Construction of a correct algorithm and spatial neural network for recognition problems with binary data

Conditions under which it is possible to design a correct algorithm and a six-level spatial neural network reproducing the computations performed by this algorithm for recognition problems with binary data ($\Omega$-regular problems) are found. A distinctive feature of this network is the use of diagonal activation functions in its internal layers, which significantly simplify intermediate computations in the inner and outer loops. Given an $\Omega$-regular problem, the network sequentially computes the rows of the classification matrix for the test sample objects. The computational process (i.e., the inner loop) for each test object consists inside the elementary 3-level network (i.e., $\mu$-block) of a single iteration determined by a single object of the training set. The proposed approach to the neural network construction does not rely on the conventional approach based on the minimization of a functional; rather, it is based on the operator theory developed by Zhuravlev for solving recognition and classification problems.