  Large Language Models (LLMs), including ChatGPT and LLaMA, are susceptible to
generating hallucinated answers in a confident tone. While efforts to elicit
and calibrate confidence scores have proven useful, recent findings show that
controlling uncertainty must go beyond calibration: predicted scores may
deviate significantly from the actual posterior probabilities due to the impact
of grouping loss. In this work, we construct a new evaluation dataset derived
from a knowledge base to assess confidence scores given to answers of Mistral
and LLaMA. Experiments show that they tend to be overconfident. Further, we
show that they are more overconfident on some answers than others, \emph{eg}
depending on the nationality of the person in the query. In
uncertainty-quantification theory, this is grouping loss. To address this, we
propose a solution to reconfidence LLMs, canceling not only calibration but
also grouping loss. The LLMs, after the reconfidencing process, indicate
improved confidence alignment with the accuracy of their responses.
