# Hyperbolic Hypergraph Neural Networks for Multi-Relational Knowledge Hypergraph Representation

arXiv: https://arxiv.org/abs/2412.12158 · HTML: https://mlsanity.com/paper/2412.12158/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 4 of its 48 references that are in the map.
- First posted on arXiv 11 Dec 2024.

## Builds on (most cited first, 4 of 4)

- [UMAP: Uniform Manifold Approximation and Projection for Dimension Reduction](https://mlsanity.com/paper/1802.03426/) (2018)
- [HyperSAGE: Generalizing Inductive Representation Learning on Hypergraphs](https://mlsanity.com/paper/2010.04558/) (2020)
- [On the Hyperbolicity of Large-Scale Networks](https://mlsanity.com/paper/1307.0031/) (2013)
- [FFHR: Fully and Flexible Hyperbolic Representation for Knowledge Graph Completion](https://mlsanity.com/paper/2302.04088/) (2023)

## Built on by (most cited first, 2 of 2)

- [Two-dimensional Taxonomy for N-ary Knowledge Representation Learning Methods](https://mlsanity.com/paper/2506.05626/) (2025)
- [Knowledge Graphs Meet Graph Neural Networks: A Comprehensive Survey](https://mlsanity.com/paper/2607.09666/) (2026)

## Abstract (arXiv)

Knowledge hypergraphs generalize knowledge graphs using hyperedges to connect multiple entities and depict complicated relations. Existing methods either transform hyperedges into an easier-to-handle set of binary relations or view hyperedges as isolated and ignore their adjacencies. Both approaches have information loss and may potentially lead to the creation of sub-optimal models. To fix these issues, we propose the Hyperbolic Hypergraph Neural Network (H2GNN), whose essential component is the hyper-star message passing, a novel scheme motivated by a lossless expansion of hyperedges into hierarchies. It implements a direct embedding that consciously incorporates adjacent entities, hyper-relations, and entity position-aware information. As the name suggests, H2GNN operates in the hyperbolic space, which is more adept at capturing the tree-like hierarchy. We compare H2GNN with 15 baselines on knowledge hypergraphs, and it outperforms state-of-the-art approaches in both node classification and link prediction tasks.