Can LLMs Express Their Uncertainty? An Empirical Evaluation of Confidence Elicitation in LLMs

The task of empowering large language models (LLMs) to accurately express their confidence, referred to as confidence elicitation, is essential in ensuring reliable and trustworthy decision-making processes. Previous methods, which primarily rely on model logits, have become less suitable for LLMs and even infeasible with the rise of closed-source LLMs (e.g., commercialized LLM APIs). This leads to a growing need to explore the untapped area of \emph{non-logit-based} approaches to estimate the uncertainty of LLMs. Hence, in this study, we investigate approaches for confidence elicitation that do not require model fine-tuning or access to proprietary information. We introduce three categories of methods: verbalize-based, consistency-based, and their hybrid methods for benchmarking, and evaluate their performance across five types of datasets and four widely-used LLMs. Our analysis of these methods uncovers several key insights: 1) LLMs often exhibit a high degree of overconfidence when verbalizing their confidence; 2) Prompting strategies such as CoT, Top-K and Multi-step confidences improve calibration of verbalized confidence; 3) Consistency-based methods outperform the verbalized confidences in most cases, with particularly notable improvements on the arithmetic reasoning task; 4) Hybrid methods consistently deliver the best performance over their baselines, thereby emerging as a promising state-of-the-art approach; 5) Despite these advancements, all investigated methods continue to struggle with challenging tasks, such as those requiring professional knowledge, leaving significant scope for improvement of confidence elicitation.