Multilayer neural networks – as determined systems

Abstract

The study of the influence of learning speed (η) on the learning process of a multilayer neural network is carried out. The program for a multilayer neural network was written in Python. The learning speed is considered as a constant value and its optimal value at which the best learning is achieved is determined. To analyze the impact of learning speed, a logistic function, which describes the learning process, is used. It is shown that the learning error function is characterized by bifurcation processes that lead to a chaotic state at η> 0.8. The optimal value of the learning speed is determined. The value determines the appearance of the process of doubling the number of local minima, and is η = 0.62 for a three-layer neural network with 4 neurons in each layer. Increasing the number of hidden layers (3 ÷ 30) and the number of neurons in each layer (4 ÷ 150) does not lead to a radical change in the diagram of the logistic function (xn, η), and hence, in the optimal value of the learning speed.