Explicit Regularisation in Gaussian Noise Injections

TL;DR

This paper derives the explicit regulariser induced by Gaussian noise injections in neural networks, revealing it penalises high-frequency functions and leads to calibrated classifiers with large margins.

Contribution

It provides the first explicit derivation of the regulariser for GNIs applied to network activations, highlighting their effect on high-frequency components.

Findings

Regulariser penalises high-frequency Fourier components.

Regularisation leads to classifiers with larger margins.

Analytical and empirical validation of the regulariser's effect.

Abstract

We study the regularisation induced in neural networks by Gaussian noise injections (GNIs). Though such injections have been extensively studied when applied to data, there have been few studies on understanding the regularising effect they induce when applied to network activations. Here we derive the explicit regulariser of GNIs, obtained by marginalising out the injected noise, and show that it penalises functions with high-frequency components in the Fourier domain; particularly in layers closer to a neural network's output. We show analytically and empirically that such regularisation produces calibrated classifiers with large classification margins.