Topological Relational Learning on Graphs

TL;DR

This paper introduces a topological relational inference framework for GNNs that integrates higher-order topological information to improve robustness and performance in graph classification tasks.

Contribution

It proposes a novel topological neural framework that rewires graphs using persistent homology and incorporates topological summaries into GNNs, enhancing robustness and expressiveness.

Findings

TRI-GNN outperforms 14 state-of-the-art baselines on 6 out of 7 graphs.

The framework exhibits up to 10% better performance under noisy conditions.

Theoretical stability guarantees are derived for the topological representations.

Abstract

Graph neural networks (GNNs) have emerged as a powerful tool for graph classification and representation learning. However, GNNs tend to suffer from over-smoothing problems and are vulnerable to graph perturbations. To address these challenges, we propose a novel topological neural framework of topological relational inference (TRI) which allows for integrating higher-order graph information to GNNs and for systematically learning a local graph structure. The key idea is to rewire the original graph by using the persistent homology of the small neighborhoods of nodes and then to incorporate the extracted topological summaries as the side information into the local algorithm. As a result, the new framework enables us to harness both the conventional information on the graph structure and information on the graph higher order topological properties. We derive theoretical stability guarantees for the new local topological representation and discuss their implications on the graph algebraic connectivity. The experimental results on node classification tasks demonstrate that the new TRI-GNN outperforms all 14 state-of-the-art baselines on 6 out 7 graphs and exhibit higher robustness to perturbations, yielding up to 10\% better performance under noisy scenarios.