Large language models (LLMs) are highly capable of many tasks but they can sometimes generate unreliable or inaccurate outputs. To tackle this issue, this paper studies the problem of uncertainty estimation and calibration for LLMs. We begin by formulating the uncertainty estimation problem for LLMs and then propose a supervised approach that takes advantage of the labeled datasets and estimates the uncertainty of the LLMs' responses. Based on the formulation, we illustrate the difference between the uncertainty estimation for LLMs and that for standard ML models and explain why the hidden activations of the LLMs contain uncertainty information. Our designed approach effectively demonstrates the benefits of utilizing hidden activations for enhanced uncertainty estimation across various tasks and shows robust transferability in out-of-distribution settings. Moreover, we distinguish the uncertainty estimation task from the uncertainty calibration task and show that a better uncertainty estimation mode leads to a better calibration performance. In practice, our method is easy to implement and is adaptable to different levels of model transparency including black box, grey box, and white box, each demonstrating strong performance based on the accessibility of the LLM's internal mechanisms.

通过使用标记的数据集，本文研究了针对大型语言模型（LLMs）的不确定性估计和校准问题，提出了一个监督学习方法来估计LLMs响应的不确定性，并展示了利用隐藏激活对不同任务进行增强不确定性估计的好处和在超出分布范围的情况下的鲁棒性，同时区分了不确定性估计任务和不确定性校准任务，并表明更好的不确定性估计模式会导致更好的校准性能。

LLMs的不确定性估计与量化：一种简单的监督方法