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

TL;DR

This paper introduces a universal master memory function (MMF) for delay-based reservoir computers with single-variable dynamics, enabling efficient prediction of their linear memory capacity across various systems.

Contribution

The authors develop an analytical and computational framework for the MMF, applicable to known and unknown dynamical systems, enhancing understanding of reservoir computer memory capabilities.

Findings

MMF accurately predicts memory capacity of delay-based reservoirs.

The approach applies to reservoirs with known and unknown dynamics.

Efficient computation of MMF accelerates reservoir performance analysis.

Abstract

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.