Graph contrastive learning (GCL) has recently emerged as a new concept which
allows for capitalizing on the strengths of graph neural networks (GNNs) to
learn rich representations in a wide variety of applications which involve
abundant unlabeled information. However, existing GCL approaches largely tend
to overlook the important latent information on higher-order graph
substructures. We address this limitation by introducing the concepts of
topological invariance and extended persistence on graphs to GCL. In
particular, we propose a new contrastive mode which targets topological
representations of the two augmented views from the same graph, yielded by
extracting latent shape properties of the graph at multiple resolutions. Along
with the extended topological layer, we introduce a new extended persistence
summary, namely, extended persistence landscapes (EPL) and derive its
theoretical stability guarantees. Our extensive numerical results on
biological, chemical, and social interaction graphs show that the new
Topological Graph Contrastive Learning (TopoGCL) model delivers significant
performance gains in unsupervised graph classification for 11 out of 12
considered datasets and also exhibits robustness under noisy scenarios.

图对比学习在图神经网络的强大优势下充分利用丰富的无标签信息来学习图的特征表示，然而现有的方法忽视了高阶图子结构的重要潜在信息，本研究通过引入拓扑不变性和扩展持久性的概念来解决这个限制，提出了一种新的对比学习模式并引入了扩展持久性景观，实验结果表明 TopoGCL 模型在无监督图分类中取得了显著的性能提升。

TopoGCL: 拓扑图对比学习

TopoGCL: Topological Graph Contrastive Learning

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.

最近，有一个新兴的趋势是将持久同调（PH）整合到图神经网络（GNNs）中，以丰富其表达能力。然而，将 PH 特征简单地插入 GNN 层中总是导致边际改善且解释性不高。在本文中，我们研究了一种新颖的机制，利用 PH 将全局拓扑不变性注入到池化层中，这受到了 PH 中过滤操作自然地对齐图池化的观察的启发。这种方式下，粗化图中的消息传递沿着持久池化拓扑进行，从而提高了性能。在实验中，我们将这一机制应用于一系列图池化方法，并观察到在几个流行的数据集上一致且显著的性能提升，证明了其广泛适用性和灵活性。

增强图池化与持久同调

Boosting Graph Pooling with Persistent Homology

Adversarial examples have been found for various deep as well as shallow
learning models, and have at various times been suggested to be either fixable
model-specific bugs, or else inherent dataset feature, or both. We present
theoretical and empirical results to show that adversarial examples are
approximate discontinuities resulting from models that specify approximately
bijective maps $f: \Bbb R^n \to \Bbb R^m; n \neq m$ over their inputs, and this
discontinuity follows from the topological invariance of dimension.

本文通过理论和实验证据表明，对于指定的输入，规定近似双射映射 $f：R^n →R^m（n≠m）$ 模型的产生了近似不连续的对抗性例子，并且这种不连续性是维数的拓扑不变性导致的。