A Kernel Perspective for Regularizing Deep Neural Networks

TL;DR

This paper introduces a novel perspective on regularizing deep neural networks using RKHS norms, unifying existing methods and proposing new strategies that improve robustness and performance on small datasets.

Contribution

It presents a kernel-based framework for regularization that unifies and extends existing principles, leading to new effective regularization techniques.

Findings

Effective on small datasets

Enhances adversarial robustness

Unifies multiple regularization methods

Abstract

We propose a new point of view for regularizing deep neural networks by using the norm of a reproducing kernel Hilbert space (RKHS). Even though this norm cannot be computed, it admits upper and lower approximations leading to various practical strategies. Specifically, this perspective (i) provides a common umbrella for many existing regularization principles, including spectral norm and gradient penalties, or adversarial training, (ii) leads to new effective regularization penalties, and (iii) suggests hybrid strategies combining lower and upper bounds to get better approximations of the RKHS norm. We experimentally show this approach to be effective when learning on small datasets, or to obtain adversarially robust models.