发表机构
Université de Montréal; Mila -- Quebec AI Institute; Boise State University; Université de Fribourg（蒙特利尔大学; 米拉-魁北克人工智能研究所; 博伊西州立大学; 弗里堡大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对有向图学习中对方向性利用不足的问题，提出基于路径拉普拉斯的谱位置编码PathLapPE，提供节点和边级特征，在多个架构上带来一致性能提升，且无需调方向性超参数。
AI 中文摘要
有向图自然地建模了许多现实世界中的系统，在这些系统中交互是不对称的，例如引文网络、网页图和信息流网络。然而，图学习方法通常依赖于使用对称化图表示的消息传递或仅部分利用边方向性的位置编码。我们引入了PathLapPE，一种从有向图的路径拉普拉斯导出的新型谱位置编码（PE）。PathLapPE提供了节点级和边级特征，这些特征编码了有向的高阶结构，并且可以整合到标准的图学习架构中。在节点级和图级基准任务上的实证结果表明，PathLapPE在多种架构上产生了一致的改进，特别是当与方向感知的消息传递结合时。与磁拉普拉斯位置编码（一种广泛研究的有向图谱位置编码）相比，PathLapPE不需要额外调整方向性超参数，同时提供了有竞争力的运行时间和性能。
英文摘要
Directed graphs naturally model many real-world systems in which interactions are asymmetric, such as citation networks, web graphs, and information-flow networks. However, graph learning methods commonly rely on message passing with symmetrized graph representations or positional encodings that only partially exploit edge directionality. We introduce PathLapPE, a novel spectral positional encoding (PE) derived from the path Laplacian on directed graphs. PathLapPE provides node- and edge-level features that encode directional higher-order structure and can be incorporated into standard graph learning architectures. Empirical results on node- and graph-level benchmark tasks show that PathLapPE yields consistent improvements across several architectures, especially when combined with direction-aware message passing. Compared with magnetic Laplacian positional encodings, a widely studied spectral positional encoding for directed graphs, PathLapPE does not require additional fine-tuning of directionality hyperparameters while offering competitive runtime and performance.
