Architectural and Markovian factors of echo state networks.

Echo State Networks (ESNs) constitute an emerging approach for efficiently modeling Recurrent Neural Networks (RNNs). In this paper we investigate some of the main aspects that can be accounted for the success and limitations of this class of models. In particular, we propose complementary classes of factors related to contractivity and architecture of reservoirs and we study their relative relevance. First, we show the existence of a class of tasks for which ESN performance is independent of the architectural design. The effect of the Markovian factor, characterizing a significant class within these cases, is shown by introducing instances of easy/hard tasks for ESNs featured by contractivity of reservoir dynamics. In the complementary cases, for which architectural design is effective, we investigate and decompose the aspects of network design that allow a larger reservoir to progressively improve the predictive performance. In particular, we introduce four key architectural factors: input variability, multiple time-scales dynamics, non-linear interactions among units and regression in an augmented feature space. To investigate the quantitative effects of the different architectural factors within this class of tasks successfully approached by ESNs, variants of the basic ESN model are proposed and tested on instances of datasets of different nature and difficulty. Experimental evidences confirm the role of the Markovian factor and show that all the identified key architectural factors have a major role in determining ESN performances.