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.

翻译：近年来，将持续同调（PH）融入图神经网络以增强表达能力的趋势日益显著。然而，将PH特征简单嵌入图神经网络层往往仅带来微小改进且可解释性较低。本文提出一种利用PH向池化层注入全局拓扑不变性的创新机制，其灵感源于PH中的滤子操作能以截断方式自然对齐图池化过程。通过这种机制，粗化图中的消息传递沿持续池化拓扑结构进行，从而提升模型性能。实验表明，我们将该机制应用于多种图池化方法，在多个公开数据集上均取得显著且稳定的性能提升，充分证明了其广泛适用性与灵活性。