# Skip-gram word embeddings in hyperbolic space

arXiv: https://arxiv.org/abs/1809.01498 · HTML: https://mlsanity.com/paper/1809.01498/

## Key facts

- Cited by 20 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 Aug 2018.

## Built on by (most cited first, 20 of 20)

- [Hyperbolic Deep Learning in Computer Vision: A Survey](https://mlsanity.com/paper/2305.06611/) (2023)
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- [HVT: A Comprehensive Vision Framework for Learning in Non-Euclidean Space](https://mlsanity.com/paper/2409.16897/) (2024)
- [A Fashion Item Recommendation Model in Hyperbolic Space](https://mlsanity.com/paper/2409.02599/) (2024)
- [On Hyperbolic Embeddings in 2D Object Detection](https://mlsanity.com/paper/2203.08049/) (2022)
- [Continual Hyperbolic Learning of Instances and Classes](https://mlsanity.com/paper/2506.10710/) (2025)
- [Multi-Relational Hyperbolic Word Embeddings from Natural Language Definitions](https://mlsanity.com/paper/2305.07303/) (2023)
- [Improving Heterogeneous Graph Learning with Weighted Mixed-Curvature Product Manifold](https://mlsanity.com/paper/2307.04514/) (2023)
- [Conformally Natural Families of Probability Distributions on Hyperbolic Disc with a View on Geometric Deep Learning](https://mlsanity.com/paper/2407.16733/) (2024)
- [Learning phylogenetic trees as hyperbolic point configurations](https://mlsanity.com/paper/2104.11430/) (2021)
- [Augmenting the User-Item Graph with Textual Similarity Models](https://mlsanity.com/paper/2109.09358/) (2021)
- [A group-theoretic framework for machine learning in hyperbolic spaces](https://mlsanity.com/paper/2501.06934/) (2025)
- [Incorporating Domain Knowledge into Health Recommender Systems using Hyperbolic Embeddings](https://mlsanity.com/paper/2106.07720/) (2021)
- [Cross-lingual Word Embeddings in Hyperbolic Space](https://mlsanity.com/paper/2205.01907/) (2022)
- [Sinhala Sentence Embedding: A Two-Tiered Structure for Low-Resource Languages](https://mlsanity.com/paper/2210.14472/) (2022)
- [A Geometry-Aware Algorithm to Learn Hierarchical Embeddings in Hyperbolic Space](https://mlsanity.com/paper/2407.16641/) (2024)
- [Kuramoto Oscillators and Swarms on Manifolds for Geometry Informed Machine Learning](https://mlsanity.com/paper/2405.09453/) (2024)
- [Hyperbolic Centroid Calculations for Text Classification](https://mlsanity.com/paper/2211.04462/) (2022)
- [Comparing Euclidean and Hyperbolic K-Means for Generalized Category Discovery](https://mlsanity.com/paper/2602.04932/) (2026)
- [Busemann energy-based attention for emotion analysis in Poincar'e discs](https://mlsanity.com/paper/2604.06752/) (2026)

## Abstract (arXiv)

Recent work has demonstrated that embeddings of tree-like graphs in hyperbolic space surpass their Euclidean counterparts in performance by a large margin. Inspired by these results and scale-free structure in the word co-occurrence graph, we present an algorithm for learning word embeddings in hyperbolic space from free text. An objective function based on the hyperbolic distance is derived and included in the skip-gram negative-sampling architecture of word2vec. The hyperbolic word embeddings are then evaluated on word similarity and analogy benchmarks. The results demonstrate the potential of hyperbolic word embeddings, particularly in low dimensions, though without clear superiority over their Euclidean counterparts. We further discuss subtleties in the formulation of the analogy task in curved spaces.