Explicit Regularisation in Gaussian Noise Injections

Alexander Camuto , Matthew Willetts , Umut Şimşekli (1, 2, 3) , Stephen Roberts , Chris Holmes

1 IP Paris - Institut Polytechnique de Paris
2 IDS - Département Images, Données, Signal
3 S2A - Signal, Statistique et Apprentissage

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.

Domaines: Machine Learning [stat.ML]

Alexander Camuto, Matthew Willetts, Umut Şimşekli, Stephen Roberts, Chris Holmes. Explicit Regularisation in Gaussian Noise Injections. Advances in Neural Processing Systems, 2020, Online, France. ⟨hal-03269116⟩