# Gromov-Wasserstein Alignment of Word Embedding Spaces

arXiv: https://arxiv.org/abs/1809.00013 · HTML: https://mlsanity.com/paper/1809.00013/

## Key facts

- Cited by 122 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 31 Aug 2018.

## Built on by (most cited first, 30 of 122)

- [A Survey on Multilingual Large Language Models: Corpora, Alignment, and Bias](https://mlsanity.com/paper/2404.00929/) (2024)
- [Harnessing the Universal Geometry of Embeddings](https://mlsanity.com/paper/2505.12540/) (2025)
- [Cross-Domain Imitation Learning via Optimal Transport](https://mlsanity.com/paper/2110.03684/) (2021)
- [Unbalanced Optimal Transport, from Theory to Numerics](https://mlsanity.com/paper/2211.08775/) (2022)
- [Shared Global and Local Geometry of Language Model Embeddings](https://mlsanity.com/paper/2503.21073/) (2025)
- [AlignMixup: Improving Representations By Interpolating Aligned Features](https://mlsanity.com/paper/2103.15375/) (2021)
- [GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomics](https://mlsanity.com/paper/2310.09254/) (2023)
- [Scalable Optimal Transport Methods in Machine Learning: A Contemporary Survey](https://mlsanity.com/paper/2305.05080/) (2023)
- [Wasserstein Task Embedding for Measuring Task Similarities](https://mlsanity.com/paper/2208.11726/) (2022)
- [Pre-training for Speech Translation: CTC Meets Optimal Transport](https://mlsanity.com/paper/2301.11716/) (2023)
- [Improving Neural Cross-Lingual Summarization via Employing Optimal Transport Distance for Knowledge Distillation](https://mlsanity.com/paper/2112.03473/) (2021)
- [Bilingual Lexicon Induction via Unsupervised Bitext Construction and Word Alignment](https://mlsanity.com/paper/2101.00148/) (2021)
- [Quantized Gromov-Wasserstein](https://mlsanity.com/paper/2104.02013/) (2021)
- [Using Optimal Transport as Alignment Objective for fine-tuning Multilingual Contextualized Embeddings](https://mlsanity.com/paper/2110.02887/) (2021)
- [Discovering Universal Geometry in Embeddings with ICA](https://mlsanity.com/paper/2305.13175/) (2023)
- [Adaptive Hierarchical Graph Reasoning with Semantic Coherence for Video-and-Language Inference](https://mlsanity.com/paper/2107.12270/) (2021)
- [An improved central limit theorem and fast convergence rates for entropic transportation costs](https://mlsanity.com/paper/2204.09105/) (2022)
- [On Transportation of Mini-batches: A Hierarchical Approach](https://mlsanity.com/paper/2102.05912/) (2021)
- [Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transport](https://mlsanity.com/paper/2305.04034/) (2023)
- [Neural Optimal Transport with Lagrangian Costs](https://mlsanity.com/paper/2406.00288/) (2024)
- [It's a (Blind) Match! Towards Vision-Language Correspondence without Parallel Data](https://mlsanity.com/paper/2503.24129/) (2025)
- [Entropic Gromov-Wasserstein between Gaussian Distributions](https://mlsanity.com/paper/2108.10961/) (2021)
- [Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wasserstein](https://mlsanity.com/paper/2402.02239/) (2024)
- [The Z-Gromov-Wasserstein Distance](https://mlsanity.com/paper/2408.08233/) (2024)
- [NeuraCrypt: Hiding Private Health Data via Random Neural Networks for Public Training](https://mlsanity.com/paper/2106.02484/) (2021)
- [Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and More](https://mlsanity.com/paper/2107.06876/) (2021)
- [Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsification](https://mlsanity.com/paper/2205.13573/) (2022)
- [InfoOT: Information Maximizing Optimal Transport](https://mlsanity.com/paper/2210.03164/) (2022)
- [Task-Agnostic Low-Rank Adapters for Unseen English Dialects](https://mlsanity.com/paper/2311.00915/) (2023)
- [Source-Free Domain Adaptation for YOLO Object Detection](https://mlsanity.com/paper/2409.16538/) (2024)

## Abstract (arXiv)

Cross-lingual or cross-domain correspondences play key roles in tasks ranging from machine translation to transfer learning. Recently, purely unsupervised methods operating on monolingual embeddings have become effective alignment tools. Current state-of-the-art methods, however, involve multiple steps, including heuristic post-hoc refinement strategies. In this paper, we cast the correspondence problem directly as an optimal transport (OT) problem, building on the idea that word embeddings arise from metric recovery algorithms. Indeed, we exploit the Gromov-Wasserstein distance that measures how similarities between pairs of words relate across languages. We show that our OT objective can be estimated efficiently, requires little or no tuning, and results in performance comparable with the state-of-the-art in various unsupervised word translation tasks.