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

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.