A Theory of Link Prediction via Relational Weisfeiler-Leman on Knowledge Graphs

TL;DR

This paper provides a theoretical framework for understanding the capabilities of graph neural networks in link prediction on knowledge graphs, using a relational Weisfeiler-Leman approach to unify and analyze model expressiveness.

Contribution

It introduces a relational Weisfeiler-Leman based theory that characterizes the expressive power of GNNs for knowledge graphs and explains practical design choices.

Findings

Theoretical characterization of GNN expressiveness on knowledge graphs

Unification of various models under a common framework

Empirical validation of theoretical insights

Abstract

Graph neural networks are prominent models for representation learning over graph-structured data. While the capabilities and limitations of these models are well-understood for simple graphs, our understanding remains incomplete in the context of knowledge graphs. Our goal is to provide a systematic understanding of the landscape of graph neural networks for knowledge graphs pertaining to the prominent task of link prediction. Our analysis entails a unifying perspective on seemingly unrelated models and unlocks a series of other models. The expressive power of various models is characterized via a corresponding relational Weisfeiler-Leman algorithm. This analysis is extended to provide a precise logical characterization of the class of functions captured by a class of graph neural networks. The theoretical findings presented in this paper explain the benefits of some widely employed practical design choices, which are validated empirically.