Critical echo state network dynamics by means of Fisher information maximization

The computational capability of an Echo State Network (ESN), expressed in terms of low prediction error and high short-term memory capacity, is maximized on the so-called “edge of criticality”. In this paper we present a novel, unsupervised approach to identify this edge and, accordingly, we determine hyperparameters configuration that maximize network performance. The proposed method is application-independent and stems from recent theoretical results consolidating the link between Fisher information and critical phase transitions. We show how to identify optimal ESN hyperparameters by relying only on the Fisher information matrix (FIM) estimated from the activations of hidden neurons. In order to take into account the particular input signal driving the network dynamics, we adopt a recently proposed non-parametric FIM estimator. Experimental results on a set of standard benchmarks are provided and discussed, demonstrating the validity of the proposed method.