Topological Graph Neural Networks

TL;DR

This paper introduces TOGL, a topological layer for GNNs that enhances their ability to recognize complex graph structures like cycles, improving performance on classification tasks by integrating persistent homology.

Contribution

The paper presents TOGL, a topological layer that can be added to any GNN, making it more expressive and capable of capturing global graph topologies.

Findings

TOGL improves GNN performance on synthetic and real-world datasets.

TOGL makes GNNs strictly more expressive than message-passing models.

Synthetic datasets classified by topology show significant gains with TOGL.

Abstract

Graph neural networks (GNNs) are a powerful architecture for tackling graph learning tasks, yet have been shown to be oblivious to eminent substructures such as cycles. We present TOGL, a novel layer that incorporates global topological information of a graph using persistent homology. TOGL can be easily integrated into any type of GNN and is strictly more expressive (in terms the Weisfeiler--Lehman graph isomorphism test) than message-passing GNNs. Augmenting GNNs with TOGL leads to improved predictive performance for graph and node classification tasks, both on synthetic data sets, which can be classified by humans using their topology but not by ordinary GNNs, and on real-world data.