Topologically-Stabilized Graph Neural Networks: Empirical Robustness Across Domains
This work addresses robustness issues in graph representation learning for domains like biochemical, social, and collaboration networks, offering a theoretically-grounded and empirically-validated approach that is incremental in nature.
The paper tackles the vulnerability of Graph Neural Networks (GNNs) to structural perturbations by integrating persistent homology features with stability regularization, resulting in minimal performance degradation (0-4% on most datasets) and significantly outperforming baseline stability across six diverse datasets.
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