Future Confidence Distillation in Large Language Models
Reliable confidence estimation is essential for deploying large language models (LLMs) in confidence-aware systems, where downstream decisions such as retrieval, tool use, and adaptive computation depend on accurately estimating answer reliability. Existing approaches, however, largely treat confidence as a property of completed responses, overlooking how confidence-related information evolves throughout the answering process. In this work, we investigate confidence from a temporal perspective by comparing pre-solution Feeling-of-Knowing (FOK) and post-solution Judgement-of-Learning (JOL) confidence estimates across frontier and open-source LLMs. We show that post-solution confidence is consistently better calibrated and more discriminative than pre-solution confidence, while linear probes trained on hidden representations recover substantially richer confidence-related information than models explicitly verbalise. Building on this observation, we introduce future confidence distillation, which trains predictors operating on pre-solution hidden representations using teacher confidence estimates produced by post-solution correctness probes. Despite requiring only pre-solution representations for inference, distilled predictors recover much of the calibration improvement achieved by post-solution confidence, remain highly sample efficient, and transfer across datasets within the same domain. Together, our findings demonstrate that confidence-related information evolves throughout the answering process and can be anticipated before answer generation is complete, enabling significantly more reliable yet low-cost confidence estimation.