Calibrating Verbalized Probabilities for Large Language Models

Calibrating verbalized probabilities presents a novel approach for reliably assessing and leveraging outputs from black-box Large Language Models (LLMs). Recent methods have demonstrated improved calibration by applying techniques like Platt scaling or temperature scaling to the confidence scores generated by LLMs. In this paper, we explore the calibration of verbalized probability distributions for discriminative tasks. First, we investigate the capability of LLMs to generate probability distributions over categorical labels. We theoretically and empirically identify the issue of re-softmax arising from the scaling of verbalized probabilities, and propose using the invert softmax trick to approximate the "logit" by inverting verbalized probabilities. Through extensive evaluation on three public datasets, we demonstrate: (1) the robust capability of LLMs in generating class distributions, and (2) the effectiveness of the invert softmax trick in estimating logits, which, in turn, facilitates post-calibration adjustments.