Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approach
arXiv:2603.15696v1 Announce Type: new Abstract: 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 r
arXiv:2603.15696v1 Announce Type: new Abstract: 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.
Executive Summary
This article proposes the Ricci Flow-guided Hypergraph Neural Diffusion (RFHND) approach, a novel message passing paradigm for hypergraphs, to tackle over-smoothing issues in hypergraph neural networks (HGNNs). Inspired by the theory of Ricci flow in differential geometry, RFHND introduces discrete Ricci flow into hypergraph structures to regulate node feature evolution and adaptively control information diffusion. Experimental results demonstrate the effectiveness of RFHND in alleviating over-smoothing and producing high-quality node representations. The approach significantly outperforms existing methods across multiple benchmark datasets and exhibits strong robustness. The proposed solution has the potential to enhance the capabilities of HGNNs in modeling complex higher-order relationships.
Key Points
- ▸ Introduction of discrete Ricci flow to regulate node feature evolution and alleviate over-smoothing in HGNNs.
- ▸ Development of the Ricci Flow-guided Hypergraph Neural Diffusion (RFHND) approach for effective control over message passing among nodes.
- ▸ Experimental validation of RFHND's performance across multiple benchmark datasets, demonstrating significant improvements over existing methods.
Merits
Strength in Addressing Over-smoothing
RFHND effectively alleviates over-smoothing and produces high-quality node representations, enhancing the capabilities of HGNNs in modeling complex higher-order relationships.
Robustness and Performance
RFHND demonstrates strong robustness and significantly outperforms existing methods across multiple benchmark datasets.
Demerits
Limited Evaluation of Hypergraph Structure
The article does not extensively evaluate the impact of hypergraph structure on the performance of RFHND, which may limit its generalizability to diverse applications.
Lack of Theoretical Guarantees
The article does not provide theoretical guarantees for the convergence of RFHND, which may hinder its adoption in certain applications where rigorous guarantees are essential.
Expert Commentary
The article presents a novel and promising approach to addressing over-smoothing in HGNNs. By introducing discrete Ricci flow, RFHND effectively regulates node feature evolution and produces high-quality node representations. The experimental results demonstrate the approach's effectiveness and robustness. However, further research is needed to extensively evaluate the impact of hypergraph structure on RFHND's performance and provide theoretical guarantees for its convergence. Nevertheless, RFHND has the potential to significantly enhance the capabilities of HGNNs in various applications.
Recommendations
- ✓ Investigate the impact of hypergraph structure on RFHND's performance and explore its generalizability to diverse applications.
- ✓ Develop theoretical guarantees for the convergence of RFHND to provide a more comprehensive understanding of its behavior.