On Subjective Uncertainty Quantification and Calibration in Natural Language Generation

Applications of large language models often involve the generation of free-form responses, in which case uncertainty quantification becomes challenging. This is due to the need to identify task-specific uncertainties (e.g., about the semantics) which appears difficult to define in general cases. This work addresses these challenges from a perspective of Bayesian decision theory, starting from the assumption that our utility is characterized by a similarity measure that compares a generated response with a hypothetical true response. We discuss how this assumption enables principled quantification of the model's subjective uncertainty and its calibration. We further derive a measure for epistemic uncertainty, based on a missing data perspective and its characterization as an excess risk. The proposed measures can be applied to black-box language models. We demonstrate the proposed methods on question answering and machine translation tasks, where they extract broadly meaningful uncertainty estimates from GPT and Gemini models and quantify their calibration.