论文标题
使用Ollivier-Ricci曲率重新访问过度光滑和过度划分
Revisiting Over-smoothing and Over-squashing Using Ollivier-Ricci Curvature
论文作者
论文摘要
已证明图形神经网络（GNN）固有地易受过度平滑和过度阵型的问题。这些问题禁止GNN通过限制其在遥远信息中的有效性来对复杂图相互作用进行建模的能力。我们的研究揭示了局部图几何形状与这两个问题的发生之间的关键联系，从而提供了一个统一的框架，用于使用Ollivier-Ricci曲率在局部规模进行研究。具体而言，我们证明了过度平滑的与正图曲率相关，而过度划分与负图曲率有关。基于我们的理论，我们提出了批处理流动流，这是一种新颖的重新布线算法，能够同时解决过度光滑和过度阵列。
Graph Neural Networks (GNNs) had been demonstrated to be inherently susceptible to the problems of over-smoothing and over-squashing. These issues prohibit the ability of GNNs to model complex graph interactions by limiting their effectiveness in taking into account distant information. Our study reveals the key connection between the local graph geometry and the occurrence of both of these issues, thereby providing a unified framework for studying them at a local scale using the Ollivier-Ricci curvature. Specifically, we demonstrate that over-smoothing is linked to positive graph curvature while over-squashing is linked to negative graph curvature. Based on our theory, we propose the Batch Ollivier-Ricci Flow, a novel rewiring algorithm capable of simultaneously addressing both over-smoothing and over-squashing.
