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The theoretical explanation for deep neural network (DNN) is still an openproblem. In this paper DNN is considered as a discrete-time dynamical systemdue to its layered structure. The complexity provided by the nonlinearity inthe dynamics is analyzed in terms of topological entropy and chaoscharacterized by Lyapunov exponents. The properties revealed for the dynamicsof DNN are applied to analyze the corresponding capabilities of classificationand generalization.

Analysis on the Nonlinear Dynamics of Deep Neural Networks: Topological Entropy and Chaos