Training-Free Message Passing for Learning on Hypergraphs

TL;DR

Training-Free Message Passing for Learning on Hypergraphs introduces TF-HNN, a hypergraph neural network that decouples hypergraph structure processing from model training via a precomputable TF-MP-Module. By removing learnable parameters and non-linearities and unifying multiple MP-Modules into a single propagation operator S, TF-HNN achieves comparable information utilization with substantially reduced training effort, while remaining robust to oversmoothing through long-range interactions. Theoretical analyses show lower training complexity, preserved information flow, and favorable inductive bias, and empirical results across seven real-world hypergraphs demonstrate competitive accuracy with dramatic efficiency gains, including a large-scale Trivago dataset where TF-HNN attains about 10% higher node-classification accuracy using roughly 1% of the training time. Overall, TF-HNN provides a practical, preprocessing-focused approach to hypergraph learning that can serve as a scalable baseline and a foundation for future hypergraph ML developments.

Abstract

Hypergraphs are crucial for modelling higher-order interactions in real-world data. Hypergraph neural networks (HNNs) effectively utilise these structures by message passing to generate informative node features for various downstream tasks like node classification. However, the message passing module in existing HNNs typically requires a computationally intensive training process, which limits their practical use. To tackle this challenge, we propose an alternative approach by decoupling the usage of hypergraph structural information from the model learning stage. This leads to a novel training-free message passing module, named TF-MP-Module, which can be precomputed in the data preprocessing stage, thereby reducing the computational burden. We refer to the hypergraph neural network equipped with our TF-MP-Module as TF-HNN. We theoretically support the efficiency and effectiveness of TF-HNN by showing that: 1) It is more training-efficient 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 based on seven real-world hypergraph benchmarks in node classification and hyperlink prediction show that, compared to state-of-the-art HNNs, TF-HNN exhibits both competitive performance and superior training efficiency. Specifically, on the large-scale benchmark, Trivago, TF-HNN outperforms the node classification accuracy of the best baseline by 10% with just 1% of the training time of that baseline.

Figures (5)

• Figure 1: Training pipeline of HNN vs. TF-HNN for node classification. Top row: HNN uses a hypergraph structure to generate node features by a learnable MP-Module, which are then used by a classifier, with the MP-Module and the classifier being trained together. For brevity, we omit the MLP in HNN for the input node features. Bottom row: TF-HNN comprises only the classifier trained for node classification and the TF-MP-Module that can be recomputed before the classifier training.
• Figure 2: The relative training time required for HNNs and TF-HNN to achieve optimal performance.
• Figure 3: Hyperlink prediction AUC (%) and relative training time for HNNs and TF-HNN.
• Figure 4: The impact from the hyperparameters of TF-MP-Module in node classification.
• Figure 5: Heatmaps of validation and test performance under varying hyperparameter combinations.

Theorems & Definitions (34)

• Proposition 3.1
• Proposition 3.2
• Proposition 3.3
• Proposition 4.1
• Proposition 4.2
• proof
• Lemma D.1
• proof
• Lemma D.2
• proof