Processing capabilities and low-pass filtering effect in a delay-based photonic reservoir computer

Abstract

We explore the performance of a photonic reservoir computer based on a semiconductor laser with bandpass filtered optoelectronic feedback, focusing on how changing the low-pass filtering affects the system’s processing capabilities: the computational ability (CA) and the memory capacity (MC). Analysis of the system’s eigenvalue spectrum lets us find the correlation between the distance from the imaginary axis to the nearest eigenvalue and the MC of the reservoir computer. The maximum of the MC is observed when many eigenvalues can be characterized as having small damping, and the overall spectral shape can also be considered as a relatively flat top. We introduce a measure that evaluates the average distance between the real parts of the pseudo-continuous (PC) spectrum and the imaginary axis. The average distance is well-correlated to the MC, and the largest values of MC correspond to the smallest values of the average distance. Despite the significant decrease in the system’s bandwidth, the maximal CA remains sufficiently unchanged with variations in the low-pass cut-off frequency. However, while MC is maximized when the average distance is minimal, the CA reduces and vanishes in the vicinity of the Hopf bifurcation borders. It can be attributed to the interference of the previous inputs kept in the reservoir’s memory. Changing the low-pass cut-off frequency changes both the memory capacity and the computational ability of an optoelectronic feedback RC. Reducing the distance between the real parts of the pseudo-continuous spectrum and the imaginary axis correlates with an increase in the memory capacity of an optoelectronic feedback RC and a decrease in its computational ability.