Modern Hopfield neural networks (HNNs), also known as dense associative memories (DAMs), enhance simple recurrent neural networks leveraging nonlinearities in their energy functions. They have broad applications in combinatorial optimization, memory storage, deep-learning transformers, and correlated pattern recognition. To date, research on DAMs has been primarily theoretical, with implementations limited to CPUs and GPUs. Here, we propose and experimentally demonstrate a nonlinear-optical Hopfield neural network (NOHNN) for realizing DAMs using correlated patterns. The NOHNN incorporates both two-body and four-body interactions. Notably, the inclusion of four-body interactions scores a minimum tenfold improvement in the storage of uncorrelated patterns, surpassing the traditional capacity limit of HNNs. For correlated patterns, the storage capacity increases by up to a factor of 50. Benchmark testing on Modified National Institute of Standards and Technology (MNIST) handwritten digits shows a 5.5 times improvement in pattern storage, with significantly cleaner and less noisy retrieval. These results highlight the potential of nonlinear-optical DAMs for large-scale data optimization, computer vision, and graph-network tasks.

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• Memory
• Neuromorphic computing
• Nonlinear optics
• Photonics
• Physics of computation
• Convolutional neural networks
• Hopfield model
• Optical computing