# Fully Hyperbolic Graph Convolution Network for Recommendation

arXiv: https://arxiv.org/abs/2108.04607 · HTML: https://mlsanity.com/paper/2108.04607/

## Key facts

- Cited by 13 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 10 Aug 2021.

## Built on by (most cited first, 13 of 13)

- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [Hyperbolic Safety-Aware Vision-Language Models](https://mlsanity.com/paper/2503.12127/) (2025)
- [HypLL: The Hyperbolic Learning Library](https://mlsanity.com/paper/2306.06154/) (2023)
- [Hyperbolic Large Language Models](https://mlsanity.com/paper/2509.05757/) (2025)
- [Time-aware Hyperbolic Graph Attention Network for Session-based Recommendation](https://mlsanity.com/paper/2301.03780/) (2023)
- [Adversarial Attacks on Hyperbolic Networks](https://mlsanity.com/paper/2412.01495/) (2024)
- [Hyperbolic Graph Representation Learning: A Tutorial](https://mlsanity.com/paper/2211.04050/) (2022)
- [Large Language Models Enhanced Hyperbolic Space Recommender Systems](https://mlsanity.com/paper/2504.05694/) (2025)
- [Hyperbolic Contrastive Learning with Model-augmentation for Knowledge-aware Recommendation](https://mlsanity.com/paper/2505.08157/) (2025)
- [Learning Protein-Ligand Binding in Hyperbolic Space](https://mlsanity.com/paper/2508.15480/) (2025)
- [Hyperbolic Knowledge Transfer in Cross-Domain Recommendation System](https://mlsanity.com/paper/2406.17289/) (2024)
- [Breaking Information Cocoons: A Hyperbolic Framework for Balancing Exploration and Exploitation in Recommender Systems](https://mlsanity.com/paper/2411.13865/) (2024)

## Abstract (arXiv)

Recently, Graph Convolution Network (GCN) based methods have achieved outstanding performance for recommendation. These methods embed users and items in Euclidean space, and perform graph convolution on user-item interaction graphs. However, real-world datasets usually exhibit tree-like hierarchical structures, which make Euclidean space less effective in capturing user-item relationship. In contrast, hyperbolic space, as a continuous analogue of a tree-graph, provides a promising alternative. In this paper, we propose a fully hyperbolic GCN model for recommendation, where all operations are performed in hyperbolic space. Utilizing the advantage of hyperbolic space, our method is able to embed users/items with less distortion and capture user-item interaction relationship more accurately. Extensive experiments on public benchmark datasets show that our method outperforms both Euclidean and hyperbolic counterparts and requires far lower embedding dimensionality to achieve comparable performance.