Search for the global extremum using the correlation indicator for neural networks supervised learning

Abstract

The article discusses the search for a global extremum in the training of artificial neural networks using a correlation indicator. A method based on a mathematical model of an artificial neural network presented as an information transmission system is proposed. Drawing attention to the fact that in information transmission systems widely used methods that allow effective analysis and recovery of useful signal against the background of various interferences: Gaussian, concentrated, pulsed, etc., it is possible to make an assumption about the effectiveness of the mathematical model of artificial neural network, presented as a system of information transmission. The article analyzes the convergence of training and experimentally obtained sequences based on a correlation indicator for fully-connected neural network. The possibility of estimating the convergence of the training and experimentally obtained sequences based on the joint correlation function as a measure of their energy similarity (difference) is confirmed. To evaluate the proposed method, a comparative analysis is made with the currently used indicators. The potential sources of errors in the least-squares method and the possibilities of the proposed indicator to overcome them are investigated. Simulation of the learning process of an artificial neural network has shown that the use of the joint correlation function together with the Adadelta optimizer allows us to get again in learning speed 2-3 times compared to CrossEntropyLoss