Robust pattern retrieval in an optical Hopfield neural network

Hopfield neural networks (HNNs) promise broad applications in areas such as combinatorial optimization, memory storage, and pattern recognition. Among various implementations, optical HNNs are particularly interesting because they can take advantage of fast optical matrix-vector multiplications. Yet their studies so far have mostly been on the theoretical side, and the effects of optical imperfections and robustness against memory errors remain to be quantified. Here we demonstrate an optical HNN in a simple experimental setup using a spatial light modulator with 100 neurons. It successfully stores and retrieves 13 patterns, which approaches the critical capacity limit of α  = 0.138. It is robust against random phase flipping errors of the stored patterns, achieving high fidelity in recognizing and storing patterns even when 30% pixels are randomly flipped. Our results highlight the potential of optical HNNs in practical applications such as real-time image processing for autonomous driving, enhanced AI with fast memory retrieval, and other scenarios requiring efficient data processing.