Recent studies demonstrate that Graph Neural Networks (GNNs) are vulnerable to slight but adversarially designed perturbations, known as adversarial examples. To address this issue, robust training methods against adversarial examples have received considerable attention in the literature. \emph{Adversarial Training (AT)} is a successful approach to learning a robust model using adversarially perturbed training samples. Existing AT methods on GNNs typically construct adversarial perturbations in terms of graph structures or node features. However, they are less effective and fraught with challenges on graph data due to the discreteness of graph structure and the relationships between connected examples. In this work, we seek to address these challenges and propose Spectral Adversarial Training (SAT), a simple yet effective adversarial training approach for GNNs. SAT first adopts a low-rank approximation of the graph structure based on spectral decomposition, and then constructs adversarial perturbations in the spectral domain rather than directly manipulating the original graph structure. To investigate its effectiveness, we employ SAT on three widely used GNNs. Experimental results on four public graph datasets demonstrate that SAT significantly improves the robustness of GNNs against adversarial attacks without sacrificing classification accuracy and training efficiency.

本文提出 Spectral Adversarial Training （SAT），基于频谱分解的简单但有效的对抗训练方法，用于提高图神经网络（GNN）对抗攻击的鲁棒性，实验结果表明 SAT 显著提高了 GNN 对抗攻击的鲁棒性，而不影响分类准确性和训练效率。

鲁棒图神经网络的频谱对抗训练