  We establish a margin based data dependent generalization error bound for a
general family of deep neural networks in terms of the depth and width, as well
as the Jacobian of the networks. Through introducing a new characterization of
the Lipschitz properties of neural network family, we achieve significantly
tighter generalization bounds than existing results. Moreover, we show that the
generalization bound can be further improved for bounded losses. Aside from the
general feedforward deep neural networks, our results can be applied to derive
new bounds for popular architectures, including convolutional neural networks
(CNNs) and residual networks (ResNets). When achieving same generalization
errors with previous arts, our bounds allow for the choice of larger parameter
spaces of weight matrices, inducing potentially stronger expressive ability for
neural networks. Numerical evaluation is also provided to support our theory.
