# Hyperbolic Graph Attention Network

arXiv: https://arxiv.org/abs/1912.03046 · HTML: https://mlsanity.com/paper/1912.03046/

## Key facts

- Cited by 70 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Dec 2019.

## Built on by (most cited first, 30 of 70)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Fully Hyperbolic Neural Networks](https://mlsanity.com/paper/2105.14686/) (2021)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Lorentzian Graph Convolutional Networks](https://mlsanity.com/paper/2104.07477/) (2021)
- [Discrete-time Temporal Network Embedding via Implicit Hierarchical Learning in Hyperbolic Space](https://mlsanity.com/paper/2107.03767/) (2021)
- [Clipped Hyperbolic Classifiers Are Super-Hyperbolic Classifiers](https://mlsanity.com/paper/2107.11472/) (2021)
- [A Hyperbolic-to-Hyperbolic Graph Convolutional Network](https://mlsanity.com/paper/2104.06942/) (2021)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [Hyperbolic Fine-Tuning for Large Language Models](https://mlsanity.com/paper/2410.04010/) (2024)
- [Poincar'e ResNet](https://mlsanity.com/paper/2303.14027/) (2023)
- [Hyperbolic Representation Learning: Revisiting and Advancing](https://mlsanity.com/paper/2306.09118/) (2023)
- [Enhancing Hyperbolic Graph Embeddings via Contrastive Learning](https://mlsanity.com/paper/2201.08554/) (2022)
- [Hyperbolic Deep Learning for Foundation Models: A Survey](https://mlsanity.com/paper/2507.17787/) (2025)
- [Hyperbolic Audio-visual Zero-shot Learning](https://mlsanity.com/paper/2308.12558/) (2023)
- [Lorentzian Residual Neural Networks](https://mlsanity.com/paper/2412.14695/) (2024)
- [Curve Your Attention: Mixed-Curvature Transformers for Graph Representation Learning](https://mlsanity.com/paper/2309.04082/) (2023)
- [Hyperbolic Dataset Distillation](https://mlsanity.com/paper/2505.24623/) (2025)
- [kHGCN: Tree-likeness Modeling via Continuous and Discrete Curvature Learning](https://mlsanity.com/paper/2212.01793/) (2022)
- [HGWaveNet: A Hyperbolic Graph Neural Network for Temporal Link Prediction](https://mlsanity.com/paper/2304.07302/) (2023)
- [Matrix Manifold Neural Networks++](https://mlsanity.com/paper/2405.19206/) (2024)
- [Node Embedding from Neural Hamiltonian Orbits in Graph Neural Networks](https://mlsanity.com/paper/2305.18965/) (2023)
- [HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modules](https://mlsanity.com/paper/2504.08912/) (2025)
- [Public Wisdom Matters! Discourse-Aware Hyperbolic Fourier Co-Attention for Social-Text Classification](https://mlsanity.com/paper/2209.13017/) (2022)
- [Cross-Modal Fusion and Attention Mechanism for Weakly Supervised Video Anomaly Detection](https://mlsanity.com/paper/2412.20455/) (2024)
- [RPT: Toward Transferable Model on Heterogeneous Researcher Data via Pre-Training](https://mlsanity.com/paper/2110.07336/) (2021)
- [Understanding and Mitigating Hyperbolic Dimensional Collapse in Graph Contrastive Learning](https://mlsanity.com/paper/2310.18209/) (2023)
- [Neural Attention Models in Deep Learning: Survey and Taxonomy](https://mlsanity.com/paper/2112.05909/) (2021)
- [D-HYPR: Harnessing Neighborhood Modeling and Asymmetry Preservation for Digraph Representation Learning](https://mlsanity.com/paper/2112.11734/) (2021)

## Abstract (arXiv)

Graph neural network (GNN) has shown superior performance in dealing with graphs, which has attracted considerable research attention recently. However, most of the existing GNN models are primarily designed for graphs in Euclidean spaces. Recent research has proven that the graph data exhibits non-Euclidean latent anatomy. Unfortunately, there was rarely study of GNN in non-Euclidean settings so far. To bridge this gap, in this paper, we study the GNN with attention mechanism in hyperbolic spaces at the first attempt. The research of hyperbolic GNN has some unique challenges: since the hyperbolic spaces are not vector spaces, the vector operations (e.g., vector addition, subtraction, and scalar multiplication) cannot be carried. To tackle this problem, we employ the gyrovector spaces, which provide an elegant algebraic formalism for hyperbolic geometry, to transform the features in a graph; and then we propose the hyperbolic proximity based attention mechanism to aggregate the features. Moreover, as mathematical operations in hyperbolic spaces could be more complicated than those in Euclidean spaces, we further devise a novel acceleration strategy using logarithmic and exponential mappings to improve the efficiency of our proposed model. The comprehensive experimental results on four real-world datasets demonstrate the performance of our proposed hyperbolic graph attention network model, by comparisons with other state-of-the-art baseline methods.