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.
@article{arxiv.2603.26178,
title = {Geometric Evolution Graph Convolutional Networks: Enhancing Graph Representation Learning via Ricci Flow},
author = {Jicheng Ma and Yunyan Yang and Juan Zhao and Liang Zhao},
journal= {arXiv preprint arXiv:2603.26178},
year = {2026}
}