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

Code

• github.com/rpaolino/loopy
  OfficialIn paperpytorch★ 12

Abstract

We introduce r-loopy Weisfeiler-Leman (r-WL), a novel hierarchy of graph isomorphism tests and a corresponding GNN framework, r-MPNN, that can count cycles up to length r + 2. Most notably, we show that r-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-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

Reproductions