Topology-aware GNNs under structural perturbations: Empirical robustness across domains
Graph neural networks learn from relational structure but can be sensitive to edge-level noise. We study a hybrid graph classifier that combines a message-passing branch (Graph Isomorphism Network, GIN) with a topological branch based on extended persistence diagrams and PersLay embeddings. Training optionally uses a paper-specific hinge penalty motivated by stable persistence-diagram representations and Lipschitz regularity, which we abbreviate as “HK-inspired.” On six TUDataset benchmarks, we compare five ablations (Full, GIN+PersLay, GIN + HK, GIN only, PersLay only) and measure robustness as accuracy drop under 10% random edge removal at test time, with persistence diagrams fixed from the original graphs; we also report targeted perturbations on MUTAG and PROTEINS and runtime on all six datasets. The regularized configurations reduce relative accuracy degradation where GIN-only is sensitive, particularly on smaller molecular and protein graphs, but do not consistently maximize clean or perturbed accuracy. On large social-network benchmarks, robustness differences are small and clean accuracy is the main differentiator. Adding PersLay to GIN can improve accuracy on several datasets, while PersLay alone performs worst. Training the full model increases per-epoch cost relative to GIN-only, with most overhead during training rather than inference. Overall, the results support a conditional empirical conclusion: combining structure, topology, and stability-oriented training can improve robustness under specified structural perturbations, with dataset-dependent accuracy–stability trade-offs rather than universal guarantees.