Graph Neural Networks (GNNs) have demonstrated state-of-the-art performance
in various graph representation learning tasks. Recently, studies revealed
their vulnerability to adversarial attacks. In this work, we theoretically
define the concept of expected robustness in the context of attributed graphs
and relate it to the classical definition of adversarial robustness in the
graph representation learning literature. Our definition allows us to derive an
upper bound of the expected robustness of Graph Convolutional Networks (GCNs)
and Graph Isomorphism Networks subject to node feature attacks. Building on
these findings, we connect the expected robustness of GNNs to the
orthonormality of their weight matrices and consequently propose an
attack-independent, more robust variant of the GCN, called the Graph
Convolutional Orthonormal Robust Networks (GCORNs). We further introduce a
probabilistic method to estimate the expected robustness, which allows us to
evaluate the effectiveness of GCORN on several real-world datasets.
Experimental experiments showed that GCORN outperforms available defense
methods. Our code is publicly available at:
\href{https://github.com/Sennadir/GCORN}{this https URL}.

在这项工作中，我们从理论上定义了属性图背景下的预期稳健性概念，并将其与图表示学习文献中的敌对鲁棒性概念相关联。我们的定义使我们能够得出图卷积网络和图同构网络在节点特征攻击下预期稳健性的上界，并基于这些发现将图卷积正交稳健网络（Graph Convolutional Orthonormal Robust Networks）作为对敌对攻击更稳健的变体提出，将 GNN 的预期稳健性与其权重矩阵的正交性联系起来。我们进一步引入了一种概率方法来估计预期稳健性，这使我们能够评估 GCORN 在几个真实世界数据集上的有效性。实验结果表明，GCORN 优于现有的防御方法。