# HyperSAGE: Generalizing Inductive Representation Learning on Hypergraphs

arXiv: https://arxiv.org/abs/2010.04558 · HTML: https://mlsanity.com/paper/2010.04558/

## Key facts

- Cited by 54 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Oct 2020.

## Built on by (most cited first, 30 of 54)

- [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)
- [Signal Processing on Higher-Order Networks: Livin' on the Edge ... and Beyond](https://mlsanity.com/paper/2101.05510/) (2021)
- [Equivariant Hypergraph Diffusion Neural Operators](https://mlsanity.com/paper/2207.06680/) (2022)
- [Architectures of Topological Deep Learning: A Survey of Message-Passing Topological Neural Networks](https://mlsanity.com/paper/2304.10031/) (2023)
- [HYTREL: Hypergraph-enhanced Tabular Data Representation Learning](https://mlsanity.com/paper/2307.08623/) (2023)
- [Sheaf Hypergraph Networks](https://mlsanity.com/paper/2309.17116/) (2023)
- [Augmentations in Hypergraph Contrastive Learning: Fabricated and Generative](https://mlsanity.com/paper/2210.03801/) (2022)
- [I'm Me, We're Us, and I'm Us: Tri-directional Contrastive Learning on Hypergraphs](https://mlsanity.com/paper/2206.04739/) (2022)
- [From Hypergraph Energy Functions to Hypergraph Neural Networks](https://mlsanity.com/paper/2306.09623/) (2023)
- [Hypergraph Convolutional Networks via Equivalency between Hypergraphs and Undirected Graphs](https://mlsanity.com/paper/2203.16939/) (2022)
- [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)
- [HEAT: Hyperedge Attention Networks](https://mlsanity.com/paper/2201.12113/) (2022)
- [Joint Entity and Relation Extraction with Span Pruning and Hypergraph Neural Networks](https://mlsanity.com/paper/2310.17238/) (2023)
- [Adaptive Neural Message Passing for Inductive Learning on Hypergraphs](https://mlsanity.com/paper/2109.10683/) (2021)
- [A Survey on Hyperlink Prediction](https://mlsanity.com/paper/2207.02911/) (2022)
- [A Hypergraph Neural Network Framework for Learning Hyperedge-Dependent Node Embeddings](https://mlsanity.com/paper/2212.14077/) (2022)
- [Principled Hyperedge Prediction with Structural Spectral Features and Neural Networks](https://mlsanity.com/paper/2106.04292/) (2021)
- [Deep Hypergraph Structure Learning](https://mlsanity.com/paper/2208.12547/) (2022)
- [ICML 2023 Topological Deep Learning Challenge : Design and Results](https://mlsanity.com/paper/2309.15188/) (2023)
- [Recent Advances in Hypergraph Neural Networks](https://mlsanity.com/paper/2503.07959/) (2025)
- [CAT-Walk: Inductive Hypergraph Learning via Set Walks](https://mlsanity.com/paper/2306.11147/) (2023)
- [DVHGNN: Multi-Scale Dilated Vision HGNN for Efficient Vision Recognition](https://mlsanity.com/paper/2503.14867/) (2025)
- [Hypergraph Foundation Model](https://mlsanity.com/paper/2503.01203/) (2025)
- [Ada-HGNN: Adaptive Sampling for Scalable Hypergraph Neural Networks](https://mlsanity.com/paper/2405.13372/) (2024)
- [Demystifying Higher-Order Graph Neural Networks](https://mlsanity.com/paper/2406.12841/) (2024)
- [Hypergraph Multi-modal Large Language Model: Exploiting EEG and Eye-tracking Modalities to Evaluate Heterogeneous Responses for Video Understanding](https://mlsanity.com/paper/2407.08150/) (2024)
- [HyperGCL: Multi-Modal Graph Contrastive Learning via Learnable Hypergraph Views](https://mlsanity.com/paper/2502.13277/) (2025)
- [CHGNN: A Semi-Supervised Contrastive Hypergraph Learning Network](https://mlsanity.com/paper/2303.06213/) (2023)

## Abstract (arXiv)

Graphs are the most ubiquitous form of structured data representation used in machine learning. They model, however, only pairwise relations between nodes and are not designed for encoding the higher-order relations found in many real-world datasets. To model such complex relations, hypergraphs have proven to be a natural representation. Learning the node representations in a hypergraph is more complex than in a graph as it involves information propagation at two levels: within every hyperedge and across the hyperedges. Most current approaches first transform a hypergraph structure to a graph for use in existing geometric deep learning algorithms. This transformation leads to information loss, and sub-optimal exploitation of the hypergraph's expressive power. We present HyperSAGE, a novel hypergraph learning framework that uses a two-level neural message passing strategy to accurately and efficiently propagate information through hypergraphs. The flexible design of HyperSAGE facilitates different ways of aggregating neighborhood information. Unlike the majority of related work which is transductive, our approach, inspired by the popular GraphSAGE method, is inductive. Thus, it can also be used on previously unseen nodes, facilitating deployment in problems such as evolving or partially observed hypergraphs. Through extensive experimentation, we show that HyperSAGE outperforms state-of-the-art hypergraph learning methods on representative benchmark datasets. We also demonstrate that the higher expressive power of HyperSAGE makes it more stable in learning node representations as compared to the alternatives.