Graph Shift Operators for, in and from Graph Neural Networks – GraspGNNs

Graph Neural Networks (GNNs) have celebrated many academic and industrial successes in the past years; providing a rich ground for theoretical analysis and achieving state-of-the-art results in several learning tasks. This has led to GNNs receiving significant academic and industrial interest. In this project, we aim to gain a better theoretical understanding of this impactful model type. The computational steps of Message Passing Neural Networks, the most common GNN framework, are the message passing and the update step. Our theoretical analysis will be focused on the impactful choice of message passing function in the message passing step, which is analogous to the study of the Graph Shift Operator (GSO) matrix used to represent the graph. Common choices of GSOs, include the adjacency and Laplacian matrices. Via the study of GSOs in GNNs we plan to find optimal graph representations in GNNS (WP1), as well as understand and address the issues of oversmoothing and oversquashing in GNNs (WP2). We furthermore, plan to explore centrality metrics as graph representations in GNNs (WP3) and apply the developed models to the biomedical domain, in which we plan to tackle the task of protein-ligand docking (WP4). The goal is to immediately use the theoretical insight gained to inspire new GNN architectures and propose better-performing models, i.e., we aim for theoretical advances that inspire direct methodological progress with real-world impact.