mlsanityData to 7 Oct 2026

Topologically-Stabilized Graph Neural Networks: Empirical Robustness Across Domains

arXiv 2512.13852 ↗First posted 15 Dec 2025cs.LG cs.SIcited by 0

Not on the map. Why?

Abstract (arXiv)

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 citecohen2007stability, 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

Key facts. No citing papers in the map yet (data through 7 Oct 2026). Builds on 21 of its 29 references that are in the map. First posted on arXiv 15 Dec 2025.

Builds on

21 of 29 references.

References · 21

  1. 2016Semi-Supervised Classification with Graph Convolutional Networkscited by 11,282
  2. 2017Graph Attention Networkscited by 8,854
  3. 2017Inductive Representation Learning on Large Graphscited by 6,284
  4. 2018How Powerful are Graph Neural Networks?cited by 4,355
  5. 2019Certified Adversarial Robustness via Randomized Smoothingcited by 1,324
  6. 2018Adversarial Attacks on Neural Networks for Graph Datacited by 395
  7. 2020Graph Structure Learning for Robust Graph Neural Networkscited by 368
  8. 2018Adversarial Attack on Graph Structured Datacited by 300
  9. 2019Adversarial Attacks on Graph Neural Networks via Meta Learningcited by 261
  10. 2015Persistence Images: A Stable Vector Representation of Persistent Homologycited by 235
  11. 2018Lipschitz-Margin Training: Scalable Certification of Perturbation Invariance for Deep Neural Networkscited by 193
  12. 2019Graph Adversarial Training: Dynamically Regularizing Based on Graph Structurecited by 93
9 more
  1. 2019Certifiable Robustness to Graph Perturbationscited by 62
  2. 2018Anonymous Walk Embeddingscited by 46
  3. 2020Adversarial Attacks and Defenses on Graphs: A Review, A Tool and Empirical Studiescited by 42
  4. 2020A Survey of Adversarial Learning on Graphscited by 42
  5. 2023Topological Deep Learning: A Review of an Emerging Paradigmcited by 34
  6. 2023Adversarial Training for Graph Neural Networks: Pitfalls, Solutions, and New Directionscited by 28
  7. 2022Improving Lipschitz-Constrained Neural Networks by Learning Activation Functionscited by 23
  8. 2024Graph Neural Networks for Vulnerability Detection: A Counterfactual Explanationcited by 12
  9. 2025Enhancing Graph Representation Learning with Localized Topological Featurescited by 6

Built on by

Not cited yet.