On Tighter Generalization Bound for Deep Neural Networks: CNNs, ResNets, and Beyond

We propose a generalization error bound for a general family of deep neural networks based on the depth and width of the networks, as well as the spectral norm of weight matrices. Through introducing a novel characterization of the Lipschitz properties of neural network family, we achieve a tighter generalization error bound. We further obtain a result that is free of linear dependence on norms for bounded losses. Besides the general deep neural networks, our results can be applied to derive new bounds for several popular architectures, including convolutional neural networks (CNNs), residual networks (ResNets), and hyperspherical networks (SphereNets). When achieving same generalization errors with previous arts, our bounds allow for the choice of much larger parameter spaces of weight matrices, inducing potentially stronger expressive ability for neural networks.