From Relational Pooling to Subgraph GNNs: A Universal Framework for More Expressive Graph Neural Networks

TL;DR

This paper introduces a universal framework called $k,l$-WL that enhances the expressivity of graph neural networks by explicitly assigning labels and extending to higher-dimensional Weisfeiler-Lehman tests, unifying various subgraph GNNs.

Contribution

It proposes the $k,l$-WL algorithm, a generalization of $k$-WL, providing a theoretical analysis of its expressivity and demonstrating its ability to improve any base GNN model.

Findings

$k,l$-GNNs outperform existing models on synthetic datasets.

The framework unifies many subgraph GNN approaches.

Experimental results confirm improved expressivity and performance.

Abstract

Relational pooling is a framework for building more expressive and permutation-invariant graph neural networks. However, there is limited understanding of the exact enhancement in the expressivity of RP and its connection with the Weisfeiler Lehman hierarchy. Starting from RP, we propose to explicitly assign labels to nodes as additional features to improve expressive power of message passing neural networks. The method is then extended to higher dimensional WL, leading to a novel $k,l$-WL algorithm, a more general framework than $k$-WL. Theoretically, we analyze the expressivity of $k,l$-WL with respect to $k$ and $l$ and unifies it with a great number of subgraph GNNs. Complexity reduction methods are also systematically discussed to build powerful and practical $k,l$-GNN instances. We theoretically and experimentally prove that our method is universally compatible and capable of improving the expressivity of any base GNN model. Our $k,l$-GNNs achieve superior performance on many synthetic and real-world datasets, which verifies the effectiveness of our framework.