用微分几何的里奇流设计新模型，解决超图神经网络过平滑问题。
Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approach
- 基于离散里奇流构建超图上的信息扩散机制
- 在多个数据集上显著优于现有方法，缓解特征同质化
- 适合研究超图表示学习与几何深度学习的学者
超图神经网络（HGNNs）在建模复杂高阶关系方面表现优异，但随着层数增加常出现过平滑问题，且缺乏对节点间消息传递的有效控制。受微分几何中里奇流理论启发，我们理论证明在超图结构中引入离散里奇流可有效调节节点特征演化，从而缓解过平滑。在此基础上，提出里奇流引导的超图神经扩散模型（RFHND），其基于描述节点特征在超图上连续演化的偏微分方程系统，从几何层面自适应调控信息扩散速率，防止特征同质化，生成高质量节点表示。实验表明，RFHND在多个基准数据集上显著优于现有方法，具备强鲁棒性，并有效缓解过平滑现象。
原文摘要 · Abstract (English)
Hypergraph neural networks (HGNNs) have demonstrated strong capabilities in modeling complex higher-order relationships. However, existing HGNNs often suffer from over-smoothing as the number of layers increases and lack effective control over message passing among nodes. Inspired by the theory of Ricci flow in differential geometry, we theoretically establish that introducing discrete Ricci flow into hypergraph structures can effectively regulate node feature evolution and thereby alleviate over-smoothing. Building on this insight, we propose Ricci Flow-guided Hypergraph Neural Diffusion(RFHND), a novel message passing paradigm for hypergraphs guided by discrete Ricci flow. Specifically, RFHND is based on a PDE system that describes the continuous evolution of node features on hypergraphs and adaptively regulates the rate of information diffusion at the geometric level, preventing feature homogenization and producing high-quality node representations. Experimental results show that RFHND significantly outperforms existing methods across multiple benchmark datasets and demonstrates strong robustness, while also effectively mitigating over-smoothing.
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