Explicit Regularisation in Gaussian Noise Injections
This work addresses the regularization effect of noise injections in neural networks, which is incremental as it builds on existing studies of noise in data.
The paper derived the explicit regularizer induced by Gaussian noise injections on network activations, showing it penalizes high-frequency components and leads to calibrated classifiers with large classification margins.
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.