Graph convolutional networks (GCNs) are powerful tools for graph-structured
data. However, they have been recently shown to be vulnerable to topological
attacks. To enhance adversarial robustness, we go beyond spectral graph theory
to robust graph theory. By challenging the classical graph Laplacian, we
propose a new convolution operator that is provably robust in the spectral
domain and is incorporated in the GCN architecture to improve expressivity and
interpretability. By extending the original graph to a sequence of graphs, we
also propose a robust training paradigm that encourages transferability across
graphs that span a range of spatial and spectral characteristics. The proposed
approaches are demonstrated in extensive experiments to simultaneously improve
performance in both benign and adversarial situations.

通过挑战经典的图形拉普拉斯算子，设计出一种可以证明在频谱域内具有鲁棒性的新卷积算子，它被纳入 GCN 体系结构中以改善其表达能力和可解释性，同时通过将原始图形扩展到一系列图形，提出了一种鲁棒的训练范式，以鼓励跨越具有一系列空间和频谱特征的图形的可转移性，这些方法在广泛的实验中得到证明，可以同时提高在良性和对抗性情况下的性能。