Most existing graph neural networks (GNNs) are limited to undirected graphs, whose restricted scope of the captured relational information hinders their expressive capabilities and deployments in real-world scenarios. Compared with undirected graphs, directed graphs (digraphs) fit the demand for modeling more complex topological systems by capturing more intricate relationships between nodes, such as formulating transportation and financial networks. While some directed GNNs have been introduced, their inspiration mainly comes from deep learning architectures, which lead to redundant complexity and computation, making them inapplicable to large-scale databases. To address these issues, we propose LightDiC, a scalable variant of the digraph convolution based on the magnetic Laplacian. Since topology-related computations are conducted solely during offline pre-processing, LightDiC achieves exceptional scalability, enabling downstream predictions to be trained separately without incurring recursive computational costs. Theoretical analysis shows that LightDiC utilizes directed information to achieve message passing based on the complex field, which corresponds to the proximal gradient descent process of the Dirichlet energy optimization function from the perspective of digraph signal denoising, ensuring its expressiveness. Experimental results demonstrate that LightDiC performs comparably well or even outperforms other SOTA methods in various downstream tasks, with fewer learnable parameters and higher training efficiency. Notably, LightDiC is the first DiGNN to provide satisfactory results in the most representative large-scale database (ogbn-papers100M).

翻译：现有的大多数图神经网络（GNN）局限于无向图，其捕获关系信息的受限范围阻碍了其在真实场景中的表达能力和部署。与无向图相比，有向图通过捕捉节点间更复杂的依赖关系（如建模交通和金融网络）更符合复杂拓扑系统的建模需求。尽管已有一些有向GNN被提出，但其灵感主要来源于深度学习架构，导致冗余的复杂性和计算开销，使其无法适用于大规模数据库。为解决这些问题，我们提出LightDiC——一种基于磁拉普拉斯算子的可扩展有向图卷积变体。由于拓扑相关计算仅在离线预处理阶段进行，LightDiC实现了卓越的可扩展性，使得下游预测可独立训练且无需递归计算成本。理论分析表明，LightDiC利用有向信息在复数域实现消息传递，这对应了有向图信号去噪视角下狄利克雷能量优化函数的近端梯度下降过程，确保了其表达能力。实验结果表明，LightDiC在各项下游任务中表现与最先进方法相当甚至更优，且具有更少的可学习参数和更高的训练效率。值得注意的是，LightDiC是首个在最具代表性的大规模数据库（ogbn-papers100M）上取得满意结果的有向图神经网络。