Pooling in Graph Neural Networks using Curvature (arXiv:2308.16516v1 [cs.LG])

The limitations of graph neural networks (GNNs) are often caused by over-squashing and over-smoothing. Over-smoothing erases node differences, while over-squashing hinders information propagation over long distances. These issues stem from the graph structure itself. To address these problems in graph classification tasks, we propose CurvPool, a novel pooling method. CurvPool leverages the concept of graph curvature to identify structures that cause over-smoothing and over-squashing. By clustering nodes based on the Balanced Forman curvature, CurvPool constructs a more suitable graph structure, enabling deeper models and the integration of distant information. We compare CurvPool with other state-of-the-art pooling approaches, demonstrating its superiority in terms of classification accuracy, computational complexity, and flexibility. CurvPool consistently outperforms comparable methods in all considered tasks. The best results are obtained by pooling densely connected clusters using the sum aggregation, which provides additional information about pool sizes.