On the training dynamics of deep networks with $L_2$ regularization

TL;DR

This paper investigates how $L_2$ regularization influences deep network training, revealing empirical relations that help optimize regularization and proposing a dynamic schedule that enhances training efficiency, supported by theoretical insights into infinitely wide networks.

Contribution

It uncovers empirical relations between regularization, learning rate, and training steps, and introduces a dynamic regularization schedule with theoretical analysis for infinitely wide networks.

Findings

Empirical relations predict optimal regularization parameters.

Dynamic regularization schedule improves training performance.

Theoretical analysis of gradient flow in infinitely wide networks.

Abstract

We study the role of $L_2$ regularization in deep learning, and uncover simple relations between the performance of the model, the $L_2$ coefficient, the learning rate, and the number of training steps. These empirical relations hold when the network is overparameterized. They can be used to predict the optimal regularization parameter of a given model. In addition, based on these observations we propose a dynamical schedule for the regularization parameter that improves performance and speeds up training. We test these proposals in modern image classification settings. Finally, we show that these empirical relations can be understood theoretically in the context of infinitely wide networks. We derive the gradient flow dynamics of such networks, and compare the role of $L_2$ regularization in this context with that of linear models.