Stochastic Function Norm Regularization of Deep Networks

TL;DR

This paper introduces a novel regularization method for deep neural networks using the $L_2$ function norm, which improves performance in small data regimes by directly controlling the network function complexity.

Contribution

It proposes two new methods to incorporate $L_2$ function norm regularization into stochastic backpropagation and analyzes their convergence, demonstrating superior results on benchmark datasets.

Findings

Outperforms state-of-the-art methods in low sample regimes

Shows significant improvement on MNIST and CIFAR10 datasets

Effective in low-dimensional manifold data scenarios

Abstract

Deep neural networks have had an enormous impact on image analysis. State-of-the-art training methods, based on weight decay and DropOut, result in impressive performance when a very large training set is available. However, they tend to have large problems overfitting to small data sets. Indeed, the available regularization methods deal with the complexity of the network function only indirectly. In this paper, we study the feasibility of directly using the $L_2$ function norm for regularization. Two methods to integrate this new regularization in the stochastic backpropagation are proposed. Moreover, the convergence of these new algorithms is studied. We finally show that they outperform the state-of-the-art methods in the low sample regime on benchmark datasets (MNIST and CIFAR10). The obtained results demonstrate very clear improvement, especially in the context of small sample regimes with data laying in a low dimensional manifold. Source code of the method can be found at \url{https://github.com/AmalRT/DNN_Reg}.