Some aspects of approximation and interpolation of functions artificial neural networks

The article deals with the issues of approximation and interpolation of functions f(x) = |x|, f(x) = sin(x), f(x) =1/(1+25x²) with the help of neural networks from those constructed on the basis of the Kolmogorov-Arnold and Tsybenko theorems. problems in training a neural network based on the initialization of weight coefficients in a random way are shown. The possibility of training a neural network to work with a variety is shown.