  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 constrained reservoir topologies in the
architectural design of deep reservoirs, through numerical experiments on
several RC benchmarks. The major outcome of our investigation is to show the
remarkable effect, in terms of predictive performance gain, achieved by the
synergy between a deep reservoir construction and a structured organization of
the recurrent units in each layer. Our results also indicate that a
particularly advantageous architectural setting is obtained in correspondence
of DeepESNs where reservoir units are structured according to a permutation
recurrent matrix.
