Graph neural networks (GNNs) hold the promise of learning efficient representations of graph-structured data, and one of its most important applications is semi-supervised node classification. However, in this application, GNN frameworks tend to fail due to the following issues: over-smoothing and heterophily. The most popular GNNs are known to be focused on the message-passing framework, and recent research shows that these GNNs are often bounded by low-pass filters from a signal processing perspective. We thus incorporate high-frequency information into GNNs to alleviate this genetic problem. In this paper, we argue that the complement of the original graph incorporates a high-pass filter and propose Complement Laplacian Regularization (CLAR) for an efficient enhancement of high-frequency components. The experimental results demonstrate that CLAR helps GNNs tackle over-smoothing, improving the expressiveness of heterophilic graphs, which adds up to 3.6% improvement over popular baselines and ensures topological robustness.

翻译：图神经网络（GNNs）有望学习图结构数据的有效表示，其最重要的应用之一是半监督节点分类。然而，在此应用中，GNN框架常因过度平滑和异质性等问题而失效。最流行的GNN以消息传递框架为核心，近期研究表明，从信号处理角度来看，这些GNN通常受限于低通滤波器。因此，我们将高频信息融入GNN以缓解这一固有问题。本文认为原始图的补图蕴含高通滤波器，并提出补图拉普拉斯正则化（CLAR）以高效增强高频分量。实验结果表明，CLAR有助于GNN应对过度平滑，提升异质性图的表达能力，在主流基线基础上提升高达3.6%，并确保拓扑鲁棒性。