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Echo State Networks are efficient time-series predictors, which highly dependon the value of the spectral radius of the reservoir connectivity matrix. Basedon recent results on the mean field theory of driven random recurrent neuralnetworks, enabling the computation of the largest Lyapunov exponent of an ESN,we develop a cheap algorithm to establish a local and operational version ofthe Echo State Property.

A local Echo State Property through the largest Lyapunov exponent