Topologically-Stabilized Graph Neural Networks: Empirical Robustness Across Domains

• URL: http://arxiv.org/abs/2512.13852v1
• Date: Mon, 15 Dec 2025 19:39:11 GMT
• Title: Topologically-Stabilized Graph Neural Networks: Empirical Robustness Across Domains
• Authors: Jelena Losic,
• Abstract summary: Graph Neural Networks (GNNs) have become the standard for graph representation learning but remain vulnerable to structural perturbations.<n>We propose a novel framework that integrates persistent homology features with stability regularization to enhance robustness.<n>Our approach demonstrates exceptional robustness to edge perturbations while maintaining competitive accuracy.
• Score: 0.0
• License: http://creativecommons.org/licenses/by/4.0/
• 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

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