Towards Efficient Confidence Estimation for Large Language Model Reasoning
Keywords: Large language models, Mathemtical reasoning, Confidence Estimation
Abstract: Recent advances have demonstrated the powerful reasoning capabilities of large language models (LLMs), and accurately measuring the confidence of reasoning paths is crucial for improving the performance and trustworthy of AI systems. Benefiting from consistency function for reasoning, the self-consistency method often provides an effective confidence estimation. However, it suffers from the variance issue, which extremely constrains the performance when the sampling is insufficient. Existing methods such as the temperature sampling cannot well resolve this problem as it not only necessitates a calibration set but also tends to sacrifice the reasoning capability of LLMs. In this paper, we propose a data-free, and highly sampling efficient method to control the variance. The merit of our approach lies in a reasonable integration of the LLM's probability estimation and the self-consistency confidence. Our theoretical analysis confirms the efficacy of our method by achieving a lower estimation error and a higher error reduction rate. Furthermore, an in-depth analysis of the error decomposition reveals an improved technique, which can significantly improve error reduction rate with only a small scale of bias induced. Experimental results across seven benchmark datasets demonstrate that our proposed approaches achieve superior confidence estimation, boosting the accuracy on both mathematical reasoning tasks and code generation tasks. Our code is provided in the supplementary material.
Supplementary Material: zip
Primary Area: foundation or frontier models, including LLMs
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Submission Number: 11871
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