Master memory function for delay-based reservoir computers with single-variable dynamics

We show that many delay-based reservoir computers considered in the\nliterature can be characterized by a universal master memory function (MMF).\n Once computed for two independent parameters, this function provides linear\nmemory capacity for any delay-based single-variable reservoir with small\ninputs. Moreover, we propose an analytical description of the MMF that enables\nits efficient and fast computation.\n Our approach can be applied not only to reservoirs governed by known\ndynamical rules such as Mackey-Glass or Ikeda-like systems but also to\nreservoirs whose dynamical model is not available. We also present results\ncomparing the performance of the reservoir computer and the memory capacity\ngiven by the MMF.\n