用拓扑特征增强GNN稳定性，抗结构扰动能力显著提升
Topologically-Stabilized Graph Neural Networks: Empirical Robustness Across Domains
- 结合持久同调特征与稳定性约束，提升GNN鲁棒性
- 六大数据集上扰动下性能下降仅0-4%，优于基线
- 适合关注模型稳定性的图学习研究者使用
图神经网络（GNN）已成为图表示学习的标准方法，但仍易受结构扰动影响。本文提出一种新框架，将持久同调特征与稳定性正则化结合，以增强鲁棒性。基于持久同调的稳定性定理，方法在GIN架构中引入多尺度拓扑特征（来自持久图像），并施加受Hiraoka-Kusano启发的稳定性约束。在涵盖生化、社交与协作网络的六个不同数据集上，该方法对边扰动表现出优异鲁棒性，多数数据集性能下降仅0-4%，显著优于基线。工作提供了理论支撑与实证验证兼备的稳健图学习方案，契合拓扑正则化最新进展。
原文摘要 · Abstract (English)
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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