Exploring the limits of multifunctionality across different reservoir computers

TL;DR

This paper investigates the capacity of reservoir computers to perform multiple tasks simultaneously, focusing on their limitations when reconstructing overlapping chaotic and circular attractors, revealing how data overlap affects multifunctionality.

Contribution

It provides new insights into the limits of multifunctionality in reservoir computers, especially under conditions of overlapping training data and parameter effects.

Findings

Reconstruction ability diminishes as attractors overlap in state space.

Certain parameters critically influence multifunctionality in overlapping scenarios.

Overlap in training data hampers reservoir computer performance.

Abstract

Multifunctional neural networks are capable of performing more than one task without changing any network connections. In this paper we explore the performance of a continuous-time, leaky-integrator, and next-generation `reservoir computer' (RC), when trained on tasks which test the limits of multifunctionality. In the first task we train each RC to reconstruct a coexistence of chaotic attractors from different dynamical systems. By moving the data describing these attractors closer together, we find that the extent to which each RC can reconstruct both attractors diminishes as they begin to overlap in state space. In order to provide a greater understanding of this inhibiting effect, in the second task we train each RC to reconstruct a coexistence of two circular orbits which differ only in the direction of rotation. We examine the critical effects that certain parameters can have in each RC to achieve multifunctionality in this extreme case of completely overlapping training data.