Graph Neural Networks (GNNs) have shown great power for learning and mining on graphs, and Graph Structure Learning (GSL) plays an important role in boosting GNNs with a refined graph. In the literature, most GSL solutions either primarily focus on structure refinement with task-specific supervision (i.e., node classification), or overlook the inherent weakness of GNNs themselves (e.g., over-squashing), resulting in suboptimal performance despite sophisticated designs. In light of these limitations, we propose to study self-supervised graph structure-feature co-refinement for effectively alleviating the issue of over-squashing in typical GNNs. In this paper, we take a fundamentally different perspective of the Ricci curvature in Riemannian geometry, in which we encounter the challenges of modeling, utilizing and computing Ricci curvature. To tackle these challenges, we present a self-supervised Riemannian model, DeepRicci. Specifically, we introduce a latent Riemannian space of heterogeneous curvatures to model various Ricci curvatures, and propose a gyrovector feature mapping to utilize Ricci curvature for typical GNNs. Thereafter, we refine node features by geometric contrastive learning among different geometric views, and simultaneously refine graph structure by backward Ricci flow based on a novel formulation of differentiable Ricci curvature. Finally, extensive experiments on public datasets show the superiority of DeepRicci, and the connection between backward Ricci flow and over-squashing. Codes of our work are given in https://github.com/RiemanGraph/.

通过自我监督的黎曼模型DeepRicci，利用黎曼几何中的里奇曲率对典型图神经网络进行超平方压缩解决的计算、建模和利用里奇曲率的挑战，通过几何对比学习在不同几何视图之间优化节点特征并通过可微的里奇曲率背向流同时优化图结构

DeepRicci：自我监督的图结构特征协同细化，缓解过度压缩