A prediction rigidity formalism for low-cost uncertainties in trained neural networks

TL;DR

This paper introduces 'prediction rigidities', a novel, low-cost method for quantifying uncertainties in pre-trained neural networks and regressors, connecting to Bayesian inference and applicable without retraining.

Contribution

It develops a new formalism for uncertainty quantification that is computationally inexpensive and compatible with existing neural networks through a last-layer approximation.

Findings

Effective across diverse regression tasks

Provides reliable uncertainty estimates without retraining

Connects to Bayesian inference for theoretical grounding

Abstract

Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of their applications. Based on the solution of a constrained optimization problem, we propose "prediction rigidities" as a method to obtain uncertainties of arbitrary pre-trained regressors. We establish a strong connection between our framework and Bayesian inference, and we develop a last-layer approximation that allows the new method to be applied to neural networks. This extension affords cheap uncertainties without any modification to the neural network itself or its training procedure. We show the effectiveness of our method on a wide range of regression tasks, ranging from simple toy models to applications in chemistry and meteorology.