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The Lyapunov spectrum of recurrent neural networks is calculated and analytical approximations through random matrix theory are provided. The dependency of attractor dimensions and entropy rates on coupling strength and input fluctuations is identified and a point symmetry of the Lyapunov spectrum is revealed. A link is shown between Lyapunov exponents to error propagation and stability in trained recurrent networks for machine-learning applications.
Engelken et al. (Mon,) studied this question.