From Relational Pooling to Subgraph GNNs: A Universal Framework for More Expressive Graph Neural Networks
This work addresses the need for more expressive graph neural networks for researchers and practitioners in graph learning, though it is incremental as it builds on existing relational pooling and WL hierarchy concepts.
The authors tackled the problem of limited expressivity in graph neural networks by proposing a universal framework that extends relational pooling to a novel $k,l$-WL algorithm, which unifies many subgraph GNNs and achieves superior performance on synthetic and real-world datasets.
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.