Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning

Abstract

We introduce $r$-loopy Weisfeiler-Leman ($r$-$\ell$WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, $r$-$\ell$MPNN, that can count cycles up to length $r{+}2$. Most notably, we show that $r$-$\ell$WL can count homomorphisms of cactus graphs. This extends 1-WL, which can only count homomorphisms of trees and, in fact, is incomparable to $k$-WL for any fixed $k$. We empirically validate the expressive and counting power of $r$-$\ell$MPNN on several synthetic datasets and demonstrate the scalability and strong performance on various real-world datasets, particularly on sparse graphs.

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Cite

Text

Paolino et al. "Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning." Neural Information Processing Systems, 2024. doi:10.52202/079017-3838

Markdown

[Paolino et al. "Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning." Neural Information Processing Systems, 2024.](https://mlanthology.org/neurips/2024/paolino2024neurips-weisfeiler/) doi:10.52202/079017-3838

BibTeX

@inproceedings{paolino2024neurips-weisfeiler,
  title     = {{Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning}},
  author    = {Paolino, Raffaele and Maskey, Sohir and Welke, Pascal and Kutyniok, Gitta},
  booktitle = {Neural Information Processing Systems},
  year      = {2024},
  doi       = {10.52202/079017-3838},
  url       = {https://mlanthology.org/neurips/2024/paolino2024neurips-weisfeiler/}
}