Stability of an Optical Neural Network Trained by the Maximum-Likelihood Algorithm

The possibility of the maximum-likelihood algorithm-based deep learning of an optical neural network is considered. Using the optimization of thermodynamic parameters of the network, the algorithm can fail when the network undergoes a phase transition caused by changes of network weights in learning. The approach based on Schraudolph–Kamenetsky [1] and Karandashev–Malsagov [2] algorithms is used in computer simulation. Both algorithms allow the free energy of the system on a planar graph to be computed exactly. The restrictions on the number of negative connections are determined that secure the stability of the system, the absence of the phase transition and unrestrained use of the maximum-likelihood algorithm.