Title: Edge-Based WL and Message Passing
Primary area: learning on graphs and other geometries & topologies
Keywords: GNNs, WL test, homomorphisms counts, message passing

Abstract: We propose EB-1WL, an edge-based color-refinement test, and a corresponding GNN architecture, EB-GNN.   Our architecture is inspired by a classic triangle counting algorithm by Chiba and Nishizeki, and explicitly uses triangles during message passing.
We achieve the following results:
(1) EB-1WL is significantly more expressive than 1-WL. Further, we provide a complete logical characterization of EB-1WL based on first-order logic, and matching distinguishability results based on homomorphism counting. 
(2) In an important distinction from previous proposals for more expressive GNN architectures, EB-1WL and EB-GNN require near-linear time and memory on practical graph learning tasks.
(3) Empirically, we show that EB-GNN is a highly-efficient general-purpose architecture: It substantially outperforms simple MPNNs, and remains competitive with task-specialized GNNs while being significantly more computationally efficient.

TL;DR: We introduce EB-1WL and EB-GNN, triangle-based extensions of 1-WL and GNNs that are provably more expressive, near-linear in complexity, and empirically efficient and competitive with specialized GNNs.