Generalization error bounds for deep neural networks trained by stochastic gradient descent (SGD) are derived by combining a dynamical control of an appropriate parameter norm and the Rademacher complexity estimate based on parameter norms. The bounds explicitly depend on the loss along the training trajectory, and work for a wide range of network architectures including multilayer perceptron (MLP) and convolutional neural networks (CNN). Compared with other algorithm-depending generalization estimates such as uniform stability-based bounds, our bounds do not require L-smoothness of the nonconvex loss function, and apply directly to SGD instead of Stochastic Langevin gradient descent (SGLD). Numerical results show that our bounds are non-vacuous and robust with the change of optimizer and network hyperparameters.Preprint. Under review.

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