On Calibration of Large Language Models: From Response To Capability

Abstract

Large language models (LLMs) are widely deployed as general-purpose problem solvers, making accurate confidence estimation critical for reliable use. Prior work on LLM calibration largely focuses on response-level confidence, which estimates the correctness of a single generated output. However, this formulation is misaligned with many practical settings where the central question is how likely a model is to solve a query overall. We show that this mismatch results from the stochastic nature of modern LLM decoding, under which single-response correctness fails to reflect underlying model capability. To address this issue, we introduce capability calibration, which targets the model's expected accuracy on a query. We formally distinguish capability calibration from response calibration and show that the two differ both theoretically and empirically. We establish an empirical evaluation setup and study a range of confidence estimation methods. Our results demonstrate that capability-calibrated confidence improves pass@$k$ prediction and inference budget allocation, establishing a foundation with potential for diverse applications.