Learning Ability of Interpolating Convolutional Neural Networks

It is frequently observed that overparameterized neural networks generalize well. Regarding such phenomena, existing theoretical work mainly devotes to linear settings or fully connected neural networks. This paper studies learning ability of an important family of deep neural networks, deep convolutional neural networks (DCNNs), under underparameterized and overparameterized settings. We establish the best learning rates of underparameterized DCNNs without parameter restrictions presented in the literature. We also show that, by adding well defined layers to an underparameterized DCNN, we can obtain some interpolating DCNNs that maintain the good learning rates of the underparameterized DCNN. This result is achieved by a novel network deepening scheme designed for DCNNs. Our work provides theoretical verification on how overfitted DCNNs generalize well.