Analytical Calculation of Weights Convolutional Neural Network

Abstract

This paper presents an algorithm for analytically calculating the weights and thresholds of convolutional neural networks (CNNs) without using standard training procedures. The algorithm enables the determination of CNN parameters based on just 10 selected images from the MNIST dataset, each representing a digit from 0 to 9. As part of the method, the number of channels in CNN layers is also derived analytically. A software module was implemented in C++ Builder, and a series of experiments were conducted using the MNIST dataset. Results demonstrate that the analytically computed CNN can recognize over half of 1000 handwritten digit images without any training, achieving inference in fractions of a second. These findings suggest that CNNs can be constructed and applied directly for classification tasks without training, using purely analytical computation of weights.