# Geometry-aware Domain Adaptation for Unsupervised Alignment of Word Embeddings

arXiv: https://arxiv.org/abs/2004.08243 · HTML: https://mlsanity.com/paper/2004.08243/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 6 Apr 2020.

## Built on by (most cited first, 14 of 14)

- [SPOT: A framework for selection of prototypes using optimal transport](https://mlsanity.com/paper/2103.10159/) (2021)
- [Manifold optimization for non-linear optimal transport problems](https://mlsanity.com/paper/2103.00902/) (2021)
- [Riemannian block SPD coupling manifold and its application to optimal transport](https://mlsanity.com/paper/2201.12933/) (2022)
- [Riemannian accelerated gradient methods via extrapolation](https://mlsanity.com/paper/2208.06619/) (2022)
- [Submodular Framework for Structured-Sparse Optimal Transport](https://mlsanity.com/paper/2406.04914/) (2024)
- [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)
- [A Riemannian Approach to Ground Metric Learning for Optimal Transport](https://mlsanity.com/paper/2409.10085/) (2024)
- [LexGen: Domain-aware Multilingual Lexicon Generation](https://mlsanity.com/paper/2405.11200/) (2024)
- [Finite-Time Analysis of Stochastic Nonconvex Nonsmooth Optimization on the Riemannian Manifolds](https://mlsanity.com/paper/2510.21468/) (2025)
- [A Riemannian Approach to Low-Rank Optimal Transport](https://mlsanity.com/paper/2606.12120/) (2026)
- [Unsupervised Alignment of Distributional Word Embeddings](https://mlsanity.com/paper/2203.04863/) (2022)
- [Zero-shot Cross-lingual Transfer without Parallel Corpus](https://mlsanity.com/paper/2310.04726/) (2023)
- [A survey of neural-network-based methods utilising comparable data for finding translation equivalents](https://mlsanity.com/paper/2410.15144/) (2024)

## Abstract (arXiv)

We propose a novel manifold based geometric approach for learning unsupervised alignment of word embeddings between the source and the target languages. Our approach formulates the alignment learning problem as a domain adaptation problem over the manifold of doubly stochastic matrices. This viewpoint arises from the aim to align the second order information of the two language spaces. The rich geometry of the doubly stochastic manifold allows to employ efficient Riemannian conjugate gradient algorithm for the proposed formulation. Empirically, the proposed approach outperforms state-of-the-art optimal transport based approach on the bilingual lexicon induction task across several language pairs. The performance improvement is more significant for distant language pairs.