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Gromov-Wasserstein Alignment of Word Embedding Spaces

arXiv 1809.00013 ↗First posted 31 Aug 2018cs.CLcited by 119

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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.

Key facts. Cited by 119 papers in the map (data through 7 Oct 2026). First posted on arXiv 31 Aug 2018.

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Citing papers per year: 2021: 22; 2022: 21; 2023: 29; 2024: 20; 2025: 12; 2026: 15.

119 papers.

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  1. 2024A Survey on Multilingual Large Language Models: Corpora, Alignment, and Biascited by 82
  2. 2025Harnessing the Universal Geometry of Embeddingscited by 54
  3. 2021Cross-Domain Imitation Learning via Optimal Transportcited by 49
  4. 2022Unbalanced Optimal Transport, from Theory to Numericscited by 45
  5. 2025Shared Global and Local Geometry of Language Model Embeddingscited by 34
  6. 2021AlignMixup: Improving Representations By Interpolating Aligned Featurescited by 33
  7. 2023Scalable Optimal Transport Methods in Machine Learning: A Contemporary Surveycited by 27
  8. 2023GENOT: Entropic (Gromov) Wasserstein Flow Matching with Applications to Single-Cell Genomicscited by 27
  9. 2023Pre-training for Speech Translation: CTC Meets Optimal Transportcited by 25
  10. 2022Wasserstein Task Embedding for Measuring Task Similaritiescited by 24
  11. 2021Improving Neural Cross-Lingual Summarization via Employing Optimal Transport Distance for Knowledge Distillationcited by 22
  12. 2021Bilingual Lexicon Induction via Unsupervised Bitext Construction and Word Alignmentcited by 19
38 more
  1. 2021Using Optimal Transport as Alignment Objective for fine-tuning Multilingual Contextualized Embeddingscited by 19
  2. 2023Discovering Universal Geometry in Embeddings with ICAcited by 19
  3. 2021Quantized Gromov-Wassersteincited by 18
  4. 2021Adaptive Hierarchical Graph Reasoning with Semantic Coherence for Video-and-Language Inferencecited by 18
  5. 2022An improved central limit theorem and fast convergence rates for entropic transportation costscited by 18
  6. 2023Wasserstein-Fisher-Rao Embedding: Logical Query Embeddings with Local Comparison and Global Transportcited by 16
  7. 2024Neural Optimal Transport with Lagrangian Costscited by 16
  8. 2021On Transportation of Mini-batches: A Hierarchical Approachcited by 15
  9. 2025It's a (Blind) Match! Towards Vision-Language Correspondence without Parallel Datacited by 13
  10. 2021Entropic Gromov-Wasserstein between Gaussian Distributionscited by 12
  11. 2024Distributional Reduction: Unifying Dimensionality Reduction and Clustering with Gromov-Wassersteincited by 12
  12. 2024The Z-Gromov-Wasserstein Distancecited by 12
  13. 2021NeuraCrypt: Hiding Private Health Data via Random Neural Networks for Public Trainingcited by 11
  14. 2022Efficient Approximation of Gromov-Wasserstein Distance Using Importance Sparsificationcited by 11
  15. 2021Scalable Optimal Transport in High Dimensions for Graph Distances, Embedding Alignment, and Morecited by 10
  16. 2022InfoOT: Information Maximizing Optimal Transportcited by 9
  17. 2023Task-Agnostic Low-Rank Adapters for Unseen English Dialectscited by 9
  18. 2021Manifold optimization for non-linear optimal transport problemscited by 8
  19. 2022Towards a Broad Coverage Named Entity Resource: A Data-Efficient Approach for Many Diverse Languagescited by 8
  20. 2024Source-Free Domain Adaptation for YOLO Object Detectioncited by 8
  21. 2022Riemannian block SPD coupling manifold and its application to optimal transportcited by 7
  22. 2022IsoVec: Controlling the Relative Isomorphism of Word Embedding Spacescited by 7
  23. 2023Globally solving the Gromov-Wasserstein problem for point clouds in low dimensional Euclidean spacescited by 7
  24. 2024A New Robust Partial p-Wasserstein-Based Metric for Comparing Distributionscited by 7
  25. 2021Cross-Lingual Word Embedding Refinement by ℓ1 Norm Optimisationcited by 6
  26. 2022Gromov-Wasserstein Discrepancy with Local Differential Privacy for Distributed Structural Graphscited by 6
  27. 2022Unbalanced CO-Optimal Transportcited by 6
  28. 2022Bilingual Lexicon Induction for Low-Resource Languages using Graph Matching via Optimal Transportcited by 6
  29. 2022Quantized Wasserstein Procrustes Alignment of Word Embedding Spacescited by 6
  30. 2023Outlier-Robust Gromov-Wasserstein for Graph Datacited by 6
  31. 2023Uncovering Challenges of Solving the Continuous Gromov-Wasserstein Problemcited by 6
  32. 2023Applications of No-Collision Transportation Maps in Manifold Learningcited by 6
  33. 2021Cycle Consistent Probability Divergences Across Different Spacescited by 5
  34. 2022Transferable Reward Learning by Dynamics-Agnostic Discriminator Ensemblecited by 5
  35. 2023Personalised Federated Learning On Heterogeneous Feature Spacescited by 5
  36. 2024Revisiting Cosine Similarity via Normalized ICA-transformed Embeddingscited by 5
  37. 2024Cross-domain Named Entity Recognition via Graph Matchingcited by 5
  38. 2024Tree-Wasserstein Distance for High Dimensional Data with a Latent Feature Hierarchycited by 5

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