# Density Matching for Bilingual Word Embedding

arXiv: https://arxiv.org/abs/1904.02343 · HTML: https://mlsanity.com/paper/1904.02343/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 4 Apr 2019.

## Built on by (most cited first, 11 of 11)

- [Survey of Hallucination in Natural Language Generation](https://mlsanity.com/paper/2202.03629/) (2022)
- [State-of-the-art generalisation research in NLP: A taxonomy and review](https://mlsanity.com/paper/2210.03050/) (2022)
- [Universal approximation property of invertible neural networks](https://mlsanity.com/paper/2204.07415/) (2022)
- [Cross-Lingual Word Embedding Refinement by ℓ1 Norm Optimisation](https://mlsanity.com/paper/2104.04916/) (2021)
- [GRI: Graph-based Relative Isomorphism of Word Embedding Spaces](https://mlsanity.com/paper/2310.12360/) (2023)
- [Word Embedding Transformation for Robust Unsupervised Bilingual Lexicon Induction](https://mlsanity.com/paper/2105.12297/) (2021)
- [Constrained Density Matching and Modeling for Cross-lingual Alignment of Contextualized Representations](https://mlsanity.com/paper/2201.13429/) (2022)
- [Sen2Pro: A Probabilistic Perspective to Sentence Embedding from Pre-trained Language Model](https://mlsanity.com/paper/2306.02247/) (2023)
- [Iterative Multilingual Spectral Attribute Erasure](https://mlsanity.com/paper/2506.11244/) (2025)
- [Single Model for Influenza Forecasting of Multiple Countries by Multi-task Learning](https://mlsanity.com/paper/2107.01760/) (2021)
- [Arbitrary Distributions Mapping via SyMOT-Flow: A Flow-based Approach Integrating Maximum Mean Discrepancy and Optimal Transport](https://mlsanity.com/paper/2308.13815/) (2023)

## Abstract (arXiv)

Recent approaches to cross-lingual word embedding have generally been based on linear transformations between the sets of embedding vectors in the two languages. In this paper, we propose an approach that instead expresses the two monolingual embedding spaces as probability densities defined by a Gaussian mixture model, and matches the two densities using a method called normalizing flow. The method requires no explicit supervision, and can be learned with only a seed dictionary of words that have identical strings. We argue that this formulation has several intuitively attractive properties, particularly with the respect to improving robustness and generalization to mappings between difficult language pairs or word pairs. On a benchmark data set of bilingual lexicon induction and cross-lingual word similarity, our approach can achieve competitive or superior performance compared to state-of-the-art published results, with particularly strong results being found on etymologically distant and/or morphologically rich languages.