Understanding the Expressivity of Graph Neural Networks in Learning Logical Rules for Knowledge Graph Reasoning

Graph Neural Networks (GNNs) with tail entity scoring have achieved state-of-the-art performance on knowledge graph reasoning, but the theoretical understanding of the types of logical rules they can learn is lacking. This paper proposes a unified framework called QL-GNN to analyze the expressivity of these GNNs, formally demonstrating their ability to learn a specific class of rule structures. It further introduces EL-GNN, a novel GNN design that can learn rule structures beyond the capacity of QL-GNN.