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

arXiv cs.LG / 3/18/2026

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Key Points

The paper identifies that hypergraph neural networks suffer from over-smoothing as the number of layers increases and proposes using discrete Ricci flow to regulate node feature evolution.
It introduces Ricci Flow-guided Hypergraph Neural Diffusion (RFHND), a novel message-passing paradigm for hypergraphs built on a PDE system describing the continuous evolution of node features.
RFHND adaptively regulates the rate of information diffusion at the geometric level, helping to prevent feature homogenization and producing higher-quality node representations.
The approach is demonstrated to significantly outperform existing methods on multiple benchmark datasets and shows robustness to over-smoothing.
The work provides theoretical justification linking discrete Ricci flow to diffusion dynamics on hypergraphs, supporting the method's ability to control feature evolution.

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.