9O2sVnEHor@OpenReview

#1 Weisfeiler and Leman Go Loopy: A New Hierarchy for Graph Representational Learning [PDF²⁶] [Copy] [Kimi³¹] [REL]

Authors: Raffaele Paolino, Sohir Maskey, Pascal Welke, Gitta Kutyniok

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.

Subject: NeurIPS.2024 - Oral

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