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Relational pooling is a framework for building more expressive andpermutation-invariant graph neural networks. However, there is limitedunderstanding of the exact enhancement in the expressivity of RP and itsconnection with the Weisfeiler Lehman hierarchy. Starting from RP, we proposeto explicitly assign labels to nodes as additional features to improveexpressive power of message passing neural networks. The method is thenextended to higher dimensional WL, leading to a novel $k,l$-WL algorithm, amore general framework than $k$-WL. Theoretically, we analyze the expressivityof $k,l$-WL with respect to $k$ and $l$ and unifies it with a great number ofsubgraph GNNs. Complexity reduction methods are also systematically discussedto build powerful and practical $k,l$-GNN instances. We theoretically andexperimentally prove that our method is universally compatible and capable ofimproving the expressivity of any base GNN model. Our $k,l$-GNNs achievesuperior performance on many synthetic and real-world datasets, which verifiesthe effectiveness of our framework.

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