Chasing the Echo State Property

Reservoir Computing (RC) provides an efficient way for designing dynamical recurrent neural models. While training is restricted to a simple output component, the recurrent connections are left untrained after initialization, subject to stability constraints specified by the Echo State Property (ESP). Literature conditions for the ESP typically fail to properly account for the effects of driving input signals, often limiting the potentialities of the RC approach. In this paper, we study the fundamental aspect of asymptotic stability of RC models in presence of driving input, introducing an empirical ESP index that enables to easily analyze the stability regimes of reservoirs. Results on two benchmark datasets reveal interesting insights on the dynamical properties of input-driven reservoirs, suggesting that the actual domain of ESP validity is much wider than what covered by literature conditions commonly used in RC practice.