Quantifying uncertainty in large language models (LLMs) is crucial for applications where safety is a concern, as it helps identify factually incorrect LLM answers, commonly referred to as hallucinations. Recently, advancements have been made in quantifying uncertainty, specifically by incorporating the semantics of sampled answers to estimate entropy. These methods typically rely on a normalized probability that is calculated using a limited number of sampled answers. However, we note these estimation methods fail to account for the effects of the semantics that are possible to be obtained as answers, but are not observed in the sample. This is a significant oversight, since a heavier tail of unobserved answer probabilities indicates a higher level of overall uncertainty. To alleviate this issue, we propose Evidential Semantic Entropy (EVSE), which leverages evidence theory to represent both total ignorance arising from unobserved answers and partial ignorance stemming from the semantic relationships among the observed answers. Experiments show that EVSE significantly improves uncertainty quantification performance. Our code is available at: https://github.com/lucieK-J/EvidentialSemanticEntropy.git.

Quantifying uncertainty in large language models (LLMs) is important for safety-critical applications because it helps spot incorrect answers, known as hallucinations. One major trend of uncertainty quantification methods is based on estimating the entropy of the distribution of the LLM’s potential output sequences. This estimation is based on a set of output sequences and associated probabilities obtained by querying the LLM several times. In this paper, we advocate and experimentally and show that the probability of unobserved sequences plays a crucial role, and we recommend future research to integrate it to enhance such LLM uncertainty quantification methods.