Limitations of the Recall Capabilities in Delay-Based Reservoir Computing Systems

We analyse 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 realization 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.

Automated summary

This paper analyzes the memory capacity of a delay-based reservoir computer using a Hopf normal form as nonlinearity, and calculates its linear as well as higher order recall capabilities. The results show that the total memory capacity is dependent on the ratio between the information input period and the time delay in the system.