提出新位置编码方法，让图神经网络更好处理标签差异大的复杂网络。
Learning Laplacian Positional Encodings for Heterophilous Graphs
- 基于图拉普拉斯谱设计可学习的位置编码，捕捉异质图结构。
- 在12个基准上提升性能，合成数据最高增35%，真实数据最高增14%。
- 适合研究异质图建模或想提升GNN表现的研究者。
本文理论证明，现有图位置编码在异质图任务中不仅无益，甚至可能损害性能，而现实网络普遍具有异质性，即使高度同质的图也存在局部强异质区域。为此，我们提出可学习的拉普拉斯位置编码（LLPE），利用图拉普拉斯矩阵的完整谱，使其能同时适应同质与异质图。理论上，我们证明了LLPE能逼近一类通用图距离并具备泛化能力。实验表明，在12个基准上，LLPE显著提升多种GNN模型（包括图变压器）的准确率，合成数据集最高提升35%，真实数据集最高提升14%。本工作为构建有效捕捉异质图复杂结构的位置编码迈出了重要一步。
原文摘要 · Abstract (English)
In this work, we theoretically demonstrate that current graph positional encodings (PEs) are not beneficial and could potentially hurt performance in tasks involving heterophilous graphs, where nodes that are close tend to have different labels. This limitation is critical as many real-world networks exhibit heterophily, and even highly homophilous graphs can contain local regions of strong heterophily. To address this limitation, we propose Learnable Laplacian Positional Encodings (LLPE), a new PE that leverages the full spectrum of the graph Laplacian, enabling them to capture graph structure on both homophilous and heterophilous graphs. Theoretically, we prove LLPE's ability to approximate a general class of graph distances and demonstrate its generalization properties. Empirically, our evaluation on 12 benchmarks demonstrates that LLPE improves accuracy across a variety of GNNs, including graph transformers, by up to 35% and 14% on synthetic and real-world graphs, respectively. Going forward, our work represents a significant step towards developing PEs that effectively capture complex structures in heterophilous graphs.
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