{"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/geometric-gan","title":"Geometric GAN","arxiv_id":"1705.02894","date":"2017-05-08","proceeding":null,"authors":["Jae Hyun Lim","Jong Chul Ye"],"abstract":"Generative Adversarial Nets (GANs) represent an important milestone for\neffective generative models, which has inspired numerous variants seemingly\ndifferent from each other. One of the main contributions of this paper is to\nreveal a unified geometric structure in GAN and its variants. Specifically, we\nshow that the adversarial generative model training can be decomposed into\nthree geometric steps: separating hyperplane search, discriminator parameter\nupdate away from the separating hyperplane, and the generator update along the\nnormal vector direction of the separating hyperplane. This geometric intuition\nreveals the limitations of the existing approaches and leads us to propose a\nnew formulation called geometric GAN using SVM separating hyperplane that\nmaximizes the margin. Our theoretical analysis shows that the geometric GAN\nconverges to a Nash equilibrium between the discriminator and generator. In\naddition, extensive numerical results show that the superior performance of\ngeometric GAN.","url_abs":"http://arxiv.org/abs/1705.02894v2","url_pdf":"http://arxiv.org/pdf/1705.02894v2.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":"geometric-gan","repo_url":"https://github.com/WangZesen/GAN-Hinge-Loss","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"geometric-gan","repo_url":"https://github.com/WangZesen/Spectral-Normalization-GAN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"geometric-gan","repo_url":"https://github.com/beresandras/gan-flavours-keras","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok","spdx":"MIT"}},{"paper_slug":"geometric-gan","repo_url":"https://github.com/ChristophReich1996/Dirac-GAN","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null},{"paper_slug":"geometric-gan","repo_url":"https://github.com/ChristophReich1996/Mode_Collapse","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":null},{"paper_slug":"geometric-gan","repo_url":"https://github.com/open-mmlab/mmgeneration","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[{"task_slug":"text-generation","task_name":"Text Generation"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"gan-hinge-loss","method_name":"GAN Hinge Loss"},{"method_slug":"svm","method_name":"SVM"}],"datasets_introduced":[],"methods_introduced":[{"slug":"gan-hinge-loss","name":"GAN Hinge Loss","full_name":"GAN Hinge Loss"}],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1705.02894","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}