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

Gitta Kutyniok, Sohir Maskey, Pascal Welke, Raffaele Paolino

Code that ran

We lifted 2 functions out of this paper's own repositories and ran 2 of them in a sandbox. "Ran" means the function executed on a synthesized input and returned a value. It is not a reproduction of the paper's results.

Repository	Role	Ran
rpaolino/loopy	canonical	2 of 2

Function	Status	Where it lives
custom_propagate	Ran	rpaolino/loopy/src/nn/loopy.py code served (permissive licence) · get_code("292508e17bb058d4")
get_nonlinearity	Ran	rpaolino/loopy/src/nn/loopy.py code served (permissive licence) · get_code("7793d0b0e246afd9")

Repositories linked to this paper

rpaolino/loopy — marked official in Papers with Code; named in the paper

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Abstract

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

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