Towards Understanding the Generalization Bias of Two Layer Convolutional Linear Classifiers with Gradient Descent

TL;DR

This paper investigates why convolutional linear classifiers with gradient descent can generalize better than non-convolutional ones, highlighting the roles of architecture, data distribution, and optimization in this phenomenon.

Contribution

It provides a theoretical framework analyzing the generalization bias of convolutional linear classifiers, incorporating data distribution, filter size, and gradient descent.

Findings

Convolutional architecture can lead to better generalization than non-convolutional models.

The generalization performance depends on data distribution and filter size.

Experimental results validate the theoretical analysis.

Abstract

A major challenge in understanding the generalization of deep learning is to explain why (stochastic) gradient descent can exploit the network architecture to find solutions that have good generalization performance when using high capacity models. We find simple but realistic examples showing that this phenomenon exists even when learning linear classifiers --- between two linear networks with the same capacity, the one with a convolutional layer can generalize better than the other when the data distribution has some underlying spatial structure. We argue that this difference results from a combination of the convolution architecture, data distribution and gradient descent, all of which are necessary to be included in a meaningful analysis. We provide a general analysis of the generalization performance as a function of data distribution and convolutional filter size, given gradient descent as the optimization algorithm, then interpret the results using concrete examples. Experimental results show that our analysis is able to explain what happens in our introduced examples.