Robustness by Cancellation: Break, Repair, and Signed Structural Responses in Graph Neural Networks

A graph neural network can appear structurally robust even when many predictions change correctness. Topology perturbations can Break initially correct predictions and Repair initially incorrect ones, while aggregate accuracy records only their net difference. We show that both transitions follow a common margin-crossing account: clean margin sets the crossing threshold, structural response provides the signed displacement, and clean-state opportunity weights conditional susceptibility into population-level flow. On the development graphs, an independently measured response signal improves held-out Break/Repair susceptibility AUC beyond clean margin by \(0.058\)-\(0.113\). On external graphs, the boundary-distance relation remains stable under perturbation-bank resampling, whereas response predictiveness is setting-dependent, including a Repair case at chance. Across competence-filtered datasets and targeted changes in architecture, perturbation operator, and graph scale, Break and Repair recur despite variation in magnitude and net direction. Aggregate accuracy therefore does not, by itself, establish prediction stability.