Recurrent Confidence Chain: Temporal-Aware Uncertainty Quantification in Large Language Models
Zhenjiang Mao, Anirudhh Venkat
TL;DR
The paper tackles the problem of quantifying uncertainty in multi-step reasoning by large language models, where traditional token-level approaches fail to capture temporal dynamics and cross-step dependencies. It introduces the Recurrent Confidence Chain (RCC), which leverages inter-step attention to model semantic correlations across reasoning steps and a recurrent confidence propagation mechanism that preserves historical uncertainty, with the final estimate given by $\\hat{\mathcal{P}}_\\mathcal{M}(\\mathbf{x}_{ans}|\\mathbf{x}_{in}) = p_n$. Key contributions include: (1) inter-step attention to overcome semantic blindness, (2) a linear-time confidence propagation to handle long-horizon reasoning, and (3) a unified framework that blends semantic correlation with temporal tracking. Empirical results on the GAOKAO MATH benchmark and the CLadder causal reasoning dataset show that RCC achieves superior calibration (lower $ECE$) while maintaining strong predictive quality (competitive $NLL$) compared to baselines, indicating more trustworthy uncertainty estimates for high-stakes applications.
Abstract
As reasoning modules, such as the chain-of-thought mechanism, are applied to large language models, they achieve strong performance on various tasks such as answering common-sense questions and solving math problems. The main challenge now is to assess the uncertainty of answers, which can help prevent misleading or serious hallucinations for users. Although current methods analyze long reasoning sequences by filtering unrelated tokens and examining potential connections between nearby tokens or sentences, the temporal spread of confidence is often overlooked. This oversight can lead to inflated overall confidence, even when earlier steps exhibit very low confidence. To address this issue, we propose a novel method that incorporates inter-step attention to analyze semantic correlations across steps. For handling long-horizon responses, we introduce a hidden confidence mechanism to retain historical confidence information, which is then combined with stepwise confidence to produce a more accurate overall estimate. We evaluate our method on the GAOKAO math benchmark and the CLadder causal reasoning dataset using mainstream open-source large language models. Our approach is shown to outperform state-of-the-art methods by achieving a superior balance between predictive quality and calibration, demonstrated by strong performance on both Negative Log-Likelihood and Expected Calibration Error.