Master memory function for delay-based reservoir computers with single-variable dynamics
This work addresses a theoretical bottleneck in reservoir computing by providing a universal tool for memory analysis, which is incremental as it builds on existing delay-based methods.
The authors tackled the problem of characterizing memory capacity in delay-based reservoir computers by introducing a universal master memory function (MMF) that provides linear memory capacity for any single-variable reservoir with small inputs, enabling efficient computation and application to systems with unknown dynamics.
We show that many delay-based reservoir computers considered in the literature can be characterized by a universal master memory function (MMF). Once computed for two independent parameters, this function provides linear memory capacity for any delay-based single-variable reservoir with small inputs. Moreover, we propose an analytical description of the MMF that enables its efficient and fast computation. Our approach can be applied not only to reservoirs governed by known dynamical rules such as Mackey-Glass or Ikeda-like systems but also to reservoirs whose dynamical model is not available. We also present results comparing the performance of the reservoir computer and the memory capacity given by the MMF.