Bayesian Prompt Ensembles: Model Uncertainty Estimation for Black-Box Large Language Models

This paper introduces Bayesian Prompt Ensembles (BayesPE), a novel method for quantifying uncertainty in black-box large language models (LLMs) without requiring access to their internal parameters or retraining. BayesPE achieves this by ensembling the outputs of an LLM prompted with various semantically equivalent instructions, learning the optimal weighting for each prompt through approximate Bayesian variational inference on a small validation dataset. The paper demonstrates that this approach effectively approximates a Bayesian input layer and provides a lower bound on the model's reducible error. Extensive experiments across various LLMs and natural language classification tasks show that BayesPE significantly improves uncertainty calibration compared to existing baselines in both zero- and few-shot settings, while also exhibiting superior efficiency in terms of the required number of LLM forward passes and labeled validation data.