Analysis of the dynamics of the echo state network model using recurrence plot

Abstract

At the beginning of the 2000s, a specific type of Recurrent Neural Networks (RNNs) was developed with the name Echo State Network (ESN). The model has become popular during the last 15 years in the area of temporal learning. The model has a RNN (named reservoir) that projects an input sequence in a feature map. The reservoir has two main parameters that impact the accuracy of the model: the reservoir size (number of neurons in the RNN) and the spectral radius of the hidden-hidden recurrent weight matrix. In this article, we analyze the impact of these parameters using the Recurrence Plot technique, which is a useful tool for visualizing chaotic systems. Experiments carried out with three well-known dynamical systems show the relevance of the spectral radius in the reservoir projections.