Exploiting graphical structures of data and neural network architectures
Andrew McDonald, William Clement Regli · 2022
The goal of this dissertation is to demonstrate the computational advantages gained by exploiting the graphical structures implicit in data, as well as the graph-theoretical underpinnings of computational architectures such as neural networks. A new computational architecture, Ortus, that uses a graph-based model to process structured data is introduced, which can be thought of as an approximation to a biologically-grounded Boltzmann machine. Next, sparse super-regular networks are developed to show the applicability of using sparse architectural network design toward solving real-world problems. Then, probabilistic hybrid graph convolutional networks show the practical applications of leveraging the inherent structural interdependencies within data by using hybrid neural network architectures. Within these networks, subnetworks are geared to extract particular types of relationships, similar to how Ortus routes specific types of information through predetermined channels. Finally, the benefits of merging structural sparsity with structured information processing are demonstrated by substituting super-regular network layers in place of fully-connected layers within the probabilistic hybrid architectures.