Universal Approximation Capabilities of Coherent Diffractive Systems

Abstract

Coherent optical computing systems are a promising avenue to increasing computation speed and solving energy requirements for machine learning applications. These systems leverage the diffraction of coherent waves to perform calculations in the optical domain. Although diffraction is inherently a linear process in complex space $\mathbb{C}$, empirical results show that these systems can outperform standard linear matrix multiplications in $\mathbb{R}$, because photo-sensors project from complex space to real space. Here we provide theoretical insights to explain this phenomenon. We demonstrate that a system consisting of multiple phase-plates, two output photo-detectors, and the appropriate input encoding is theoretically able to learn any one-dimensional function. Additionally, we show that encoding input information exclusively in the intensity of the diffractive system is never sufficient for the system to be a universal function approximator. These findings enhance our understanding of the capabilities of diffractive optical systems and offer guidance for improving their training methods.