HGNNv2: Stable Hypergraph Neural Networks.

Area of Science:

• Artificial Intelligence
• Machine Learning
• Data Science

Background:

• Hypergraph neural networks (HGNNs) are essential for analyzing higher-order relational data.
• HGNNs face performance degradation as network layers increase.
• Existing hypergraph dynamic systems (HDS) lack positional information and use isotropic diffusion, limiting their precision.

Purpose of the Study:

• To introduce HGNNv2, a stable hypergraph neural network model.
• To address the limitations of existing HGNNs and HDS by incorporating positional awareness and anisotropic diffusion.
• To improve the stability and accuracy of hypergraph data analysis.

Main Methods:

• Developed HGNNv2 as a hypergraph dynamic system utilizing partial differential equations (PDEs).
• Incorporated a position-aware anisotropic diffusion term and an external control term.
• Introduced the vertex-rooted subtree method to determine anisotropic diffusion intensity.

Main Results:

• HGNNv2 demonstrated superior performance across 6 hypergraph and 3 graph datasets, outperforming 12 other methods.
• The model achieved stable final representations and task accuracy, even under noisy conditions.
• HGNNv2 required fewer layers for stable performance compared to isotropic diffusion-based HDS.

Conclusions:

• HGNNv2 offers a stable and effective approach to hypergraph neural network analysis.
• The integration of position-aware anisotropic diffusion significantly enhances information propagation and representation learning.
• HGNNv2 represents a significant advancement in handling complex relational data with improved robustness and efficiency.