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We study the propagation and distribution of information-carrying signals injected in dynamical systems serving as reservoir computers. Through different combinations of repeated input signals, a multivariate correlation analysis reveals measures known as the consistency spectrum and consistency capacity. These are high-dimensional portraits of the nonlinear functional dependence between input and reservoir state. For multiple inputs, a hierarchy of capacities characterizes the interference of signals from each source. For an individual input, the time-resolved capacities form a profile of the reservoir's nonlinear fading memory. We illustrate this methodology for a range of echo state networks.
|Number of pages
|IEEE Transactions on Neural Networks and Learning Systems
|Early online date
|Published - 1 Jun 2022