Over-squashing and over-smoothing are two critical issues, that limit the capabilities of graph neural networks (GNNs). While over-smoothing eliminates the differences between nodes making them indistinguishable, over-squashing refers to the inability of GNNs to propagate information over long distances, as exponentially many node states are squashed into fixed-size representations. Both phenomena share similar causes, as both are largely induced by the graph topology. To mitigate these problems in graph classification tasks, we propose CurvPool, a novel pooling method. CurvPool exploits the notion of curvature of a graph to adaptively identify structures responsible for both over-smoothing and over-squashing. By clustering nodes based on the Balanced Forman curvature, CurvPool constructs a graph with a more suitable structure, allowing deeper models and the combination of distant information. We compare it to other state-of-the-art pooling approaches and establish its competitiveness in terms of classification accuracy, computational complexity, and flexibility. CurvPool outperforms several comparable methods across all considered tasks. The most consistent results are achieved by pooling densely connected clusters using the sum aggregation, as this allows additional information about the size of each pool.

翻译：过平滑与过挤压是限制图神经网络（GNN）能力的两个关键问题。过平滑消除节点间差异使其无法区分，而过挤压则指GNN无法远距离传播信息，因为指数级增长的节点状态被压缩到固定大小的表征中。这两个现象具有相似成因，主要均由图拓扑结构诱发。为缓解图分类任务中的这些问题，我们提出CurvPool——一种新型池化方法。CurvPool利用图曲率概念自适应识别导致过平滑与过挤压的结构。通过基于平衡福尔曼曲率对节点进行聚类，CurvPool构建出结构更优的图，从而支持更深层模型并融合远距离信息。我们将其与现有先进池化方法比较，在分类精度、计算复杂度和灵活性方面验证其竞争力。CurvPool在所有任务中均优于多种可比方法。采用求和聚合函数池化密集连接簇可获得最一致的结果，因为该方法能保留每个池的规模信息。