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

Xingyue Huang, Miguel Romero Orth, Ismail Ilkan Ceylan, Pablo Barcelo

Keywords: graph neural networks, knowledge graphs, expressivity, logical characterization

TL;DR: We provide a characterisation of the expressive power of a wide class of graph neural networks for link prediction.

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.

Submission Number: 13804