Structural and Spectral Properties of Artificial Neural Networks in the Problem of Image Classification

In the modern world, computer science is developing very rapidly and one of the most discussed topics in this scientific field is machine learning, specifically artificial neural networks. These networks help with a wide variety of tasks such as regression, classification and clustering. But despite the fact that neural networks have already found their application in a large number of scientific branches, relatively little attention has been paid to their structural and spectral properties. While the main focus is on increasing the accuracy due to the development of new architectures and hyperparameters of neural networks, understanding of their internal structure and properties that allow them to solve these tasks suffers. Understanding the mechanisms and principles underlying these networks is a very important step towards developing artificial intelligence systems that could effectively replace human labor with machines. In my research work, I am considering fully connected convolutional neural networks for binary and multiclass image classification based on the CIFAR-10 dataset. The CIFAR-10 dataset contains 60 000 32 x 32 color images evenly distributed across 10 different classes. Neural network models can be represented as weighted graphs with a certain structure, where the vertices of the graph are neurons, and the edges are connections between neurons. Weights of those links of such models are determined in the process of learning. My research focuses on such graphs built on fully connected layers of a neural network, more precise on their structural and spectral properties.