Optical Hopfield neural networks with enhanced storage capacity

Hopfield neural networks, classic examples of associative memories, are well-established models for pattern storage and retrieval. However, the original Hopfield network, characterized by quadratic interactions among neurons, exhibits limited storage capacity. To enhance this capacity, researchers have introduced nonlinear functions-such as polynomial and exponential functions-to generalize the network's energy landscape. In this work, we propose an optical implementation of the Hopfield network that employs optical parametric amplification to realize a hyperbolic interaction function. We numerically simulate the pattern storage and retrieval dynamics of our optical model and compare its storage capacity with that of Hopfield networks using polynomial interaction functions. Our results show that the storage capacity of the proposed model increases exponentially with the number of neurons and depends on optical parameters such as pump laser power and nonlinear medium properties. This dependence enables further enhancement of storage capacity by tuning the physical hardware alone, without modifying the network architecture.