The problem of computing machine passing the maze is one of theoretical computer science key tasks. This task was partially considered by the classics of computer science, e.g. A. Turing, C. Shannon, L. Budach and Z. Pawlak. Labyrinth problem solving includes fundamental knowledges in the main three branches, namely  environment (labyrinth) knowledge, computing machines features knowledge and behavior of computing machines in labyrinth knowledge. These three components are built on the fundamental basis of the theoretical computer science. Nowadays the labyrinth passing task is complemented by intellectuality as an additional criterion. That is, computing machines must acquire intelligent functions, and this task gets a new component and a new statement, which is briefly formulated as the search for a way out of the labyrinth by intelligent computing machines. The main concept of this article is to develop artificial neural networks based intelligent functions for calculating machine to pass the maze. Besides this visual aspect is emphasized, i.e. the computational machine includes a maze viewing function. Authors accentuate fundamental principles of artificial neural networks technologies building  and engage backpropagation algorithm, which is used in a artificial neural network learning process. The article discusses maze, dataset construction, artificial neural network training, maze recognition computational experiment and analysis of the hyperparameters effect on artificial neural network training. The aim of the article is to build mathematical model based on backpropagation algorithm and to identify how hyperparameters affect the learning process of artificial neural networks. Thus the research is based on the methods of computational experiment and step-by-step detailing to implement the algorithm. The results of the research include theoretical basis of computing machines intellectualization for the maze and computing machine ability to recognize the maze. These results may be useful to theorists for a detailed description of the process and to practitioners for ability to test this algorithm and approach while solving a problem of maze passing by intelligent agents.