From Entropy to Calibrated Uncertainty: Training Language Models to Reason About Uncertainty

TL;DR

This paper introduces a three-stage post-training pipeline for large language models to produce calibrated, interpretable uncertainty estimates efficiently, improving their reliability in high-stakes applications.

Contribution

It presents a novel post-training method combining entropy-based scoring, calibration, and reinforcement learning to enhance LLM uncertainty estimation.

Findings

Models achieve better calibration than baselines.

Uncertainty estimates are interpretable and computationally efficient.

Models generalize to unseen tasks without additional training.

Abstract

Large Language Models (LLMs) that can express interpretable and calibrated uncertainty are crucial in high-stakes domains. While methods to compute uncertainty post-hoc exist, they are often sampling-based and therefore computationally expensive or lack calibration. We propose a three-stage pipeline to post-train LLMs to efficiently infer calibrated uncertainty estimates for their responses. First, we compute fine-grained entropy-based uncertainty scores on the training data, capturing the distributional variability of model outputs in embedding space. Second, these scores are calibrated via Platt scaling, producing reliable and human-interpretable uncertainty signals. Finally, the target LLM is post-trained via reinforcement learning to align its policy with these calibrated signals through a verifiable reward function. Unlike post-hoc uncertainty estimation methods, our approach provides interpretable and computationally efficient uncertainty estimates at test time. Experiments show that models trained with our pipeline achieve better calibration than baselines and generalize to unseen tasks without further processing, suggesting that they learn a robust uncertainty reasoning behavior.