Whiteout: Gaussian Adaptive Noise Regularization in Deep Neural Networks

TL;DR

Whiteout introduces a novel Gaussian noise regularization technique for deep neural networks that promotes sparsity and stabilizes training without relying on traditional $l_2$ regularization, demonstrating superior performance especially on small datasets.

Contribution

It is the first to thoroughly analyze and develop Gaussian noise-based regularization for deep NNs, extending to adaptive lasso and group lasso, with theoretical and empirical validation.

Findings

Whiteout stabilizes neural network training.

Whiteout outperforms Bernoulli NIRTs, dropout, and shakeout on small datasets.

Whiteout effectively induces $l_{eta}$ sparsity regularization.

Abstract

Noise injection (NI) is an efficient technique to mitigate over-fitting in neural networks (NNs). The Bernoulli NI procedure as implemented in dropout and shakeout has connections with $l_1$ and $l_2$ regularization for the NN model parameters. We propose whiteout, a family NI regularization techniques (NIRT) through injecting adaptive Gaussian noises during the training of NNs. Whiteout is the first NIRT than imposes a broad range of the $l_{\gamma}$ sparsity regularization $(\gamma\in(0,2))$ without having to involving the $l_2$ regularization. Whiteout can also be extended to offer regularizations similar to the adaptive lasso and group lasso. We establish the regularization effect of whiteout in the framework of generalized linear models with closed-form penalty terms and show that whiteout stabilizes the training of NNs with decreased sensitivity to small perturbations in the input. We establish that the noise-perturbed empirical loss function (pelf) with whiteout converges almost surely to the ideal loss function (ilf), and the minimizer of the pelf is consistent for the minimizer of the ilf. We derive the tail bound on the pelf to establish the practical feasibility in its minimization. The superiority of whiteout over the Bernoulli NIRTs, dropout and shakeout, in learning NNs with relatively small-sized training sets and non-inferiority in large-sized training sets is demonstrated in both simulated and real-life data sets. This work represents the first in-depth theoretical, methodological, and practical examination of the regularization effects of both additive and multiplicative Gaussian NI in deep NNs.