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

Oral Poster

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

Raffaele Paolino · Sohir Maskey · Pascal Welke · Gitta Kutyniok

East Exhibit Hall A-C #3009

[ Abstract ] [ Project Page ]

[ Paper] [ OpenReview]

Fri 13 Dec 11 a.m. PST — 2 p.m. PST

Oral presentation: Oral Session 5A: Graph Neural Networks
Fri 13 Dec 10 a.m. PST — 11 a.m. PST

Abstract: We introduce

r

$r$ -loopy Weisfeiler-Leman (

r

$r$ -

ℓ

$\ell$ WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework,

r

$r$ -

ℓ

$\ell$ MPNN, that can count cycles up to length

r + 2

$r{+}2$ . Most notably, we show that

r

$r$ -

ℓ

$\ell$ 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

$k$ -WL for any fixed

k

$k$ . We empirically validate the expressive and counting power of

r

$r$ -

ℓ

$\ell$ 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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