# Hyperbolic Graph Neural Networks

arXiv: https://arxiv.org/abs/1910.12892 · HTML: https://mlsanity.com/paper/1910.12892/

## Key facts

- Cited by 244 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 28 Oct 2019.

## Built on by (most cited first, 30 of 244)

- [Understanding over-squashing and bottlenecks on graphs via curvature](https://mlsanity.com/paper/2111.14522/) (2021)
- [Graph neural networks for materials science and chemistry](https://mlsanity.com/paper/2208.09481/) (2022)
- [A Survey on Graph Neural Networks for Time Series: Forecasting, Classification, Imputation, and Anomaly Detection](https://mlsanity.com/paper/2307.03759/) (2023)
- [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 Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [Size-Invariant Graph Representations for Graph Classification Extrapolations](https://mlsanity.com/paper/2103.05045/) (2021)
- [Beltrami Flow and Neural Diffusion on Graphs](https://mlsanity.com/paper/2110.09443/) (2021)
- [When Do Flat Minima Optimizers Work?](https://mlsanity.com/paper/2202.00661/) (2022)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [Graph-MLP: Node Classification without Message Passing in Graph](https://mlsanity.com/paper/2106.04051/) (2021)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [GIMLET: A Unified Graph-Text Model for Instruction-Based Molecule Zero-Shot Learning](https://mlsanity.com/paper/2306.13089/) (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)
- [Hyperbolic Contrastive Learning for Visual Representations beyond Objects](https://mlsanity.com/paper/2212.00653/) (2022)
- [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)
- [Dorylus: Affordable, Scalable, and Accurate GNN Training with Distributed CPU Servers and Serverless Threads](https://mlsanity.com/paper/2105.11118/) (2021)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [Learning the Predictability of the Future](https://mlsanity.com/paper/2101.01600/) (2021)
- [HoroPCA: Hyperbolic Dimensionality Reduction via Horospherical Projections](https://mlsanity.com/paper/2106.03306/) (2021)
- [HYperbolic Self-Paced Learning for Self-Supervised Skeleton-based Action Representations](https://mlsanity.com/paper/2303.06242/) (2023)
- [Hypformer: Exploring Efficient Transformer Fully in Hyperbolic Space](https://mlsanity.com/paper/2407.01290/) (2024)
- [Hyperbolic Busemann Learning with Ideal Prototypes](https://mlsanity.com/paper/2106.14472/) (2021)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [RiemannGFM: Learning a Graph Foundation Model from Riemannian Geometry](https://mlsanity.com/paper/2502.03251/) (2025)
- [HRCF: Enhancing Collaborative Filtering via Hyperbolic Geometric Regularization](https://mlsanity.com/paper/2204.08176/) (2022)
- [A Self-supervised Mixed-curvature Graph Neural Network](https://mlsanity.com/paper/2112.05393/) (2021)
- [Self-Supervised Continual Graph Learning in Adaptive Riemannian Spaces](https://mlsanity.com/paper/2211.17068/) (2022)

## Abstract (arXiv)

Learning from graph-structured data is an important task in machine learning and artificial intelligence, for which Graph Neural Networks (GNNs) have shown great promise. Motivated by recent advances in geometric representation learning, we propose a novel GNN architecture for learning representations on Riemannian manifolds with differentiable exponential and logarithmic maps. We develop a scalable algorithm for modeling the structural properties of graphs, comparing Euclidean and hyperbolic geometry. In our experiments, we show that hyperbolic GNNs can lead to substantial improvements on various benchmark datasets.