  Convolutional neural networks (CNNs) have achieved breakthrough performances
in a wide range of applications including image classification, semantic
segmentation, and object detection. Previous research on characterizing the
generalization ability of neural networks mostly focuses on fully connected
neural networks (FNNs), regarding CNNs as a special case of FNNs without taking
into account the special structure of convolutional layers. In this work, we
propose a tighter generalization bound for CNNs by exploiting the sparse and
permutation structure of its weight matrices. As the generalization bound
relies on the spectral norm of weight matrices, we further study spectral norms
of three commonly used convolution operations including standard convolution,
depthwise convolution, and pointwise convolution. Theoretical and experimental
results both demonstrate that our bounds for CNNs are tighter than existing
bounds.
