Weisfeiler and Lehman Go Paths: Learning Topological Features via Path Complexes

TL;DR

This paper introduces a novel topological message-passing approach for GNNs based on simple paths and path complexes, surpassing previous models by removing restrictive assumptions and achieving state-of-the-art results.

Contribution

It presents a new path-based topological GNN framework that generalizes existing models without relying on specific graph sub-structure assumptions.

Findings

Outperforms previous topological GNNs on benchmarks

Achieves state-of-the-art results in graph classification tasks

Provides theoretical foundations linking path complexes to simplicial complexes

Abstract

Graph Neural Networks (GNNs), despite achieving remarkable performance across different tasks, are theoretically bounded by the 1-Weisfeiler-Lehman test, resulting in limitations in terms of graph expressivity. Even though prior works on topological higher-order GNNs overcome that boundary, these models often depend on assumptions about sub-structures of graphs. Specifically, topological GNNs leverage the prevalence of cliques, cycles, and rings to enhance the message-passing procedure. Our study presents a novel perspective by focusing on simple paths within graphs during the topological message-passing process, thus liberating the model from restrictive inductive biases. We prove that by lifting graphs to path complexes, our model can generalize the existing works on topology while inheriting several theoretical results on simplicial complexes and regular cell complexes. Without making prior assumptions about graph sub-structures, our method outperforms earlier works in other topological domains and achieves state-of-the-art results on various benchmarks.