While Graph Neural Networks (GNNs) have been successfully leveraged for learning on graph-structured data across domains, several potential pitfalls have been described recently. Those include the inability to accurately leverage information encoded in long-range connections (over-squashing), as well as difficulties distinguishing the learned representations of nearby nodes with growing network depth (over-smoothing). An effective way to characterize both effects is discrete curvature: Long-range connections that underlie over-squashing effects have low curvature, whereas edges that contribute to over-smoothing have high curvature. This observation has given rise to rewiring techniques, which add or remove edges to mitigate over-smoothing and over-squashing. Several rewiring approaches utilizing graph characteristics, such as curvature or the spectrum of the graph Laplacian, have been proposed. However, existing methods, especially those based on curvature, often require expensive subroutines and careful hyperparameter tuning, which limits their applicability to large-scale graphs. Here we propose a rewiring technique based on Augmented Forman-Ricci curvature (AFRC), a scalable curvature notation, which can be computed in linear time. We prove that AFRC effectively characterizes over-smoothing and over-squashing effects in message-passing GNNs. We complement our theoretical results with experiments, which demonstrate that the proposed approach achieves state-of-the-art performance while significantly reducing the computational cost in comparison with other methods. Utilizing fundamental properties of discrete curvature, we propose effective heuristics for hyperparameters in curvature-based rewiring, which avoids expensive hyperparameter searches, further improving the scalability of the proposed approach.

翻译：尽管图神经网络（GNN）在跨领域图结构数据学习中已取得成功，但近期研究揭示了若干潜在缺陷。这些缺陷包括无法准确利用长程连接编码的信息（过挤压效应），以及随着网络深度增加难以区分邻近节点的学习表征（过平滑效应）。离散曲率能有效刻画这两种效应：导致过挤压的长程连接具有低曲率，而引发过平滑的边则呈现高曲率。该发现催生了重连技术——通过增删边来缓解过平滑与过挤压。已有研究提出了多种利用图特征（如曲率或图拉普拉斯谱）的重连方法。但现有方法（尤其是基于曲率的方法）通常需要昂贵的子程序与精细的超参数调优，限制了其在大规模图上的应用。本文提出基于增强Forman-Ricci曲率（AFRC）的重连技术，这是一种可在线性时间内计算的可扩展曲率符号。我们证明了AFRC能有效刻画消息传递GNN中的过平滑与过挤压效应。通过实验验证了理论结果，表明所提方法在显著降低计算成本的同时实现了最先进性能。利用离散曲率的基本性质，我们提出了曲率重连中超参数的有效启发式策略，避免了昂贵的超参数搜索，进一步提升了方法的可扩展性。