{"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/sobolev-gan","title":"Sobolev GAN","arxiv_id":"1711.04894","date":"2017-11-14","proceeding":"ICLR 2018 1","authors":["Youssef Mroueh","Chun-Liang Li","Tom Sercu","Anant Raj","Yu Cheng"],"abstract":"We propose a new Integral Probability Metric (IPM) between distributions: the\nSobolev IPM. The Sobolev IPM compares the mean discrepancy of two distributions\nfor functions (critic) restricted to a Sobolev ball defined with respect to a\ndominant measure $\\mu$. We show that the Sobolev IPM compares two distributions\nin high dimensions based on weighted conditional Cumulative Distribution\nFunctions (CDF) of each coordinate on a leave one out basis. The Dominant\nmeasure $\\mu$ plays a crucial role as it defines the support on which\nconditional CDFs are compared. Sobolev IPM can be seen as an extension of the\none dimensional Von-Mises Cram\\'er statistics to high dimensional\ndistributions. We show how Sobolev IPM can be used to train Generative\nAdversarial Networks (GANs). We then exploit the intrinsic conditioning implied\nby Sobolev IPM in text generation. Finally we show that a variant of Sobolev\nGAN achieves competitive results in semi-supervised learning on CIFAR-10,\nthanks to the smoothness enforced on the critic by Sobolev GAN which relates to\nLaplacian regularization.","url_abs":"http://arxiv.org/abs/1711.04894v1","url_pdf":"http://arxiv.org/pdf/1711.04894v1.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":"sobolev-gan","repo_url":"https://github.com/chanshing/sobolev_gan","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":{"status":"ok"}},{"paper_slug":"sobolev-gan","repo_url":"https://github.com/zzmtsvv/adversarial","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"pytorch","reach":null}],"tasks":[{"task_slug":"text-generation","task_name":"Text Generation"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1711.04894","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}