On the Size of Convolutional Neural Networks and Generalization Performance

While Convolutional Neural Networks (CNNs) have recently achieved impressive results on many classification tasks, it is still unclear why they perform so well and how to properly design them. In this work, we investigate the effect of the convolutional depth of a CNN on its generalization performance for binary classification problems. We prove a sufficient condition-polynomial in the depth of the CNN-on the training database size to guarantee such performance. We empirically test our theory on the problem of gender classification and explore the effect of varying the CNN depth, as well as the training distribution and set size.