# Hyperbolic Representation Learning: Revisiting and Advancing

arXiv: https://arxiv.org/abs/2306.09118 · HTML: https://mlsanity.com/paper/2306.09118/

## Key facts

- Cited by 21 papers in the map (data through 14 Oct 2026).
- Builds on 47 of its 74 references that are in the map.
- First posted on arXiv 15 Jun 2023.

## Builds on (most cited first, 30 of 47)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Semi-Supervised Classification with Graph Convolutional Networks](https://mlsanity.com/paper/1609.02907/) (2016)
- [Graph Attention Networks](https://mlsanity.com/paper/1710.10903/) (2017)
- [Inductive Representation Learning on Large Graphs](https://mlsanity.com/paper/1706.02216/) (2017)
- [Simplifying Graph Convolutional Networks](https://mlsanity.com/paper/1902.07153/) (2019)
- [Geom-GCN: Geometric Graph Convolutional Networks](https://mlsanity.com/paper/2002.05287/) (2020)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Hyperbolic Neural Networks](https://mlsanity.com/paper/1805.09112/) (2018)
- [Hyperbolic Graph Convolutional Neural Networks](https://mlsanity.com/paper/1910.12933/) (2019)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Hyperbolic Graph Neural Networks](https://mlsanity.com/paper/1910.12892/) (2019)
- [Hyperbolic Image Embeddings](https://mlsanity.com/paper/1904.02239/) (2019)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Low-Dimensional Hyperbolic Knowledge Graph Embeddings](https://mlsanity.com/paper/2005.00545/) (2020)
- [Riemannian Adaptive Optimization Methods](https://mlsanity.com/paper/1810.00760/) (2018)
- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Hyperbolic Attention Networks](https://mlsanity.com/paper/1805.09786/) (2018)
- [Constant Curvature Graph Convolutional Networks](https://mlsanity.com/paper/1911.05076/) (2019)
- [Hyperbolic Image Segmentation](https://mlsanity.com/paper/2203.05898/) (2022)
- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
- [Hyperbolic Graph Attention Network](https://mlsanity.com/paper/1912.03046/) (2019)
- [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)
- [STAR-GCN: Stacked and Reconstructed Graph Convolutional Networks for Recommender Systems](https://mlsanity.com/paper/1905.13129/) (2019)
- [Hyperbolic Variational Graph Neural Network for Modeling Dynamic Graphs](https://mlsanity.com/paper/2104.02228/) (2021)
- [Spectral Feature Augmentation for Graph Contrastive Learning and Beyond](https://mlsanity.com/paper/2212.01026/) (2022)
- [HyperML: A Boosting Metric Learning Approach in Hyperbolic Space for Recommender Systems](https://mlsanity.com/paper/1809.01703/) (2018)
- [Hyperbolic Graph Neural Networks: A Review of Methods and Applications](https://mlsanity.com/paper/2202.13852/) (2022)
- [Modeling Scale-free Graphs with Hyperbolic Geometry for Knowledge-aware Recommendation](https://mlsanity.com/paper/2108.06468/) (2021)
- [Modeling Heterogeneous Hierarchies with Relation-specific Hyperbolic Cones](https://mlsanity.com/paper/2110.14923/) (2021)

## Built on by (most cited first, 21 of 21)

- [LSEnet: Lorentz Structural Entropy Neural Network for Deep Graph Clustering](https://mlsanity.com/paper/2405.11801/) (2024)
- [DeepRicci: Self-supervised Graph Structure-Feature Co-Refinement for Alleviating Over-squashing](https://mlsanity.com/paper/2401.12780/) (2024)
- [Understanding and Mitigating Hyperbolic Dimensional Collapse in Graph Contrastive Learning](https://mlsanity.com/paper/2310.18209/) (2023)
- [Learning Fine-grained Domain Generalization via Hyperbolic State Space Hallucination](https://mlsanity.com/paper/2504.08020/) (2025)
- [Robust Hyperbolic Learning with Curvature-Aware Optimization](https://mlsanity.com/paper/2405.13979/) (2024)
- [Learning Along the Arrow of Time: Hyperbolic Geometry for Backward-Compatible Representation Learning](https://mlsanity.com/paper/2506.05826/) (2025)
- [Hyperbolic Image-and-Pointcloud Contrastive Learning for 3D Classification](https://mlsanity.com/paper/2409.15810/) (2024)
- [MoE-Enhanced Explainable Deep Manifold Transformation for Complex Data Embedding and Visualization](https://mlsanity.com/paper/2410.19504/) (2024)
- [HyperPath: Knowledge-Guided Hyperbolic Semantic Hierarchy Modeling for WSI Analysis](https://mlsanity.com/paper/2506.16398/) (2025)
- [Manifold GCN: Diffusion-based Convolutional Neural Network for Manifold-valued Graphs](https://mlsanity.com/paper/2401.14381/) (2024)
- [On Probabilistic Pullback Metrics for Latent Hyperbolic Manifolds](https://mlsanity.com/paper/2410.20850/) (2024)
- [Hyperbolic Additive Margin Softmax with Hierarchical Information for Speaker Verification](https://mlsanity.com/paper/2601.19709/) (2026)
- [HypRAG: Hyperbolic Dense Retrieval for Retrieval Augmented Generation](https://mlsanity.com/paper/2602.07739/) (2026)
- [Tempered Calculus for ML: Application to Hyperbolic Model Embedding](https://mlsanity.com/paper/2402.04163/) (2024)
- [Enhance Hyperbolic Representation Learning via Second-order Pooling](https://mlsanity.com/paper/2410.22026/) (2024)
- [DoubleCCA: Improving Foundation Model Group Robustness with Random Sentence Embeddings](https://mlsanity.com/paper/2411.16236/) (2024)
- [Influence Strength Estimation in Hyperbolic Space for Social Influence Maximization](https://mlsanity.com/paper/2502.13571/) (2025)
- [Multi-Scale Representation of Follicular Lymphoma Pathology Images in a Single Hyperbolic Space](https://mlsanity.com/paper/2506.18523/) (2025)
- [Causality-Induced Positional Encoding for Transformer-Based Representation Learning of Non-Sequential Features](https://mlsanity.com/paper/2509.16629/) (2025)
- [HSG: Hyperbolic Scene Graph](https://mlsanity.com/paper/2604.17454/) (2026)
- [Cascade: Hierarchical Recoverability Control for Large Language Model Unlearning](https://mlsanity.com/paper/2609.16890/) (2026)

## Abstract (arXiv)

The non-Euclidean geometry of hyperbolic spaces has recently garnered considerable attention in the realm of representation learning. Current endeavors in hyperbolic representation largely presuppose that the underlying hierarchies can be automatically inferred and preserved through the adaptive optimization process. This assumption, however, is questionable and requires further validation. In this work, we first introduce a position-tracking mechanism to scrutinize existing prevalent hlms, revealing that the learned representations are sub-optimal and unsatisfactory. To address this, we propose a simple yet effective method, hyperbolic informed embedding (HIE), by incorporating cost-free hierarchical information deduced from the hyperbolic distance of the node to origin (i.e., induced hyperbolic norm) to advance existing hlms. The proposed method HIE is both task-agnostic and model-agnostic, enabling its seamless integration with a broad spectrum of models and tasks. Extensive experiments across various models and different tasks demonstrate the versatility and adaptability of the proposed method. Remarkably, our method achieves a remarkable improvement of up to 21.4% compared to the competing baselines.