{"ID":2829157,"CreatedAt":"2026-06-01T04:54:23.091178241Z","UpdatedAt":"2026-06-01T04:54:23.091178241Z","DeletedAt":null,"paper_url":"https://arxiv.org/abs/2512.13852","arxiv_id":"2512.13852","title":"Topologically-Stabilized Graph Neural Networks: Empirical Robustness Across Domains","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","short_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 homol...","url_abs":"https://arxiv.org/abs/2512.13852","url_pdf":"https://arxiv.org/pdf/2512.13852v1","authors":"[\"Jelena Losic\"]","published":"2025-12-15T19:39:11Z","proceeding":"cs.LG","tasks":"[\"cs.LG\",\"cs.SI\"]","methods":"[\"Graph Neural Network\"]","has_code":false}