用可学习的局部拓扑编码提升图神经网络性能
LEAP: Local ECT-Based Learnable Positional Encodings for Graphs
- 基于局部欧拉特征变换构建可训练的位置编码
- 在真实与合成数据上均显著提升图表示效果
- 适合需要捕捉图结构拓扑特性的研究者
图神经网络主要依赖消息传递机制，但标准消息传递网络存在理论和实践上的局限。图位置编码（PE）成为解决这一问题的有前景方向。欧拉特征变换（ECT）是一种高效计算的几何拓扑不变量，能表征图形结构。本文结合可微分近似版ECT（DECT）及其局部变体（ℓ-ECT），提出LEAP——一种端到端可训练的图局部结构位置编码方法。我们在多个真实世界数据集及一个专门测试拓扑特征提取能力的合成任务上评估该方法。结果表明，基于LEAP的编码能有效增强图表示学习能力。
原文摘要 · Abstract (English)
Graph neural networks (GNNs) largely rely on the message-passing paradigm, where nodes iteratively aggregate information from their neighbors. Yet, standard message passing neural networks (MPNNs) face well-documented theoretical and practical limitations. Graph positional encoding (PE) has emerged as a promising direction to address these limitations. The Euler Characteristic Transform (ECT) is an efficiently computable geometric-topological invariant that characterizes shapes and graphs. In this work, we combine the differentiable approximation of the ECT (DECT) and its local variant ($\ell$-ECT) to propose LEAP, a new end-to-end trainable local structural PE for graphs. We evaluate our approach on multiple real-world datasets as well as on a synthetic task designed to test its ability to extract topological features. Our results underline the potential of LEAP-based encodings as a powerful component for graph representation learning pipelines.
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