# Deep Hyperedges: a Framework for Transductive and Inductive Learning on Hypergraphs

arXiv: https://arxiv.org/abs/1910.02633 · HTML: https://mlsanity.com/paper/1910.02633/

## Key facts

- Cited by 9 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 7 Oct 2019.

## Built on by (most cited first, 9 of 9)

- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [Adaptive Neural Message Passing for Inductive Learning on Hypergraphs](https://mlsanity.com/paper/2109.10683/) (2021)
- [Hypergraph Pre-training with Graph Neural Networks](https://mlsanity.com/paper/2105.10862/) (2021)
- [CAT-Walk: Inductive Hypergraph Learning via Set Walks](https://mlsanity.com/paper/2306.11147/) (2023)
- [AI-driven Hypergraph Network of Organic Chemistry: Network Statistics and Applications in Reaction Classification](https://mlsanity.com/paper/2208.01647/) (2022)
- [Hypergraph Dissimilarity Measures](https://mlsanity.com/paper/2106.08206/) (2021)
- [The CAT SET on the MAT: Cross Attention for Set Matching in Bipartite Hypergraphs](https://mlsanity.com/paper/2111.00243/) (2021)
- [Self-Supervised Pretraining for Heterogeneous Hypergraph Neural Networks](https://mlsanity.com/paper/2311.11368/) (2023)
- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)

## Abstract (arXiv)

From social networks to protein complexes to disease genomes to visual data, hypergraphs are everywhere. However, the scope of research studying deep learning on hypergraphs is still quite sparse and nascent, as there has not yet existed an effective, unified framework for using hyperedge and vertex embeddings jointly in the hypergraph context, despite a large body of prior work that has shown the utility of deep learning over graphs and sets. Building upon these recent advances, we propose textitDeep Hyperedges (DHE), a modular framework that jointly uses contextual and permutation-invariant vertex membership properties of hyperedges in hypergraphs to perform classification and regression in transductive and inductive learning settings. In our experiments, we use a novel random walk procedure and show that our model achieves and, in most cases, surpasses state-of-the-art performance on benchmark datasets. Additionally, we study our framework's performance on a variety of diverse, non-standard hypergraph datasets and propose several avenues of future work to further enhance DHE.