How Curvature Enhance the Adaptation Power of Framelet GCNs

TL;DR

This paper introduces a novel GNN enhancement using discrete Ricci curvature to improve learning performance, especially in heterophily graphs, by alleviating issues like over-smoothing and selectively dropping edges.

Contribution

The paper proposes integrating graph Ricci curvature into GNNs, providing a geometric perspective that improves adaptability and performance across different graph types.

Findings

Outperforms state-of-the-art baselines on various datasets.

Alleviates over-smoothing in GNNs.

Enhances GNN adaptability to heterophily graphs.

Abstract

Graph neural network (GNN) has been demonstrated powerful in modeling graph-structured data. However, despite many successful cases of applying GNNs to various graph classification and prediction tasks, whether the graph geometrical information has been fully exploited to enhance the learning performance of GNNs is not yet well understood. This paper introduces a new approach to enhance GNN by discrete graph Ricci curvature. Specifically, the graph Ricci curvature defined on the edges of a graph measures how difficult the information transits on one edge from one node to another based on their neighborhoods. Motivated by the geometric analogy of Ricci curvature in the graph setting, we prove that by inserting the curvature information with different carefully designed transformation function $\zeta$, several known computational issues in GNN such as over-smoothing can be alleviated in our proposed model. Furthermore, we verified that edges with very positive Ricci curvature (i.e., $\kappa_{i,j} \approx 1$) are preferred to be dropped to enhance model's adaption to heterophily graph and one curvature based graph edge drop algorithm is proposed. Comprehensive experiments show that our curvature-based GNN model outperforms the state-of-the-art baselines in both homophily and heterophily graph datasets, indicating the effectiveness of involving graph geometric information in GNNs.