Simplifying Hypergraph Neural Networks

Hypergraphs, with hyperedges connecting multiple nodes, are crucial for modelling higher-order interactions in real-world data. In frameworks utilising hypergraphs for downstream tasks, a task-specific model is typically paired with a hypergraph neural network (HNN). HNNs enhance the task-specific model by generating node features with hypergraph structural information via message passing. However, the training for HNNs is often computationally intensive, which limits their practical use. To tackle this challenge, we propose an alternative approach by integrating hypergraph structural information into node features using a training-free model called simplified hypergraph neural network (SHNN) that only contains a predefined propagation step. We theoretically show the efficiency and effectiveness of SHNN by showing that: 1) It largely reduces the training complexity when solving hypergraph-related downstream tasks compared to existing HNNs; 2) It utilises as much information as existing HNNs for node feature generation; and 3) It is robust against the oversmoothing issue while using long-range interactions. Experiments in node classification and hyperedge prediction showcase that, compared to state-of-the-art HNNs, SHNN leads to both competitive performance and superior training efficiency. Notably, on Cora-CA, the SHNN-based framework achieves the highest node classification accuracy with just 2% training time of the best baseline.