  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.
