Topologically-Stabilized Graph Neural Networks: Empirical Robustness Across Domains

TL;DR

This paper introduces a topologically-informed regularization framework for Graph Neural Networks that significantly improves robustness to structural perturbations across diverse datasets, grounded in persistent homology theory.

Contribution

It presents a novel integration of persistent homology features with stability regularization in GNNs, enhancing robustness while maintaining accuracy.

Findings

Achieves minimal performance degradation (0-4%) under edge perturbations.

Outperforms baseline stability methods across six datasets.

Demonstrates theoretical and empirical robustness of the proposed approach.

Abstract

Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations. We propose a novel framework that integrates persistent homology features with stability regularization to enhance robustness. Building on the stability theorems of persistent homology \cite{cohen2007stability}, our method combines GIN architectures with multi-scale topological features extracted from persistence images, enforced by Hiraoka-Kusano-inspired stability constraints. Across six diverse datasets spanning biochemical, social, and collaboration networks , our approach demonstrates exceptional robustness to edge perturbations while maintaining competitive accuracy. Notably, we observe minimal performance degradation (0-4\% on most datasets) under perturbation, significantly outperforming baseline stability. Our work provides both a theoretically-grounded and empirically-validated approach to robust graph learning that aligns with recent advances in topological regularization