用拓扑特征增强图神经网络，提升节点分类与链接预测性能
Enhancing Graph Representation Learning with Localized Topological Features
- 基于持久同调理论提取图的高阶连接结构特征
- 在多个基准上达到当前最优效果，显著提升模型表达能力
- 支持端到端可微学习，为拓扑特征应用提供新范式
图表示学习是诸多任务中的核心问题。尽管图神经网络是主流方法，但其表征能力仍受限。为此，显式提取并融合高阶拓扑与几何信息具有重要意义。本文提出一种基于持久同调理论的系统性方法，用于捕获图的丰富连通性特征，并将其融入图神经网络以增强表示学习，在多个节点分类与链接预测基准上取得当前最优性能。我们还探索了拓扑特征的端到端可微学习，即将拓扑计算作为可微算子参与训练。理论分析与实证研究为拓扑特征在图学习任务中的应用提供了深入洞察与潜在指导。
原文摘要 · Abstract (English)
Representation learning on graphs is a fundamental problem that can be crucial in various tasks. Graph neural networks, the dominant approach for graph representation learning, are limited in their representation power. Therefore, it can be beneficial to explicitly extract and incorporate high-order topological and geometric information into these models. In this paper, we propose a principled approach to extract the rich connectivity information of graphs based on the theory of persistent homology. Our method utilizes the topological features to enhance the representation learning of graph neural networks and achieve state-of-the-art performance on various node classification and link prediction benchmarks. We also explore the option of end-to-end learning of the topological features, i.e., treating topological computation as a differentiable operator during learning. Our theoretical analysis and empirical study provide insights and potential guidelines for employing topological features in graph learning tasks.
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