On the construction of an explicit neural network architecture that approximates particle-linear functions

This work considers the question of discovering an upper-bound estimation of parameters quantity of neural network architecture well-approximating particle-linear dependances. The main result of this article consists of the theorem asserting that any particle-linear function can be approximated with any degree of precision on the big part of space by neural network with sigmoidal activation functions. This theorem has a constructive proof, i.e. neural network architecture with mentioned features building explicitly.