Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning
<|reference_start|>Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning: 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 strictly extends classical 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 the proposed $r$-$\ell{}$MPNN on several synthetic datasets and present state-of-the-art predictive performance on various real-world datasets. The code is available at https://github.com/RPaolino/loopy<|reference_end|>
@article{paolino2024weisfeiler,
    title={Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph
  Representational Learning},
    author={Raffaele Paolino, Sohir Maskey, Pascal Welke, Gitta Kutyniok},
    journal={arXiv preprint arXiv:2403.13749},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.13749},
    primaryClass={cs.LG}
}