The Spectral Radius Remains A Valid Indicator Of The Echo State Property For Large Reservoirs

In the field of Reservoir Computing, scaling the spectral radius of the weight matrix of a random recurrent neural network to below unity is a commonly used method to ensure the Echo State Property. Recently it has been shown that this condition is too weak. To overcome this problem, other more involved - sufficient conditions for the Echo State Property have been proposed. In this paper we provide a large-scale experimental verification of the Echo State Property for large recurrent neural networks with zero input and zero bias. Our main conclusion is that the spectral radius method remains a valid indicator of the Echo State Property; the probability that the Echo State Property does not hold, drops for larger networks with spectral radius below unity, which are the ones of practical interest.