O b j e c t i v e s. The article examines the features of using two-layer artificial neural network in problems of approximating binary functions of many binary variables. The issues of choosing the initial values of the model weights and choosing the number of neurons on the hidden layer are studied. M e t h o d s. The problem of approximating a binary function using an artificial neural network is reduced to the geometric problem of dividing the vertices of a multidimensional cube by hyperplanes. Combinatorial methods are used to prove lemmas on ways of dividing a hypercube by a hyperplane and to construct a lower estimate for the number of binary functions that can be approximated using one neuron on the hidden layer. R e s u l t s. The features of setting the initial values of weights of an artificial neural network are considered. A lower bound is constructed for the number of binary functions that can be approximated using an artificial neural network with one neuron on the hidden layer. The algorithmic complexity of calculating such an estimate is found. Numerical results are presented for using two-layer artificial neural networks to approximate binary functions in information security problems. C o n c l u s i o n. The results of the article allow choosing the parameters of an artificial neural network to improve the accuracy of approximation of binary functions of many variables.
Latushkin et al. (Fri,) studied this question.