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

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