The theoretical approach to the search for a global extremum in the training of neural networks

The article deals with the search for the global extremum in the training of artificial neural networks using the correlation index. The proposed method is based on a mathematical model of an artificial neural network, represented as an information transmission system. The efficiency of the proposed model is confirmed by its broad application in information transmission systems for analyzing and recovering the useful signal against the background of various interferences: Gaussian, concentrated, pulsed, etc. The analysis of the convergence of training and experimentally obtained sequences based on the correlation index is carried out. The possibility of estimating the convergence of the training and experimentally obtained sequences by the cross-correlation function as a measure of their energy similarity (difference) is confirmed. To evaluate the proposed method, a comparative analysis is carried out with the currently used target indicators. Possible sources of errors of the least squares method and the possibility of the proposed index to overcome them are investigated.