  Large language models (LLMs) often generate inaccurate or fabricated
information and generally fail to indicate their confidence, which limits their
broader applications. Previous work elicits confidence from LLMs by direct or
self-consistency prompting, or constructing specific datasets for supervised
finetuning. The prompting-based approaches have inferior performance, and the
training-based approaches are limited to binary or inaccurate group-level
confidence estimates. In this work, we present the advanced SaySelf, a training
framework that teaches LLMs to express more accurate fine-grained confidence
estimates. In addition, beyond the confidence scores, SaySelf initiates the
process of directing LLMs to produce self-reflective rationales that clearly
identify gaps in their parametric knowledge and explain their uncertainty. This
is achieved by using an LLM to automatically summarize the uncertainties in
specific knowledge via natural language. The summarization is based on the
analysis of the inconsistency in multiple sampled reasoning chains, and the
resulting data is utilized for supervised fine-tuning. Moreover, we utilize
reinforcement learning with a meticulously crafted reward function to calibrate
the confidence estimates, motivating LLMs to deliver accurate, high-confidence
predictions and to penalize overconfidence in erroneous outputs. Experimental
results in both in-distribution and out-of-distribution datasets demonstrate
the effectiveness of SaySelf in reducing the confidence calibration error and
maintaining the task performance. We show that the generated self-reflective
rationales are reasonable and can further contribute to the calibration. The
code is made public at https://github.com/xu1868/SaySelf.
