{"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/qp-wasserstein-gans-comparing-ground-metrics","title":"(q,p)-Wasserstein GANs: Comparing Ground Metrics for Wasserstein GANs","arxiv_id":"1902.03642","date":"2019-02-10","proceeding":null,"authors":["Anton Mallasto","Jes Frellsen","Wouter Boomsma","Aasa Feragen"],"abstract":"Generative Adversial Networks (GANs) have made a major impact in computer\nvision and machine learning as generative models. Wasserstein GANs (WGANs)\nbrought Optimal Transport (OT) theory into GANs, by minimizing the\n$1$-Wasserstein distance between model and data distributions as their\nobjective function. Since then, WGANs have gained considerable interest due to\ntheir stability and theoretical framework. We contribute to the WGAN literature\nby introducing the family of $(q,p)$-Wasserstein GANs, which allow the use of\nmore general $p$-Wasserstein metrics for $p\\geq 1$ in the GAN learning\nprocedure. While the method is able to incorporate any cost function as the\nground metric, we focus on studying the $l^q$ metrics for $q\\geq 1$. This is a\nnotable generalization as in the WGAN literature the OT distances are commonly\nbased on the $l^2$ ground metric. We demonstrate the effect of different\n$p$-Wasserstein distances in two toy examples. Furthermore, we show that the\nground metric does make a difference, by comparing different $(q,p)$ pairs on\nthe MNIST and CIFAR-10 datasets. Our experiments demonstrate that changing the\nground metric and $p$ can notably improve on the common $(q,p) = (2,1)$ case.","url_abs":"http://arxiv.org/abs/1902.03642v1","url_pdf":"http://arxiv.org/pdf/1902.03642v1.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":"qp-wasserstein-gans-comparing-ground-metrics","repo_url":"https://github.com/sverdoot/qp-wgan","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}}],"tasks":[],"methods":[{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"wgan","method_name":"WGAN"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1902.03642","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}