用局部欧拉变换提升图神经网络对局部结构的表达与可解释性
Diss-l-ECT: Dissecting Graph Data with Local Euler Characteristic Transforms
- 提出局部欧拉变换（ℓ-ECT），保留图数据局部邻域的完整结构
- 在节点分类任务中优于传统GNN，且具备旋转不变性对齐能力
- 适合关注图结构细节与模型可解释性的研究者
欧拉特征变换（ECT）是一种高效计算的几何拓扑不变量，能够刻画数据的整体形状。本文提出局部欧拉特征变换（ℓ-ECT），作为ECT的新型扩展，专为增强图表示学习中的表达力与可解释性而设计。与传统图神经网络（GNN）通过聚合导致关键局部细节丢失不同，ℓ-ECT能提供无损的局部邻域表示。该方法通过保留细微局部结构的同时保持全局可解释性，有效解决了GNN的核心局限。此外，我们基于ℓ-ECT构建了旋转不变度量，用于数据空间的时空对齐。实验表明，该方法在多种节点分类任务中表现优于标准GNN，同时具备理论有效性保证。
原文摘要 · Abstract (English)
The Euler Characteristic Transform (ECT) is an efficiently-computable geometrical-topological invariant that characterizes the global shape of data. In this paper, we introduce the Local Euler Characteristic Transform ($\ell$-ECT), a novel extension of the ECT particularly designed to enhance expressivity and interpretability in graph representation learning. Unlike traditional Graph Neural Networks (GNNs), which may lose critical local details through aggregation, the $\ell$-ECT provides a lossless representation of local neighborhoods. This approach addresses key limitations in GNNs by preserving nuanced local structures while maintaining global interpretability. Moreover, we construct a rotation-invariant metric based on $\ell$-ECTs for spatial alignment of data spaces. Our method exhibits superior performance compared to standard GNNs on a variety of node-classification tasks, while also offering theoretical guarantees that demonstrate its effectiveness.
Thank you to arXiv for use of its open access interoperability. PaperDance 不是 arXiv 官方产品；中文卡片由大模型生成，请以原文为准。