提出新型拓扑学习框架，提升图神经网络的表达能力与稳定性。
Contraction and Hourglass Persistence for Learning on Graphs, Simplices, and Cells
- 通过收缩序列构建新拓扑表示，突破传统包含序列局限
- 小时钟持久性使模型在多个数据集上性能显著提升
- 适用于图、单纯复形和细胞网络，可直接嵌入训练流程
持久同调（PH）能编码全局结构信息如环路，正被越来越多地融入图神经网络（GNN）。现有方法通常依赖递增子图序列，本文揭示其局限性。为此，我们系统研究收缩这一严谨的拓扑操作，提出收缩同调（CH），并证明其表达能力优于传统前向持久同调。进一步提出小时钟持久性，通过交错包含与收缩序列，增强表达能力、可学习性和稳定性。该框架还扩展至单纯复形与细胞网络，并设计了可插入端到端可微分GNN管道的高效算法，在多个标准真实世界图数据集上实现一致性能提升。代码已开源。
原文摘要 · Abstract (English)
Persistent homology (PH) encodes global information, such as cycles, and is thus increasingly integrated into graph neural networks (GNNs). PH methods in GNNs typically traverse an increasing sequence of subgraphs. In this work, we first expose limitations of this inclusion procedure. To remedy these shortcomings, we analyze contractions as a principled topological operation, in particular, for graph representation learning. We study the persistence of contraction sequences, which we call Contraction Homology (CH). We establish that forward PH and CH differ in expressivity. We then introduce Hourglass Persistence, a class of topological descriptors that interleave a sequence of inclusions and contractions to boost expressivity, learnability, and stability. We also study related families parametrized by two paradigms. We also discuss how our framework extends to simplicial and cellular networks. We further design efficient algorithms that are pluggable into end-to-end differentiable GNN pipelines, enabling consistent empirical improvements over many PH methods across standard real-world graph datasets. Code is available at \href{https://github.com/Aalto-QuML/Hourglass}{this https URL}.
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