Asymmetric Heavy Tails and Implicit Bias in Gaussian Noise Injections - Inria - Institut national de recherche en sciences et technologies du numérique Access content directly
Conference Papers Year : 2021

Asymmetric Heavy Tails and Implicit Bias in Gaussian Noise Injections

Abstract

Gaussian noise injections (GNIs) are a family of simple and widely-used regularisation methods for training neural networks, where one injects additive or multiplicative Gaussian noise to the network activations at every iteration of the optimisation algorithm, which is typically chosen as stochastic gradient descent (SGD). In this paper we focus on the so-called `implicit effect' of GNIs, which is the effect of the injected noise on the dynamics of SGD. We show that this effect induces an asymmetric heavy-tailed noise on SGD gradient updates. In order to model this modified dynamics, we first develop a Langevin-like stochastic differential equation that is driven by a general family of asymmetric heavy-tailed noise. Using this model we then formally prove that GNIs induce an `implicit bias', which varies depending on the heaviness of the tails and the level of asymmetry. Our empirical results confirm that different types of neural networks trained with GNIs are well-modelled by the proposed dynamics and that the implicit effect of these injections induces a bias that degrades the performance of networks.

Dates and versions

hal-03530315 , version 1 (17-01-2022)

Identifiers

Cite

Alexander Camuto, Xiaoyu Wang, Lingjiong Zhu, Chris Holmes, Mert Gürbüzbalaban, et al.. Asymmetric Heavy Tails and Implicit Bias in Gaussian Noise Injections. ICML 2021 - Thirty-eighth annual conference International Conference on Machine Learning, Jul 2021, Virtual, France. ⟨hal-03530315⟩
48 View
0 Download

Altmetric

Share

Gmail Mastodon Facebook X LinkedIn More