensive experiments to verify the effectiveness of our proposed framework. under extensive evaluations, cot-uq achieves superior performance compared with different baselines, which reveals that llms have the potential to use their own reasoning to better express the trustworthiness of their generations. we also conduct a range of ablation studies and provide in-depth discussions via case studies. our contributions can be summarized as the following: ## preliminaries in this section, we briefly introduce the preliminaries of response-wise uncertainty quantification (uq) in llms, including problem settings and two popular uq strategies, namely aggregated probabilities and self-evaluation. further details on these two strategies can be found in appendix a.2. ## methodology in this section, we introduce our new framework, i.e., chain-of-thought enhanced uncertainty quantification (cot-uq), as illustrated in figure 2 . unlike common uq strategies that directly assess the confidence of the generated answer, cot-uq is a two-stage paradigm containing four steps during inference. the first three steps focus on refining multi-step reasoning by extracting keywords and their corresponding importance scores to the final answer (section 4.1). the fourth step illustrates how to integrate this crucial reasoning information into the two common uq strategies (section 4.2). ## conclusion in this paper, we introduce chain-of-thought enhanced uncertainty quantification (cot-uq), the first approach that leveraging llm's internal knowledge through cot for uncertainty quantification. cot-uq consistently and significantly boosts the performance of current aggregated probabilities and self-evaluation strategies by using crucial information from the reasoning path. we conduct extensive experiments to validate the effectiveness of our framework and provide detailed ablation studies and discussions.