An Algebraic Method for the Synthesis of Error-Free Binary Neural Network

A mathematical model of the problem of calculating the weight coefficients of a binary neural network is presented. It is proved that in the case of step functions of neuron activation, this model is a system of linear inequalities, which is inconsistent for most practical problems. A method for analyzing the system of inequalities is proposed, which allows calculating the values of the weight coefficients and synthesizing the structure of the neural network, thus ensuring the absolute accuracy of the output signals. The algorithm and an example of implementing the proposed method are given.