Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations [1, 2]. We propose a novel framework that integrates persistent homology features with stability regularization to enhance robustness. Building on the stability theorems of persistent homology [3], our method combines GIN architectures [6] with multi-scale topological features extracted from persistence images [5], enforced by Hiraoka-Kusano-inspired stability constraints [4]. Across six diverse datasets spanning biochemical, social, and collaboration networks [7], 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 [8].

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Topologically-Stabilized Graph Neural Networks: Empirical Robustness Across Domains

  • Jelena Losic

摘要

Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations [1, 2]. We propose a novel framework that integrates persistent homology features with stability regularization to enhance robustness. Building on the stability theorems of persistent homology [3], our method combines GIN architectures [6] with multi-scale topological features extracted from persistence images [5], enforced by Hiraoka-Kusano-inspired stability constraints [4]. Across six diverse datasets spanning biochemical, social, and collaboration networks [7], 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 [8].