# Training-Free Message Passing for Learning on Hypergraphs

arXiv: https://arxiv.org/abs/2402.05569 · HTML: https://mlsanity.com/paper/2402.05569/

## Key facts

- Cited by 7 papers in the map (data through 14 Oct 2026).
- Builds on 29 of its 52 references that are in the map.
- First posted on arXiv 8 Feb 2024.

## Builds on (most cited first, 29 of 29)

- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [A Comprehensive Survey on Graph Neural Networks](https://mlsanity.com/paper/1901.00596/) (2019)
- [Predict then Propagate: Graph Neural Networks meet Personalized PageRank](https://mlsanity.com/paper/1810.05997/) (2018)
- [Graph Neural Networks in Recommender Systems: A Survey](https://mlsanity.com/paper/2011.02260/) (2020)
- [Hypergraph Neural Networks](https://mlsanity.com/paper/1809.09401/) (2018)
- [Graph Signal Processing: Overview, Challenges and Applications](https://mlsanity.com/paper/1712.00468/) (2017)
- [SIGN: Scalable Inception Graph Neural Networks](https://mlsanity.com/paper/2004.11198/) (2020)
- [Hypergraph Convolution and Hypergraph Attention](https://mlsanity.com/paper/1901.08150/) (2019)
- [UniGNN: a Unified Framework for Graph and Hypergraph Neural Networks](https://mlsanity.com/paper/2105.00956/) (2021)
- [You are AllSet: A Multiset Function Framework for Hypergraph Neural Networks](https://mlsanity.com/paper/2106.13264/) (2021)
- [HNHN: Hypergraph Networks with Hyperedge Neurons](https://mlsanity.com/paper/2006.12278/) (2020)
- [What are higher-order networks?](https://mlsanity.com/paper/2104.11329/) (2021)
- [Graph Neural Networks Inspired by Classical Iterative Algorithms](https://mlsanity.com/paper/2103.06064/) (2021)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [Sheaf Hypergraph Networks](https://mlsanity.com/paper/2309.17116/) (2023)
- [Dynamic-Group-Aware Networks for Multi-Agent Trajectory Prediction with Relational Reasoning](https://mlsanity.com/paper/2206.13114/) (2022)
- [Semi-supervised Hypergraph Node Classification on Hypergraph Line Expansion](https://mlsanity.com/paper/2005.04843/) (2020)
- [Introducing Hypergraph Signal Processing: Theoretical Foundation and Practical Applications](https://mlsanity.com/paper/1907.09203/) (2019)
- [Preventing Over-Smoothing for Hypergraph Neural Networks](https://mlsanity.com/paper/2203.17159/) (2022)
- [From Hypergraph Energy Functions to Hypergraph Neural Networks](https://mlsanity.com/paper/2306.09623/) (2023)
- [Revisiting Graph Convolutional Network on Semi-Supervised Node Classification from an Optimization Perspective](https://mlsanity.com/paper/2009.11469/) (2020)
- [Hypergraph Neural Networks through the Lens of Message Passing: A Common Perspective to Homophily and Architecture Design](https://mlsanity.com/paper/2310.07684/) (2023)
- [Equivariant Hypergraph Neural Networks](https://mlsanity.com/paper/2208.10428/) (2022)
- [Higher-Order Label Homogeneity and Spreading in Graphs](https://mlsanity.com/paper/2002.07833/) (2020)
- [A Survey on Hyperlink Prediction](https://mlsanity.com/paper/2207.02911/) (2022)
- [Learning Hypergraphs From Signals With Dual Smoothness Prior](https://mlsanity.com/paper/2211.01717/) (2022)
- [A Markov Random Field model for Hypergraph-based Machine Learning](https://mlsanity.com/paper/2308.14172/) (2023)
- [Hypergraph-MLP: Learning on Hypergraphs without Message Passing](https://mlsanity.com/paper/2312.09778/) (2023)
- [LightHGNN: Distilling Hypergraph Neural Networks into MLPs for 100× Faster Inference](https://mlsanity.com/paper/2402.04296/) (2024)

## Built on by (most cited first, 7 of 7)

- [HyperSkill: Self-Evolving LLM Agents via Hypergraph-Structured Skill Memory](https://mlsanity.com/paper/2608.16114/) (2026)
- [Commonality in Few: Few-Shot Multimodal Anomaly Detection via Hypergraph-Enhanced Memory](https://mlsanity.com/paper/2511.05966/) (2025)
- [DHG-Bench: A Comprehensive Benchmark for Deep Hypergraph Learning](https://mlsanity.com/paper/2508.12244/) (2025)
- [NGDB-Zoo: Towards Efficient and Scalable Neural Graph Databases Training](https://mlsanity.com/paper/2602.21597/) (2026)
- [Heterophily-Agnostic Hypergraph Neural Networks with Riemannian Local Exchanger](https://mlsanity.com/paper/2603.00599/) (2026)
- [Anchor-guided Hypergraph Condensation with Dual-level Discrimination](https://mlsanity.com/paper/2605.10001/) (2026)
- [The WidthWall: A Strict Expressivity Hierarchy for Hypergraph Neural Networks](https://mlsanity.com/paper/2605.13690/) (2026)

## Abstract (arXiv)

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.