A prediction rigidity formalism for low-cost uncertainties in trained neural networks
This provides a practical solution for scientists and engineers needing reliable uncertainty estimates in regression applications, though it is incremental as it builds on existing Bayesian inference frameworks.
The authors tackled the problem of unreliable neural network predictions outside the training domain by proposing 'prediction rigidities' as a method to quantify uncertainties for pre-trained regressors, achieving low-cost uncertainties without modifying the network or training, as demonstrated across tasks from toy models to chemistry and meteorology.
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.