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

The theoretical explanation for deep neural network (DNN) is still an open problem. In this paper DNN is considered as a discrete-time dynamical system due to its layered structure. The complexity provided by the nonlinearity in the dynamics is analyzed in terms of topological entropy and chaos characterized by Lyapunov exponents. The properties revealed for the dynamics of DNN are applied to analyze the corresponding capabilities of classification and generalization.