{"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/banach-wasserstein-gan","title":"Banach Wasserstein GAN","arxiv_id":"1806.06621","date":"2018-06-18","proceeding":"NeurIPS 2018 12","authors":["Jonas Adler","Sebastian Lunz"],"abstract":"Wasserstein Generative Adversarial Networks (WGANs) can be used to generate\nrealistic samples from complicated image distributions. The Wasserstein metric\nused in WGANs is based on a notion of distance between individual images, which\ninduces a notion of distance between probability distributions of images. So\nfar the community has considered $\\ell^2$ as the underlying distance. We\ngeneralize the theory of WGAN with gradient penalty to Banach spaces, allowing\npractitioners to select the features to emphasize in the generator. We further\ndiscuss the effect of some particular choices of underlying norms, focusing on\nSobolev norms. Finally, we demonstrate a boost in performance for an\nappropriate choice of norm on CIFAR-10 and CelebA.","url_abs":"http://arxiv.org/abs/1806.06621v2","url_pdf":"http://arxiv.org/pdf/1806.06621v2.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":"banach-wasserstein-gan","repo_url":"https://github.com/adler-j/bwgan","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}},{"paper_slug":"banach-wasserstein-gan","repo_url":"https://github.com/new-okaerinasai/bwgan_pytorch","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=1806.06621","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}