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.
After rebuttal: The authors have nicely addressed my comments. I have increased my rating to 7.
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This paper proposes a generalization error bound for DNNs (and their generalizations) based on the depth and width of the networks, as well as the spectral norm of weight matrices. The proposed work is shown to provide a tighter generalization error bounds compared with a few existing literatures. 
Pros: This paper makes theoretical contributions to the understanding of DNNs. This is an important but difficult task. As a theoretical paper, this one is relatively easy to follow. 
Cons: In spite of its theoretical contributions, this paper has a few major issues. 
Q1: This paper fails to fairly compare with the most recent work, Arora et al. (2018), Zhou and Feng (2018). For instance, Arora et al. (2018) uses error-resilience parameters instead of the norms of weight matrices to obtain a better generalization error. The authors claim that the error-resilience parameters are less interpretable than the norms of weight matrices. This claim could be subjective and is not convincing. 
Q2: The error bounds of Bartlett et al. (2017), Neyshabur et al. (2017) could be improved for low-rank weight matrices, in which case the proposed Theorem 1 is tighter only if $p \le D^2$. This holds only when DNN is very deep. Can theorem 1 be improved by similarly considering the low-rankness of weight matrices?
Q3: In Corollary 2, the error bound for CNN, the authors assume that the filters are orthogonal with unit norm. Can the authors provide some justification on the orthogonal filters? In addition, Zhou and Feng (2018) have achieved similar bound for CNN. Can the authors provide some justification why this latest result is not included in Table 2?