Topologically-Stabilized Graph Neural Networks: Empirical Robustness Across Domains

2025/12/15 by Losic, Jelena
#FOS: Computer and information sciences #Machine Learning (cs.LG) #Social and Information Networks (cs.SI)

paper · doi:10.48550/arxiv.2512.13852

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 \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

Citations

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Related

• Neural Approximation of Graph Topological Features
• On the Trade-Off between Stability and Representational Capacity in Graph Neural Networks
• Graph Persistence goes Spectral
• Going beyond persistent homology using persistent homology
• TopoGCL: Topological Graph Contrastive Learning