Gradients of unitary optical neural networks using parameter-shift rule

TL;DR

This paper introduces a method using the parameter-shift rule to compute exact gradients in unitary optical neural networks, enabling hardware-based training without relying on traditional backpropagation.

Contribution

It adapts the parameter-shift rule for optical neural networks, leveraging optical interference properties to directly compute gradients from hardware measurements.

Findings

Demonstrates the feasibility of PSR for optical systems

Provides a theoretical framework for hardware gradient computation

Offers an alternative to all-optical backpropagation

Abstract

This paper explores the application of the parameter-shift rule (PSR) for computing gradients in unitary optical neural networks (UONNs). While backpropagation has been fundamental to training conventional neural networks, its implementation in optical neural networks faces significant challenges due to the physical constraints of optical systems. We demonstrate how PSR, which calculates gradients by evaluating functions at shifted parameter values, can be effectively adapted for training UONNs constructed from Mach-Zehnder interferometer meshes. The method leverages the inherent Fourier series nature of optical interference in these systems to compute exact analytical gradients directly from hardware measurements. This approach offers a promising alternative to traditional in silico training methods and circumvents the limitations of both finite difference approximations and all-optical backpropagation implementations. We present the theoretical framework and practical methodology for applying PSR to optimize phase parameters in optical neural networks, potentially advancing the development of efficient hardware-based training strategies for optical computing systems.