# Embedding Text in Hyperbolic Spaces

arXiv: https://arxiv.org/abs/1806.04313 · HTML: https://mlsanity.com/paper/1806.04313/

## Key facts

- Cited by 76 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Jun 2018.

## Built on by (most cited first, 30 of 76)

- [Hyperbolic Deep Neural Networks: A Survey](https://mlsanity.com/paper/2101.04562/) (2021)
- [Compositional Entailment Learning for Hyperbolic Vision-Language Models](https://mlsanity.com/paper/2410.06912/) (2024)
- [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)
- [Pseudo-Riemannian Graph Convolutional Networks](https://mlsanity.com/paper/2106.03134/) (2021)
- [Language Models as Hierarchy Encoders](https://mlsanity.com/paper/2401.11374/) (2024)
- [Poincar'e ResNet](https://mlsanity.com/paper/2303.14027/) (2023)
- [A polar coordinate system represents syntax in large language models](https://mlsanity.com/paper/2412.05571/) (2024)
- [Where are we in embedding spaces? A Comprehensive Analysis on Network Embedding Approaches for Recommender Systems](https://mlsanity.com/paper/2105.08908/) (2021)
- [CAPE: Context-Aware Private Embeddings for Private Language Learning](https://mlsanity.com/paper/2108.12318/) (2021)
- [The Euclidean Space is Evil: Hyperbolic Attribute Editing for Few-shot Image Generation](https://mlsanity.com/paper/2211.12347/) (2022)
- [Emergent Visual-Semantic Hierarchies in Image-Text Representations](https://mlsanity.com/paper/2407.08521/) (2024)
- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [Hyperbolic Safety-Aware Vision-Language Models](https://mlsanity.com/paper/2503.12127/) (2025)
- [Learning Structured Representations with Hyperbolic Embeddings](https://mlsanity.com/paper/2412.01023/) (2024)
- [Self-Supervised Graph Learning with Hyperbolic Embedding for Temporal Health Event Prediction](https://mlsanity.com/paper/2106.04751/) (2021)
- [Curved Geometric Networks for Visual Anomaly Recognition](https://mlsanity.com/paper/2208.01188/) (2022)
- [HyperExpan: Taxonomy Expansion with Hyperbolic Representation Learning](https://mlsanity.com/paper/2109.10500/) (2021)
- [You Are What You Write: Preserving Privacy in the Era of Large Language Models](https://mlsanity.com/paper/2204.09391/) (2022)
- [Small Transformers Compute Universal Metric Embeddings](https://mlsanity.com/paper/2209.06788/) (2022)
- [Hyperbolic Learning with Synthetic Captions for Open-World Detection](https://mlsanity.com/paper/2404.05016/) (2024)
- [HyperCore: The Core Framework for Building Hyperbolic Foundation Models with Comprehensive Modules](https://mlsanity.com/paper/2504.08912/) (2025)
- [Label-Aware Hyperbolic Embeddings for Fine-grained Emotion Classification](https://mlsanity.com/paper/2306.14822/) (2023)
- [Hyperbolic Learning with Multimodal Large Language Models](https://mlsanity.com/paper/2408.05097/) (2024)
- [Hyperbolic Hierarchical Contrastive Hashing](https://mlsanity.com/paper/2212.08904/) (2022)
- [Voices in a Crowd: Searching for Clusters of Unique Perspectives](https://mlsanity.com/paper/2407.14259/) (2024)
- [Hyperbolic Relevance Matching for Neural Keyphrase Extraction](https://mlsanity.com/paper/2205.02047/) (2022)
- [PHyCLIP: ℓ1-Product of Hyperbolic Factors Unifies Hierarchy and Compositionality in Vision-Language Representation Learning](https://mlsanity.com/paper/2510.08919/) (2025)
- [Low-distortion and GPU-compatible Tree Embeddings in Hyperbolic Space](https://mlsanity.com/paper/2502.17130/) (2025)
- [Hierarchical Mamba Meets Hyperbolic Geometry: A New Paradigm for Structured Language Embeddings](https://mlsanity.com/paper/2505.18973/) (2025)

## Abstract (arXiv)

Natural language text exhibits hierarchical structure in a variety of respects. Ideally, we could incorporate our prior knowledge of this hierarchical structure into unsupervised learning algorithms that work on text data. Recent work by Nickel & Kiela (2017) proposed using hyperbolic instead of Euclidean embedding spaces to represent hierarchical data and demonstrated encouraging results when embedding graphs. In this work, we extend their method with a re-parameterization technique that allows us to learn hyperbolic embeddings of arbitrarily parameterized objects. We apply this framework to learn word and sentence embeddings in hyperbolic space in an unsupervised manner from text corpora. The resulting embeddings seem to encode certain intuitive notions of hierarchy, such as word-context frequency and phrase constituency. However, the implicit continuous hierarchy in the learned hyperbolic space makes interrogating the model's learned hierarchies more difficult than for models that learn explicit edges between items. The learned hyperbolic embeddings show improvements over Euclidean embeddings in some -- but not all -- downstream tasks, suggesting that hierarchical organization is more useful for some tasks than others.