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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 is a form of Tikhonov regularisation which penalises functions with high-frequency components in the Fourier domain. We show analytically and empirically that such regularisation produces calibrated classifiers with large classification margins and that the explicit regulariser we derive is able to reproduce these effects.'
author:
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    ${}^{1}$Department of Statistics, University of Oxford\
    ${}^{2}$Alan Turing Institute, London\
    ${}^{3}$LCTI, Télécom Paris, Institute Polytechnique de Paris\
    ${}^{4}$Oxford-Man Institute, University of Oxford
bibliography:
- 'references.bib'
title: Explicit Regularisation in Gaussian Noise Injections
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Introduction {#intro}
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Noise injections are a family of methods that involve adding or multiplying samples from a noise distribution, typically an isotropic Gaussian, to the weights and activations of a neural network during training. The benefits of such methods are well documented. Models trained with noise often generalise better to unseen data 