Expectation consistency for calibration of neural networks
This work addresses calibration for better uncertainty quantification in deep learning, offering a principled alternative to existing methods, though it is incremental as it builds on prior techniques like temperature scaling.
The paper tackles the problem of neural network overconfidence by introducing expectation consistency (EC), a post-training calibration method that rescales last layer weights to align average validation confidence with correct label proportion, achieving similar performance to temperature scaling across architectures and datasets while being grounded in Bayesian optimality principles.
Despite their incredible performance, it is well reported that deep neural networks tend to be overoptimistic about their prediction confidence. Finding effective and efficient calibration methods for neural networks is therefore an important endeavour towards better uncertainty quantification in deep learning. In this manuscript, we introduce a novel calibration technique named expectation consistency (EC), consisting of a post-training rescaling of the last layer weights by enforcing that the average validation confidence coincides with the average proportion of correct labels. First, we show that the EC method achieves similar calibration performance to temperature scaling (TS) across different neural network architectures and data sets, all while requiring similar validation samples and computational resources. However, we argue that EC provides a principled method grounded on a Bayesian optimality principle known as the Nishimori identity. Next, we provide an asymptotic characterization of both TS and EC in a synthetic setting and show that their performance crucially depends on the target function. In particular, we discuss examples where EC significantly outperforms TS.