Message passing neural networks (MPNNs) have emerged as the most popular
framework of graph neural networks (GNNs) in recent years. However, their
expressive power is limited by the 1-dimensional Weisfeiler-Lehman (1-WL) test.
Some works are inspired by k-WL/FWL (Folklore WL) and design the
corresponding neural versions. Despite the high expressive power, there are
serious limitations in this line of research. In particular, (1) k-WL/FWL
requires at least O(nk) space complexity, which is impractical for large
graphs even when k=3; (2) The design space of k-WL/FWL is rigid, with the
only adjustable hyper-parameter being k. To tackle the first limitation, we
propose an extension, (k,t)-FWL. We theoretically prove that even if we fix
the space complexity to O(nk) (for any k≥2) in (k,t)-FWL, we can
construct an expressiveness hierarchy up to solving the graph isomorphism
problem. To tackle the second problem, we propose k-FWL+, which considers any
equivariant set as neighbors instead of all nodes, thereby greatly expanding
the design space of k-FWL. Combining these two modifications results in a
flexible and powerful framework (k,t)-FWL+. We demonstrate (k,t)-FWL+ can
implement most existing models with matching expressiveness. We then introduce
an instance of (k,t)-FWL+ called Neighborhood2-FWL (N2-FWL), which is
practically and theoretically sound. We prove that N2-FWL is no less
powerful than 3-WL, and can encode many substructures while only requiring
O(n2) space. Finally, we design its neural version named N2-GNN and
evaluate its performance on various tasks. N2-GNN achieves record-breaking
results on ZINC-Subset (0.059), outperforming previous SOTA results by 10.6%.
Moreover, N2-GNN achieves new SOTA results on the BREC dataset (71.8%) among
all existing high-expressive GNN methods.Comment: Accepted to NeurIPS 202