Graph neural networks (GNNs) have gained popularity for various graph-related tasks. However, similar to deep neural networks, GNNs are also vulnerable to adversarial attacks. Empirical studies have shown that adversarially robust generalization has a pivotal role in establishing effective defense algorithms against adversarial attacks. In this paper, we contribute by providing adversarially robust generalization bounds for two kinds of popular GNNs, graph convolutional network (GCN) and message passing graph neural network, using the PAC-Bayesian framework. Our result reveals that spectral norm of the diffusion matrix on the graph and spectral norm of the weights as well as the perturbation factor govern the robust generalization bounds of both models. Our bounds are nontrivial generalizations of the results developed in (Liao et al., 2020) from the standard setting to adversarial setting while avoiding exponential dependence of the maximum node degree. As corollaries, we derive better PAC-Bayesian robust generalization bounds for GCN in the standard setting, which improve the bounds in (Liao et al., 2020) by avoiding exponential dependence on the maximum node degree.

翻译：图神经网络（GNN）在各种图相关任务中广受欢迎。然而，与深度神经网络类似，GNN也易受对抗攻击影响。实证研究表明，对抗鲁棒泛化在建立有效的对抗攻击防御算法中具有关键作用。本文基于PAC-Bayes框架，为两类主流GNN——图卷积网络（GCN）和消息传递图神经网络——提供了对抗鲁棒泛化界。我们的结果表明，图上的扩散矩阵谱范数、权重谱范数以及扰动因子共同决定了这两种模型的鲁棒泛化界。本文的界是将（Liao等，2020）的结果从标准设置推广到对抗设置的非平凡泛化，同时避免了最大节点度的指数依赖。作为推论，我们在标准设置下推导出了更优的GCN PAC-Bayes鲁棒泛化界，通过避免对最大节点度的指数依赖，改进了（Liao等，2020）中的界。