Abstract <p>This study provides a description of the algorithm on the basis of which weights, thresholds, and the number of channels in the layers of a convolutional neural network are analytically calculated. The results of the experiments described in this work showed that the time for calculating the weights of convolutional neural networks is relatively short and amounts to fractions of a second or a minute. The experimental results also showed that using only 10 selected images from the MNIST database, analytically calculated convolutional neural networks are able to recognize more than half of the images of the MNIST test database, without using neural network training algorithms. Preliminary analytical calculation of the value of the weights of a convolutional neural network allows to speed up the training procedure of a convolutional neural network.</p>