Multiple recent studies show a paradox in graph convolutional networks (GCNs), that is, shallow architectures limit the capability of learning information from high-order neighbors, while deep architectures suffer from over-smoothing or over-squashing. To enjoy the simplicity of shallow architectures and overcome their limits of neighborhood extension, in this work, we introduce Biaffine technique to improve the expressiveness of graph convolutional networks with a shallow architecture. The core design of our method is to learn direct dependency on long-distance neighbors for nodes, with which only one-hop message passing is capable of capturing rich information for node representation. Besides, we propose a multi-view contrastive learning method to exploit the representations learned from long-distance dependencies. Extensive experiments on nine graph benchmark datasets suggest that the shallow biaffine graph convolutional networks (BAGCN) significantly outperforms state-of-the-art GCNs (with deep or shallow architectures) on semi-supervised node classification. We further verify the effectiveness of biaffine design in node representation learning and the performance consistency on different sizes of training data.

翻译：近期多项研究表明图卷积网络存在一个悖论：浅层架构限制了从高阶邻居学习信息的能力，而深层架构则面临过平滑或过压缩问题。为兼顾浅层架构的简洁性并克服其邻域扩展限制，本文引入双仿射技术提升浅层图卷积网络的表达能力。该方案的核心设计在于为节点学习与远距离邻居的直接依赖关系，使得仅通过单跳消息传递即可获取节点表征所需的丰富信息。此外，我们提出多视角对比学习方法，充分利用从长距离依赖中学到的表征。在九个图基准数据集上的大量实验表明，浅层双仿射图卷积网络在半监督节点分类任务中显著超越现有最优的图卷积网络（包括深层与浅层架构）。我们进一步验证了双仿射设计在节点表征学习中的有效性，以及该方法在不同规模训练数据上的性能一致性。