{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/learning-wasserstein-embeddings","title":"Learning Wasserstein Embeddings","arxiv_id":"1710.07457","date":"2017-10-20","proceeding":"ICLR 2018 1","authors":["Nicolas Courty","Rémi Flamary","Mélanie Ducoffe"],"abstract":"The Wasserstein distance received a lot of attention recently in the\ncommunity of machine learning, especially for its principled way of comparing\ndistributions. It has found numerous applications in several hard problems,\nsuch as domain adaptation, dimensionality reduction or generative models.\nHowever, its use is still limited by a heavy computational cost. Our goal is to\nalleviate this problem by providing an approximation mechanism that allows to\nbreak its inherent complexity. It relies on the search of an embedding where\nthe Euclidean distance mimics the Wasserstein distance. We show that such an\nembedding can be found with a siamese architecture associated with a decoder\nnetwork that allows to move from the embedding space back to the original input\nspace. Once this embedding has been found, computing optimization problems in\nthe Wasserstein space (e.g. barycenters, principal directions or even\narchetypes) can be conducted extremely fast. Numerical experiments supporting\nthis idea are conducted on image datasets, and show the wide potential benefits\nof our method.","url_abs":"http://arxiv.org/abs/1710.07457v1","url_pdf":"http://arxiv.org/pdf/1710.07457v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"learning-wasserstein-embeddings","repo_url":"https://github.com/doronhav/jax_dwe","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"jax","reach":{"status":"ok"}},{"paper_slug":"learning-wasserstein-embeddings","repo_url":"https://github.com/jlacombe/learning-to-generate-wasserstein-barycenters","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"decoder","task_name":"Decoder"},{"task_slug":"dimensionality-reduction","task_name":"Dimensionality Reduction"},{"task_slug":"domain-adaptation","task_name":"Domain Adaptation"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1710.07457","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1710.07457"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-24T18:15:14+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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