Statistical physical properties of four-wave mixing optical neural network

The paper investigates the statistical physical properties of an optical neural network. The conditions for training a neural network by the maximum likelihood algorithm are identified. The study uses a three-dimensional Ising model, to which a long-range action is sequentially added so that in the limit the model can be described by the mean-field theory. Analytical estimates of the critical neural network temperature were obtained considering the interaction with the second and third-order neighbors. The estimates for the entire interval of the interaction parameters are in good agreement with the results obtained by Monte Carlo methods. It is found that as the number of positive interconnections increase, the critical temperature value decreases and the maximum likelihood algorithm can be applied virtually without any restrictions.