# Cross-lingual Word Embeddings in Hyperbolic Space

arXiv: https://arxiv.org/abs/2205.01907 · HTML: https://mlsanity.com/paper/2205.01907/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 30 of its 43 references that are in the map.
- First posted on arXiv 4 May 2022.

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

- [SemEval-2017 Task 1: Semantic Textual Similarity - Multilingual and Cross-lingual Focused Evaluation](https://mlsanity.com/paper/1708.00055/) (2017)
- [Poincar'e Embeddings for Learning Hierarchical Representations](https://mlsanity.com/paper/1705.08039/) (2017)
- [Learning Word Vectors for 157 Languages](https://mlsanity.com/paper/1802.06893/) (2018)
- [Unsupervised Machine Translation Using Monolingual Corpora Only](https://mlsanity.com/paper/1711.00043/) (2017)
- [Learning Continuous Hierarchies in the Lorentz Model of Hyperbolic Geometry](https://mlsanity.com/paper/1806.03417/) (2018)
- [Representation Tradeoffs for Hyperbolic Embeddings](https://mlsanity.com/paper/1804.03329/) (2018)
- [Exploiting Similarities among Languages for Machine Translation](https://mlsanity.com/paper/1309.4168/) (2013)
- [Transfer Learning for Low-Resource Neural Machine Translation](https://mlsanity.com/paper/1604.02201/) (2016)
- [Hyperbolic Entailment Cones for Learning Hierarchical Embeddings](https://mlsanity.com/paper/1804.01882/) (2018)
- [Poincar'e GloVe: Hyperbolic Word Embeddings](https://mlsanity.com/paper/1810.06546/) (2018)
- [A Survey Of Cross-lingual Word Embedding Models](https://mlsanity.com/paper/1706.04902/) (2017)
- [Offline bilingual word vectors, orthogonal transformations and the inverted softmax](https://mlsanity.com/paper/1702.03859/) (2017)
- [Margin-based Parallel Corpus Mining with Multilingual Sentence Embeddings](https://mlsanity.com/paper/1811.01136/) (2018)
- [Embedding Text in Hyperbolic Spaces](https://mlsanity.com/paper/1806.04313/) (2018)
- [Universal Neural Machine Translation for Extremely Low Resource Languages](https://mlsanity.com/paper/1802.05368/) (2018)
- [From Trees to Continuous Embeddings and Back: Hyperbolic Hierarchical Clustering](https://mlsanity.com/paper/2010.00402/) (2020)
- [Inferring Concept Hierarchies from Text Corpora via Hyperbolic Embeddings](https://mlsanity.com/paper/1902.00913/) (2019)
- [Adversarial Deep Averaging Networks for Cross-Lingual Sentiment Classification](https://mlsanity.com/paper/1606.01614/) (2016)
- [Hyperbolic Interaction Model For Hierarchical Multi-Label Classification](https://mlsanity.com/paper/1905.10802/) (2019)
- [HyperText: Endowing FastText with Hyperbolic Geometry](https://mlsanity.com/paper/2010.16143/) (2020)
- [HyperLex: A Large-Scale Evaluation of Graded Lexical Entailment](https://mlsanity.com/paper/1608.02117/) (2016)
- [Hearst Patterns Revisited: Automatic Hypernym Detection from Large Text Corpora](https://mlsanity.com/paper/1806.03191/) (2018)
- [Skip-gram word embeddings in hyperbolic space](https://mlsanity.com/paper/1809.01498/) (2018)
- [Building Subject-aligned Comparable Corpora and Mining it for Truly Parallel Sentence Pairs](https://mlsanity.com/paper/1509.08881/) (2015)
- [Cross-lingual Models of Word Embeddings: An Empirical Comparison](https://mlsanity.com/paper/1604.00425/) (2016)
- [Robust Cross-lingual Embeddings from Parallel Sentences](https://mlsanity.com/paper/1912.12481/) (2019)
- [Social Centralization and Semantic Collapse: Hyperbolic Embeddings of Networks and Text](https://mlsanity.com/paper/2001.09493/) (2020)
- [Trans-gram, Fast Cross-lingual Word-embeddings](https://mlsanity.com/paper/1601.02502/) (2016)
- [Cross-lingual Word Analogies using Linear Transformations between Semantic Spaces](https://mlsanity.com/paper/1807.04175/) (2018)
- [Crosslingual Document Embedding as Reduced-Rank Ridge Regression](https://mlsanity.com/paper/1904.03922/) (2019)

## Built on by (most cited first, 2 of 2)

- [Position: Beyond Euclidean -- Foundation Models Should Embrace Non-Euclidean Geometries](https://mlsanity.com/paper/2504.08896/) (2025)
- [Number Theory Meets Linguistics: Modelling Noun Pluralisation Across 1497 Languages Using 2-adic Metrics](https://mlsanity.com/paper/2211.13124/) (2022)

## Abstract (arXiv)

Cross-lingual word embeddings can be applied to several natural language processing applications across multiple languages. Unlike prior works that use word embeddings based on the Euclidean space, this short paper presents a simple and effective cross-lingual Word2Vec model that adapts to the Poincar'e ball model of hyperbolic space to learn unsupervised cross-lingual word representations from a German-English parallel corpus. It has been shown that hyperbolic embeddings can capture and preserve hierarchical relationships. We evaluate the model on both hypernymy and analogy tasks. The proposed model achieves comparable performance with the vanilla Word2Vec model on the cross-lingual analogy task, the hypernymy task shows that the cross-lingual Poincar'e Word2Vec model can capture latent hierarchical structure from free text across languages, which are absent from the Euclidean-based Word2Vec representations. Our results show that by preserving the latent hierarchical information, hyperbolic spaces can offer better representations for cross-lingual embeddings.