We study the propagation and distribution of information-carrying signals injected in dynamical systems serving as a reservoir computers. A multivariate correlation analysis in tailored replica tests reveals consistency spectra and capacities of a reservoir. These measures provide a high-dimensional portrait of the nonlinear functional dependence on the inputs. For multiple inputs a hierarchy of capacity measures characterizes the interference of signals from each source. For each input the time-resolved capacity forms a nonlinear fading memory profile. We illustrate the methodology with various types of echo state networks.
@article{arxiv.2105.13473,
title = {Consistency capacity of reservoir computers},
author = {Thomas Jüngling and Thomas Lymburn and Michael Small},
journal= {arXiv preprint arXiv:2105.13473},
year = {2021}
}