Disentangling the Mechanisms Behind Implicit Regularization in SGD

TL;DR

This paper empirically investigates the mechanisms behind why small-batch SGD generalizes better than large-batch SGD, focusing on the role of implicit regularization and how different regularizers affect generalization across datasets.

Contribution

It provides the first extensive empirical evaluation of various hypotheses on implicit regularization in SGD, highlighting the effectiveness of gradient norm and Fisher information regularizations.

Findings

Explicit regularization of gradient norm and Fisher trace recovers small-batch generalization.

Jacobian regularizations do not replicate small-batch benefits.

Regularization effects vary across datasets like CIFAR10 and CIFAR100.

Abstract

A number of competing hypotheses have been proposed to explain why small-batch Stochastic Gradient Descent (SGD)leads to improved generalization over the full-batch regime, with recent work crediting the implicit regularization of various quantities throughout training. However, to date, empirical evidence assessing the explanatory power of these hypotheses is lacking. In this paper, we conduct an extensive empirical evaluation, focusing on the ability of various theorized mechanisms to close the small-to-large batch generalization gap. Additionally, we characterize how the quantities that SGD has been claimed to (implicitly) regularize change over the course of training. By using micro-batches, i.e. disjoint smaller subsets of each mini-batch, we empirically show that explicitly penalizing the gradient norm or the Fisher Information Matrix trace, averaged over micro-batches, in the large-batch regime recovers small-batch SGD generalization, whereas Jacobian-based regularizations fail to do so. This generalization performance is shown to often be correlated with how well the regularized model's gradient norms resemble those of small-batch SGD. We additionally show that this behavior breaks down as the micro-batch size approaches the batch size. Finally, we note that in this line of inquiry, positive experimental findings on CIFAR10 are often reversed on other datasets like CIFAR100, highlighting the need to test hypotheses on a wider collection of datasets.