Analytical Calculation of Weights Convolutional Neural Network

Abstract

In this paper proposes an algorithm for the analytical calculation of convolutional neural networks without using neural network training algorithms. A description of the algorithm is given, on the basis of which the weights and threshold values of a convolutional neural network are analytically calculated. In this case, to calculate the parameters of the convolutional neural network, only 10 selected samples were used from the MNIST digit database, each of which is an image of one of the recognizable classes of digits from 0 to 9, and was randomly selected from the MNIST digit database. As a result of the operation of this algorithm, the number of channels of the convolutional neural network layers is also determined analytically. Based on the proposed algorithm, a software module was implemented in the Builder environment C++, on the basis of which a number of experiments were carried out with recognition of the MNIST database. The results of the experiments described in the work showed that the computation time of convolutional neural networks is very short and amounts to fractions of a second or a minute. Analytically computed convolutional neural networks were tested on the MNIST digit database, consisting of 1000 images of handwritten digits. The experimental results showed that already 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 database, without application of neural network training algorithms. In general, the study showed that artificial neural networks, and in particular convolutional neural networks, are capable of not only being trained by learning algorithms, but also recognizing images almost instantly, without the use of learning algorithms using preliminary analytical calculation of the values of the neural network’s weights.