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

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.

D4PM: A Dual-branch Driven Denoising Diffusion Probabilistic Model with Joint Posterior Diffusion Sampling for EEG Artifacts Removal

Artifact removal is critical for accurate analysis and interpretation of Electroencephalogram (EEG) signals. Traditional methods perform poorly with strong artifact-EEG correlations or single-channel data. Recent advances in diffusion-based generative models have demonstrated strong potential for EEG denoising, notably improving fine-grained noise suppression and reducing over-smoothing. However, existing methods face two main limitations: lack of temporal modeling limits interpretability and the use of single-artifact training paradigms ignore inter-artifact differences. To address these issues, we propose D4PM, a dual-branch driven denoising diffusion probabilistic model that unifies multi-type artifact removal. We introduce a dual-branch conditional diffusion architecture to implicitly model the data distribution of clean EEG and artifacts. A joint posterior sampling strategy is further designed to collaboratively integrate complementary priors for high-fidelity EEG reconstruction. Extensive experiments on two public datasets show that D4PM delivers superior denoising. It achieves new state-of-the-art performance in EOG artifact removal, outperforming all publicly available baselines. The code is available at https://github.com/flysnow1024/D4PM.