Monte Carlo optimization for real-time magnetic domain learning in magneto-optical diffractive deep neural networks

Department of Materials Science and Bioengineering, Nagaoka University of Technology, 1603-1 Kamitomioka, Nagaoka, 940-2188, Japan

^* Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 13 December 2025
Accepted: 7 March 2026

Abstract

We propose an optimized algorithm using Monte Carlo Method (MCM) tailored for online learning in magneto-optical diffractive deep neural networks (MO-D²NN), a physical neural network platform where binary-weight are determined by magneto-optical modulation of light through the Faraday effect. Our derivative-free approach based MCM, iteratively adjusts the magnetic domain patterns to minimize cross-entropy loss without relying on gradients at a much lower computational cost. Our findings reveal that the MCM-based optimization algorithm serves as a robust and viable alternative to gradient descent-based training, achieving an accuracy of 96% for MNIST (Modified National Institute of Standard and Technology) handwritten digits classification with only a single hidden layer, highlighting its potential as a powerful approach for training MO-D²NN. We further validate its feasibility through physical implementation in an experimental optical setup, confirming its practical applicability for online image recognition tasks. We successfully demonstrate real-time learning of MO-D²NN using the MCM algorithm.