Local-to-global Perspectives on Graph Neural Networks

TL;DR

This thesis explores the relationship between local message passing neural networks and global graph transformers, analyzing their convergence, connections, and applications in graph coarsening to advance understanding of GNN architectures.

Contribution

It categorizes GNNs into local and global types, studies their convergence, links their mechanisms, and applies local MPNNs to graph coarsening, providing new insights into GNN design.

Findings

Invariant Graph Networks have specific convergence properties

Connections established between local MPNN and global Graph Transformers

Local MPNN can be effectively used for graph coarsening

Abstract

This thesis presents a local-to-global perspective on graph neural networks (GNN), the leading architecture to process graph-structured data. After categorizing GNN into local Message Passing Neural Networks (MPNN) and global Graph transformers, we present three pieces of work: 1) study the convergence property of a type of global GNN, Invariant Graph Networks, 2) connect the local MPNN and global Graph Transformer, and 3) use local MPNN for graph coarsening, a standard subroutine used in global modeling.