Graph convolutional networks (GCNs) are currently the most promising paradigm for dealing with graph-structure data, while recent studies have also shown that GCNs are vulnerable to adversarial attacks. Thus developing GCN models that are robust to such attacks become a hot research topic. However, the structural purification learning-based or robustness constraints-based defense GCN methods are usually designed for specific data or attacks, and introduce additional objective that is not for classification. Extra training overhead is also required in their design. To address these challenges, we conduct in-depth explorations on mid-frequency signals on graphs and propose a simple yet effective Mid-pass filter GCN (Mid-GCN). Theoretical analyses guarantee the robustness of signals through the mid-pass filter, and we also shed light on the properties of different frequency signals under adversarial attacks. Extensive experiments on six benchmark graph data further verify the effectiveness of our designed Mid-GCN in node classification accuracy compared to state-of-the-art GCNs under various adversarial attack strategies.

翻译：图卷积网络（GCNs）当前是处理图结构数据最有前景的范式，但近期研究也表明GCNs易受对抗攻击影响。因此，开发对此类攻击具有鲁棒性的GCN模型成为研究热点。然而，基于结构净化学习或鲁棒性约束的防御型GCN方法通常针对特定数据或攻击设计，且引入了非分类用途的额外目标函数，其设计还需额外的训练开销。针对这些挑战，我们对图上的中频信号进行了深入探索，并提出一种简洁高效的中通滤波图卷积网络（Mid-GCN）。理论分析保证了中通滤波信号的鲁棒性，同时揭示了不同频率信号在对抗攻击下的特性。在六个基准图数据上的大量实验进一步验证，在多种对抗攻击策略下，我们设计的Mid-GCN在节点分类准确率方面优于现有最优的GCN方法。