Reservoir Topology in Deep Echo State Networks

Deep Echo State Networks (DeepESNs) recently extended the applicability of Reservoir Computing (RC) methods towards the field of deep learning. In this paper we study the impact of constra ined reservoir topologies in the architectural design of deep reservo irs, through numerical experiments on several RC benchmarks. The major o utcome of our investigation is to show the remarkable effect, in term s of predictive performance gain, achieved by the synergy between a dee p reservoir construction and a structured organization of the recurren t units in each layer. Our results also indicate that a particularly advant ageous architectural setting is obtained in correspondence of DeepESNs whe re reservoir units are structured according to a permutation recurrent m atrix.