Theoretically Improving Graph Neural Networks via Anonymous Walk Graph Kernels

TL;DR

This paper introduces GSKN, a graph neural network model based on anonymous walks and graph kernels, which theoretically surpasses the 1-WL test and enhances the ability to distinguish graph substructures.

Contribution

The paper proposes GSKN, a novel GNN model that leverages anonymous walks and graph kernels to theoretically improve substructure modeling beyond existing MPGNNs.

Findings

GSKN outperforms various baseline models in experiments.

GSKN extends the 1-WL test in theory.

GSKN demonstrates improved substructure discrimination capabilities.

Abstract

Graph neural networks (GNNs) have achieved tremendous success in graph mining. However, the inability of GNNs to model substructures in graphs remains a significant drawback. Specifically, message-passing GNNs (MPGNNs), as the prevailing type of GNNs, have been theoretically shown unable to distinguish, detect or count many graph substructures. While efforts have been paid to complement the inability, existing works either rely on pre-defined substructure sets, thus being less flexible, or are lacking in theoretical insights. In this paper, we propose GSKN, a GNN model with a theoretically stronger ability to distinguish graph structures. Specifically, we design GSKN based on anonymous walks (AWs), flexible substructure units, and derive it upon feature mappings of graph kernels (GKs). We theoretically show that GSKN provably extends the 1-WL test, and hence the maximally powerful MPGNNs from both graph-level and node-level viewpoints. Correspondingly, various experiments are leveraged to evaluate GSKN, where GSKN outperforms a wide range of baselines, endorsing the analysis.