Tackling Over-smoothing on Hypergraphs: A Ricci Flow-guided Neural Diffusion Approach
This addresses over-smoothing in hypergraph neural networks for applications like social network analysis or recommendation systems, representing a novel method for a known bottleneck.
The paper tackles over-smoothing in hypergraph neural networks by proposing a Ricci flow-guided neural diffusion approach, which significantly outperforms existing methods on benchmark datasets and effectively mitigates over-smoothing.
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.