DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashing

TL;DR

DeepRicci introduces a self-supervised Riemannian geometry-based method to co-refine graph structures and features, effectively alleviating over-squashing in GNNs and improving their performance.

Contribution

It proposes a novel self-supervised model using Ricci curvature and backward Ricci flow to enhance GNNs by addressing over-squashing through geometric co-refinement.

Findings

DeepRicci outperforms existing methods on public datasets.

The approach effectively alleviates over-squashing in GNNs.

The connection between Ricci flow and over-squashing is demonstrated.

Abstract

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/.