Graph Neural Ricci Flow: Evolving Feature from a Curvature Perspective
Jialong Chen Bowen Deng Zhen WANG Chuan Chen Zibin Zheng
Differential equations provide a dynamical perspective for understanding and designing graph neural networks (GNNs). By generalizing the discrete Ricci flow (DRF) to attributed graphs, we can leverage a new paradigm for the evolution of node features with the help of curvature. We show that in the attributed graphs, DRF guarantees a vital property: The curvature of each edge concentrates toward zero over time. This property leads to two interesting consequences: 1) graph Dirichlet energy with bilateral bounds and 2) data-independent curvature decay rate. Based on these theoretical results, we propose the Graph Neural Ricci Flow (GNRF), a novel curvature-aware continuous-depth GNN. Compared to traditional curvature-based graph learning methods, GNRF is not limited to a specific curvature definition. It computes and adjusts time-varying curvature efficiently in linear time. We also empirically illustrate the operating mechanism of GNRF and verify that it performs excellently on diverse datasets.
Graph neural network, Differential equation, Curvature, Ricci flow
Continuous-depth GNN based on attributed discrete Ricci flow