Optical Implementation of Equilibrium Propagation Using Spatial Photonic Ising Machines

2026-06-11

AI Summary

This work proposes an energy-efficient and physically realizable implementation of Equilibrium Propagation (EP) as an alternative to power-intensive backpropagation. By integrating optical and digital computation on a Spatial Photonic Ising Machine, the approach encodes continuous neuronal states and binary trainable parameters into phase modulation via a gauge transformation using a spatial light modulator, and performs inference through finite-difference approximation. This study presents the first demonstration of EP on photonic hardware capable of supporting continuous coupling weights and structured coupling matrices, substantially improving energy efficiency. Feasibility is experimentally validated on the Wine dataset, while numerical simulations on MNIST highlight its potential for tackling more complex tasks, thereby opening a new pathway toward brain-inspired photonic computing.

Abstract

Equilibrium Propagation offers a compelling alternative to traditional machine learning for training energy-based networks. Here we demonstrate a hybrid optical-digital implementation of EP using a Spatial Photonic Ising Machine (SPIM). The SPIM exploits the gauge transformation method to optically encode both continuous neuron states and rank-1 binary trainable patterns as phase modulations via a spatial light modulator, with inference realized using a finite difference scheme. The experimental system is evaluated on the Wine classification dataset. The potential of this approach, including the use of continuous couplings and structured coupling matrices, is evaluated numerically on the more complex MNIST dataset. Our work provides a concrete pathway toward energy-efficient physical implementations of Equilibrium Propagation.

Problem

• Equilibrium Propagation
• energy-based networks
• optical implementation
• Spatial Photonic Ising Machine
• physical implementation

Innovation

• Equilibrium Propagation
• Spatial Photonic Ising Machine
• optical computing
• energy-based models
• phase modulation