  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.
