DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for
  Alleviating Over-squashing
Li Sun Zhenhao Huang Hua Wu Junda Ye Hao Peng Zhengtao Yu Philip S. Yu
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/.