利用持续同调增强图池化
Boosting Graph Pooling with Persistent Homology
AI总结：
本文提出利用持续同调将全局拓扑不变性注入图池化层的新机制，使粗化图中的消息传递沿持续池化拓扑进行，并在多个数据集上验证了其对多种图池化方法的显著性能提升。
摘要：
近年来，将持续同调（PH）集成到图神经网络（GNN）中以增强表达能力的趋势日益兴起。然而，简单地将 PH 特征插入 GNN 层通常只能带来微弱的性能提升，且可解释性较低。本文研究了一种利用 PH 将全局拓扑不变性注入池化层的新机制，其动机源于观察到 PH 中的过滤操作天然地以截断方式与图池化对齐。通过这种方式，粗化图中的消息传递沿着持续池化后的拓扑结构进行，从而提升性能。在实验方面，我们将该机制应用于多种图池化方法，并在多个常用数据集上观察到一致且显著的性能提升，证明了其广泛的适用性和灵活性。
英文摘要：
Recently, there has been an emerging trend to integrate persistent homology (PH) into graph neural networks (GNNs) to enrich expressive power. However, naively plugging PH features into GNN layers always results in marginal improvement with low interpretability. In this paper, we investigate a novel mechanism for injecting global topological invariance into pooling layers using PH, motivated by the observation that filtration operation in PH naturally aligns graph pooling in a cut-off manner. In this fashion, message passing in the coarsened graph acts along persistent pooled topology, leading to improved performance. Experimentally, we apply our mechanism to a collection of graph pooling methods and observe consistent and substantial performance gain over several popular datasets, demonstrating its wide applicability and flexibility.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
