In this paper, we study the problem of uncertainty estimation and calibration for LLMs. We first formulate 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 neurons of the LLMs may contain uncertainty information. Our designed approach demonstrates the benefits of utilizing hidden activations to enhance uncertainty estimation across various tasks and shows robust transferability in out-of-distribution settings. 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. Furthermore, our method is easy to implement and adaptable to different levels of model accessibility including black box, grey box, and white box.
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