Towards Understanding the Generalization Bias of Two Layer Convolutional Linear Classifiers with Gradient Descent
This work addresses the generalization bias in deep learning for researchers, but it is incremental as it focuses on linear models rather than full neural networks.
The paper tackles the problem of explaining why gradient descent can find well-generalizing solutions in high-capacity models by showing that convolutional linear classifiers generalize better than fully-connected ones when data has spatial structure, with experimental results confirming their analysis.
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.