@inproceedings{
paolino2024weisfeiler,
title={Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning},
author={Raffaele Paolino and Sohir Maskey and Pascal Welke and Gitta Kutyniok},
booktitle={The Thirty-eighth Annual Conference on Neural Information Processing Systems},
year={2024},
url={https://openreview.net/forum?id=9O2sVnEHor}
}
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.
Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning
Raffaele Paolino Sohir Maskey Pascal Welke Gitta Kutyniok