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Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approach

Mengyao Zhou, Zhiheng Zhou, Xiao Han, Xingqin Qi, Guanghui Wang, Guiying Yan

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.

Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approach

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.
Paper Structure (32 sections, 95 equations, 5 figures, 5 tables, 1 algorithm)

This paper contains 32 sections, 95 equations, 5 figures, 5 tables, 1 algorithm.

Table of Contents

  1. Introduction
  2. Related Work
  3. Hypergraph Neural Networks
  4. Over-smoothing in HGNNs
  5. Preliminary
  6. Notations
  7. Hyperedge Curvature on Weighted Hypergraph
  8. Dirichlet Energy
  9. Discrete Ricci Flow(DRF)
  10. Applying DRF on Hypergraph
  11. Dirichlet Energy Bound
  12. Convergence Analysis
  13. Methodology
  14. Ricci Flow-guided Hypergraph Feature Diffusion
  15. Ricci Flow-guided Hypergraph Neural Diffusion
  16. ...and 17 more sections

Figures (5)

  • Figure 1: Ricci flow-guided evolution. (a) Evolution of the manifold geometry under Ricci flow. (b) Evolution of hyperedge weight guided by Ricci flow. (c) Evolution of node feature distributions driven by the updated hyperedge weights.
  • Figure 2: (a) shows the accuracy(%) with various depths on Cora. (b) shows the accuracy(%) with various depths on Cora-CA. (c) shows the accuracy(%) with various depths on Citeseer. (d) shows the dirichlet energy with various depths on Cora. (e) shows the dirichlet energy with various depths on Cora-CA. (f) shows the dirichlet energy with various depths on Citeseer.
  • Figure 3: (a) shows the performance on Citeseer under feature gaussian noise. (b) shows the performance on Citeseer under feature uniform noise. (c) shows the performance on Citeseer under feature mask noise. (d) shows the performance on Cora-CA under structure noise.
  • Figure 4: (a) shows RFHND accuracy on NTU2012 and ModelNet40 with various hidden dimensions. (b) shows RFHND accuracy on NTU2012 and ModelNet40 with various $\tau$.
  • Figure 5: (a)(b)(c) show the visualization of Pubmed node features at $t = 0$, $t = 1$ and $t = 2$. (d)(e)(f) show the visualization of DBLP node features at $t = 0$, $t = 1$ and $t = 2$.

Theorems & Definitions (10)

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