DETERMINING AND MODELING THE TOTAL NUMBER OF PARAMETERS OF ARTIFICIAL NEURAL NETWORKS

Abstract

Research shows that the implementation of artificial neural networks based on ultralarge-scale integrated circuits provide 80 times greater performance than traditional computing systems. The work considers the rules, which are the starting point in the process of designing artificial neural networks, the number of neurons in the hidden layer, which should be between the neurons of the output and input layers, the number of neurons in one hidden layer. Threshold elements used in artificial neural networks are investigated. It is shown that with one linear threshold element it is impossible to implement all the functions of the Boolean algebra. When using a square threshold element, the number of implemented Boolean functions increases significantly, and when applyng an n - power polynomial threshold element, it is possible to implement all Boolean functions with n variables.     Studies show that in order to increase the functionality of neural networks, a promising tool is the transition to the use of multi-threshold neural elements which allow to implement any Boolean algebra function for a given number of inputs. The paper substantiates that the calculation of the total number of weight coefficients given in  literature is not correct. As a result of the study, an expression for calculating the total number of parameters of an artificial neural network is introduced, and the corresponding expressions are obtained for the linear, square and polynomial threshold elements, as well as for the proposed multithreshold neuron. The total number of neural network parameters depending on the number of layers for various three-input formal neurons, as well as the dependence of the total number of artificial neural network parameters on the number of layers modeled by the MATLAB package, are given.