提出首个考虑边方向的图神经网络，显著提升关系数据建模能力
Sheaves Reloaded: A Directional Awakening
- 构建定向胞腔层（Directed Cellular Sheaf）显式建模边方向
- 设计定向层拉普拉斯算子，在9个真实数据集上性能全面超越基线
- 适合需要捕捉复杂关系方向性的应用场景，如社交网络、交通流
层神经网络（SNN）是图神经网络（GNN）的有力推广，能更好建模复杂关系数据。尽管方向性在图学习任务中已被证明可显著提升性能，并对众多实际应用至关重要，现有SNN仍无法有效表示方向信息。为此，我们提出定向胞腔层（Directed Cellular Sheaf），一种专门用于显式建模边方向的胞腔层结构。基于此，定义新的层拉普拉斯算子——定向层拉普拉斯算子，该算子同时捕捉图拓扑与方向信息。该算子构成定向层神经网络（DSNN）的核心，是首个在架构中嵌入方向偏置的SNN模型。在九个真实世界基准上的大量实验表明，DSNN始终优于基线方法。
原文摘要 · Abstract (English)
Sheaf Neural Networks (SNNs) represent a powerful generalization of Graph Neural Networks (GNNs) that significantly improve our ability to model complex relational data. While directionality has been shown to substantially boost performance in graph learning tasks and is key to many real-world applications, existing SNNs fall short in representing it. To address this limitation, we introduce the Directed Cellular Sheaf, a special type of cellular sheaf designed to explicitly account for edge orientation. Building on this structure, we define a new sheaf Laplacian, the Directed Sheaf Laplacian, which captures both the graph's topology and its directional information. This operator serves as the backbone of the Directed Sheaf Neural Network (DSNN), the first SNN model to embed a directional bias into its architecture. Extensive experiments on nine real-world benchmarks show that DSNN consistently outperforms baseline methods.
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