Synthesis of neural network for solving logical-arithmetic problems

One of the main problems facing the developer of a system with a neural network is the choice of the structure of a neural network that could solve the tasks. At present there are no unambiguous recommendations for choosing such a structure and such parameters as: the number of layers, the number of neurons in the layer, the type of neuron nonlinearity, the training method, the parameters of the training method, and others.
The article considers an approach to the synthesis of a neural network for a class of logical-arithmetic problems, based on the formation of a network of pre-constructed elementary functions. The novelty of the proposed approach is the formation of a neural network using a well-known algorithm using pre-built functions. Thus, in the article elementary logical-arithmetic functions such as “and”, “or”, “exclusive or”, “and-not”, “or-not”, "$\geqslant$", "$\leqslant$", “>”, “<” are built, which can be used to solve more complex problems. An example of a solution to the problem of constructing a function for selecting the maximum number of four numbers represented in binary form in three digits is given. Synthesis of a neural network in the manner described above is performed with the further goal of obtaining a generalized structure of the neural network.