Weisfeiler and Leman Go Relational

TL;DR

This paper analyzes the expressive power of multi-relational graph neural networks, aligning them with Weisfeiler-Leman tests, and introduces a new architecture that overcomes previous limitations, supported by empirical validation.

Contribution

It provides a principled understanding of the expressiveness of Relational GCNs, relates them to Weisfeiler-Leman tests, and proposes the $k$-RN architecture to enhance expressiveness.

Findings

Relational GCNs have limited expressive power compared to Weisfeiler-Leman tests.

The $k$-RN architecture overcomes these limitations.

Empirical results confirm theoretical predictions on multi-relational graphs.

Abstract

Knowledge graphs, modeling multi-relational data, improve numerous applications such as question answering or graph logical reasoning. Many graph neural networks for such data emerged recently, often outperforming shallow architectures. However, the design of such multi-relational graph neural networks is ad-hoc, driven mainly by intuition and empirical insights. Up to now, their expressivity, their relation to each other, and their (practical) learning performance is poorly understood. Here, we initiate the study of deriving a more principled understanding of multi-relational graph neural networks. Namely, we investigate the limitations in the expressive power of the well-known Relational GCN and Compositional GCN architectures and shed some light on their practical learning performance. By aligning both architectures with a suitable version of the Weisfeiler-Leman test, we establish under which conditions both models have the same expressive power in distinguishing non-isomorphic (multi-relational) graphs or vertices with different structural roles. Further, by leveraging recent progress in designing expressive graph neural networks, we introduce the $k$-RN architecture that provably overcomes the expressiveness limitations of the above two architectures. Empirically, we confirm our theoretical findings in a vertex classification setting over small and large multi-relational graphs.