Geometric Evolution Graph Convolutional Networks: Enhancing Graph Representation Learning via Ricci Flow

2026-03-27

AI Summary

This work proposes a novel approach that integrates discrete Ricci flow with graph neural networks to address the representational learning bottleneck arising from structural complexity in heterogeneous graphs. By modeling the geometric evolution driven by Ricci flow and employing an LSTM to dynamically capture temporal changes in graph structure, the method effectively injects evolving geometric information into the graph convolutional framework. This is the first study to combine Ricci flow–induced dynamic topology with deep learning architectures, achieving state-of-the-art performance across multiple heterogeneous graph benchmark datasets. Notably, the proposed method demonstrates significant improvements over existing approaches in graph classification tasks, highlighting the efficacy of leveraging geometric dynamics for enhanced structural representation learning.

Abstract

We introduce the Geometric Evolution Graph Convolutional Network (GEGCN), a novel framework that enhances graph representation learning by modeling geometric evolution on graphs. Specifically, GEGCN employs a Long Short-Term Memory to model the structural sequence generated by discrete Ricci flow, and the learned dynamic representations are infused into a Graph Convolutional Network. Extensive experiments demonstrate that GEGCN achieves state-of-the-art performance on classification tasks across various benchmark datasets, with its performance being particularly outstanding on heterophilic graphs.

Problem

• graph representation learning
• heterophilic graphs
• geometric evolution
• Ricci flow

Innovation

• Geometric Evolution
• Ricci Flow
• Graph Convolutional Network
• Dynamic Representation
• Heterophilic Graphs