# Learning Multilingual Word Embeddings in Latent Metric Space: A Geometric Approach

arXiv: https://arxiv.org/abs/1808.08773 · HTML: https://mlsanity.com/paper/1808.08773/

## Key facts

- Cited by 22 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Aug 2018.

## Built on by (most cited first, 22 of 22)

- [On Riemannian Optimization over Positive Definite Matrices with the Bures-Wasserstein Geometry](https://mlsanity.com/paper/2106.00286/) (2021)
- [Improving Word Translation via Two-Stage Contrastive Learning](https://mlsanity.com/paper/2203.08307/) (2022)
- [Crosslingual Transfer Learning for Low-Resource Languages Based on Multilingual Colexification Graphs](https://mlsanity.com/paper/2305.12818/) (2023)
- [IsoVec: Controlling the Relative Isomorphism of Word Embedding Spaces](https://mlsanity.com/paper/2210.05098/) (2022)
- [Improving Bilingual Lexicon Induction with Cross-Encoder Reranking](https://mlsanity.com/paper/2210.16953/) (2022)
- [Multi-Way Representation Alignment](https://mlsanity.com/paper/2602.06205/) (2026)
- [Riemannian coordinate descent algorithms on matrix manifolds](https://mlsanity.com/paper/2406.02225/) (2024)
- [RAPO: An Adaptive Ranking Paradigm for Bilingual Lexicon Induction](https://mlsanity.com/paper/2210.09926/) (2022)
- [GRI: Graph-based Relative Isomorphism of Word Embedding Spaces](https://mlsanity.com/paper/2310.12360/) (2023)
- [GARI: Graph Attention for Relative Isomorphism of Arabic Word Embeddings](https://mlsanity.com/paper/2310.13068/) (2023)
- [Denoising Word Embeddings by Averaging in a Shared Space](https://mlsanity.com/paper/2106.02954/) (2021)
- [Learning a Reversible Embedding Mapping using Bi-Directional Manifold Alignment](https://mlsanity.com/paper/2107.00124/) (2021)
- [An Analysis of Euclidean vs. Graph-Based Framing for Bilingual Lexicon Induction from Word Embedding Spaces](https://mlsanity.com/paper/2109.12640/) (2021)
- [ProMap: Effective Bilingual Lexicon Induction via Language Model Prompting](https://mlsanity.com/paper/2310.18778/) (2023)
- [Robust Unsupervised Cross-Lingual Word Embedding using Domain Flow Interpolation](https://mlsanity.com/paper/2210.03319/) (2022)
- [Leveraging knowledge graphs to update scientific word embeddings using latent semantic imputation](https://mlsanity.com/paper/2210.15358/) (2022)
- [Multilingual Word Embeddings for Low-Resource Languages using Anchors and a Chain of Related Languages](https://mlsanity.com/paper/2311.12489/) (2023)
- [TokAlign++: Advancing Vocabulary Adaptation via Better Token Alignment](https://mlsanity.com/paper/2605.13429/) (2026)
- [Unsupervised Alignment of Distributional Word Embeddings](https://mlsanity.com/paper/2203.04863/) (2022)
- [Effective vocabulary expansion of multilingual language models for extremely low-resource languages](https://mlsanity.com/paper/2602.09388/) (2026)
- [Fr'echet Regression on the Bures-Wasserstein Manifold](https://mlsanity.com/paper/2604.03566/) (2026)
- [Geometry-Preserving Unsupervised Alignment for Heterogeneous Foundation Models](https://mlsanity.com/paper/2606.04385/) (2026)

## Abstract (arXiv)

We propose a novel geometric approach for learning bilingual mappings given monolingual embeddings and a bilingual dictionary. Our approach decouples learning the transformation from the source language to the target language into (a) learning rotations for language-specific embeddings to align them to a common space, and (b) learning a similarity metric in the common space to model similarities between the embeddings. We model the bilingual mapping problem as an optimization problem on smooth Riemannian manifolds. We show that our approach outperforms previous approaches on the bilingual lexicon induction and cross-lingual word similarity tasks. We also generalize our framework to represent multiple languages in a common latent space. In particular, the latent space representations for several languages are learned jointly, given bilingual dictionaries for multiple language pairs. We illustrate the effectiveness of joint learning for multiple languages in zero-shot word translation setting. Our implementation is available at https://github.com/anoopkunchukuttan/geomm .