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

TL;DR

This paper presents GEGCN, a new graph neural network that models geometric evolution using Ricci flow and LSTM to improve graph classification performance.

Contribution

It introduces a novel framework combining Ricci flow with LSTM and GCNs for enhanced graph representation learning.

Findings

GEGCN outperforms existing methods on multiple benchmark datasets.

The framework effectively captures dynamic structural changes in graphs.

Experimental results show significant improvements in classification accuracy.

Abstract

We introduce the Geometric Evolution Graph Convolutional Network (GEGCN), a novel framework that enhances graph representation learning through explicit modeling of geometric evolution on graph structures. Specifically, GEGCN leverages a Long Short-Term Memory (LSTM) network to capture the dynamic structural sequence generated by discrete Ricci flow, and infuses the learned dynamic representations into a graph convolutional network. Extensive experiments demonstrate that GEGCN achieves excellent performance on classification tasks across various benchmark datasets, including homophilic/heterophilic graphs, filtered graphs, and large-scale graphs.