A statistically consistent measure of semantic uncertainty using Language Models

To address the challenge of quantifying uncertainty in the outputs generated by language models, we propose a novel measure of semantic uncertainty, semantic spectral entropy, that is statistically consistent under mild assumptions. This measure is implemented through a straightforward algorithm that relies solely on standard, pretrained language models, without requiring access to the internal generation process. Our approach imposes minimal constraints on the choice of language models, making it broadly applicable across different architectures and settings. Through comprehensive simulation studies, we demonstrate that the proposed method yields an accurate and robust estimate of semantic uncertainty, even in the presence of the inherent randomness characteristic of generative language model outputs.