Understanding Task Performance of Time-Multiplexed Optical Reservoir Computing via Polynomial Expansion

TL;DR

This paper analyzes a linear optical reservoir computing system's computational capabilities, emphasizing how transient dynamics and delay effects influence task performance and nonlinear transformation capabilities.

Contribution

It provides a systematic framework to analyze the contributions of nonlinearity, transient dynamics, and delay in linear optical reservoirs, highlighting how these factors interact.

Findings

Transient coupling and delayed feedback improve performance.

Explicit monomial analysis links task needs to system nonlinearity.

Larger virtual node count is needed for enhanced capabilities.

Abstract

We investigate the computational potential and limitations of a passive linear optical reservoir with a photodetector at the optical-to-electrical interface as the sole source of nonlinearity. In contrast to conventional nonlinear reservoirs, where transient dynamics and delay jointly enhance complexity and distribute nonlinear responses, the proposed linear architecture isolates these contributions, as intrinsic nonlinear spreading is absent. We thus provide a framework that enables the independent and systematic analysis of key factors, including nonlinear transformations, transient dynamics, and time-delay effects, as well as their interactions. By explicitly identifying the contributing monomials for different tasks, we establish the relationship between task requirements and the nonlinearity provided by the system. Incorporating transient coupling and delayed feedback is shown to significantly enhance performance and attractor reconstruction capabilities by compensating for missing higher-order nonlinearities through access to multi-step integration schemes. This improvement, however, comes at the cost of requiring a larger number of virtual nodes.