We explore uncertainty quantification in large language models (LLMs), with the goal to identify when uncertainty in responses given a query is large. We simultaneously consider both epistemic and aleatoric uncertainties, where the former comes from the lack of knowledge about the ground truth (such as about facts or the language), and the latter comes from irreducible randomness (such as multiple possible answers). In particular, we derive an information-theoretic metric that allows to reliably detect when only epistemic uncertainty is large, in which case the output of the model is unreliable. This condition can be computed based solely on the output of the model obtained simply by some special iterative prompting based on the previous responses. Such quantification, for instance, allows to detect hallucinations (cases when epistemic uncertainty is high) in both single- and multi-answer responses. This is in contrast to many standard uncertainty quantification strategies (such as thresholding the log-likelihood of a response) where hallucinations in the multi-answer case cannot be detected. We conduct a series of experiments which demonstrate the advantage of our formulation. Further, our investigations shed some light on how the probabilities assigned to a given output by an LLM can be amplified by iterative prompting, which might be of independent interest.

我们在大型语言模型中探索不确定性量化，旨在确定查询结果的不确定性何时较大。我们同时考虑认识论不确定性和偶然性不确定性，从中推论出一种信息论度量，可可靠地检测只有认识论不确定性较大的情况，从模型的输出中可以仅通过一些特殊的迭代提示来计算。这种量化可以检测出幻觉，在单答案和多答案响应中均适用。与许多标准的不确定性量化策略（例如，将响应的对数似然度阈值化）不同，无法检测到多答案情况下的幻觉。我们进行了一系列实验证明了我们的公式的优势。此外，我们的研究还揭示了大型语言模型给定输出的概率如何通过迭代提示来放大，这可能具有独立的研究价值。

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