Limitations of the recall capabilities in delay based reservoir computing systems

TL;DR

This paper investigates the memory capacity limitations of delay-based reservoir computing systems with a Hopf normal form nonlinearity, revealing how the ratio of input period to delay affects performance.

Contribution

It provides a numerical analysis of recall capabilities and identifies optimal delay-to-input period ratios for enhanced memory capacity.

Findings

Total memory capacity depends on the ratio of input period to delay.

Optimal performance occurs when delay is approximately 1.6 times the clock cycle.

Memory capacity is limited even with constant readout dimension.

Abstract

We analyze the memory capacity of a delay based reservoir computer with a Hopf normal form as nonlinearity and numerically compute the linear as well as the higher order recall capabilities. A possible physical realisation could be a laser with external cavity, for which the information is fed via electrical injection. A task independent quantification of the computational capability of the reservoir system is done via a complete orthonormal set of basis functions. Our results suggest that even for constant readout dimension the total memory capacity is dependent on the ratio between the information input period, also called the clock cycle, and the time delay in the system. Optimal performance is found for a time delay about 1.6 times the clock cycle