Function-Space Regularization in Neural Networks: A Probabilistic Perspective

TL;DR

This paper introduces a probabilistic approach to regularization in neural networks, enabling explicit encoding of desired predictive functions and improving generalization, uncertainty estimation, and task adaptation.

Contribution

It proposes a novel function-space empirical Bayes regularization method that combines parameter- and function-space regularization with minimal computational cost.

Findings

Achieves near-perfect semantic shift detection

Provides highly-calibrated predictive uncertainty

Enhances generalization under covariate shift

Abstract

Parameter-space regularization in neural network optimization is a fundamental tool for improving generalization. However, standard parameter-space regularization methods make it challenging to encode explicit preferences about desired predictive functions into neural network training. In this work, we approach regularization in neural networks from a probabilistic perspective and show that by viewing parameter-space regularization as specifying an empirical prior distribution over the model parameters, we can derive a probabilistically well-motivated regularization technique that allows explicitly encoding information about desired predictive functions into neural network training. This method -- which we refer to as function-space empirical Bayes (FSEB) -- includes both parameter- and function-space regularization, is mathematically simple, easy to implement, and incurs only minimal computational overhead compared to standard regularization techniques. We evaluate the utility of this regularization technique empirically and demonstrate that the proposed method leads to near-perfect semantic shift detection, highly-calibrated predictive uncertainty estimates, successful task adaption from pre-trained models, and improved generalization under covariate shift.