  Reliable confidence estimation is a challenging yet fundamental requirement
in many risk-sensitive applications. However, modern deep neural networks are
often overconfident for their incorrect predictions, i.e., misclassified
samples from known classes, and out-of-distribution (OOD) samples from unknown
classes. In recent years, many confidence calibration and OOD detection methods
have been developed. In this paper, we find a general, widely existing but
actually-neglected phenomenon that most confidence estimation methods are
harmful for detecting misclassification errors. We investigate this problem and
reveal that popular calibration and OOD detection methods often lead to worse
confidence separation between correctly classified and misclassified examples,
making it difficult to decide whether to trust a prediction or not. Finally, we
propose to enlarge the confidence gap by finding flat minima, which yields
state-of-the-art failure prediction performance under various settings
including balanced, long-tailed, and covariate-shift classification scenarios.
Our study not only provides a strong baseline for reliable confidence
estimation but also acts as a bridge between understanding calibration, OOD
detection, and failure prediction. The code is available at
\url{https://github.com/Impression2805/FMFP}.
