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.

翻译：图形革命网络(GCN)是图表结构化数据的强大工具。 但是,它们最近被证明很容易受到地形攻击。为了提高对抗性强力,我们从光谱图理论到强力图形理论。通过挑战古典图Laplacian,我们提议一个新的图组运营商,在光谱领域具有可辨称的强力,并被纳入GCN结构,以提高表达性和可解释性。通过将原始图组扩展为一系列图表,我们还提议了一个强有力的培训模式,鼓励跨越空间和光谱特征的图组的可转移性。提议的方法体现在广泛的实验中,同时改善良性和对抗性以及对抗性情况下的性能。