{"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/gradient-descent-gan-optimization-is-locally","title":"Gradient descent GAN optimization is locally stable","arxiv_id":"1706.04156","date":"2017-06-13","proceeding":"NeurIPS 2017 12","authors":["Vaishnavh Nagarajan","J. Zico Kolter"],"abstract":"Despite the growing prominence of generative adversarial networks (GANs),\noptimization in GANs is still a poorly understood topic. In this paper, we\nanalyze the \"gradient descent\" form of GAN optimization i.e., the natural\nsetting where we simultaneously take small gradient steps in both generator and\ndiscriminator parameters. We show that even though GAN optimization does not\ncorrespond to a convex-concave game (even for simple parameterizations), under\nproper conditions, equilibrium points of this optimization procedure are still\n\\emph{locally asymptotically stable} for the traditional GAN formulation. On\nthe other hand, we show that the recently proposed Wasserstein GAN can have\nnon-convergent limit cycles near equilibrium. Motivated by this stability\nanalysis, we propose an additional regularization term for gradient descent GAN\nupdates, which \\emph{is} able to guarantee local stability for both the WGAN\nand the traditional GAN, and also shows practical promise in speeding up\nconvergence and addressing mode collapse.","url_abs":"http://arxiv.org/abs/1706.04156v3","url_pdf":"http://arxiv.org/pdf/1706.04156v3.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":"gradient-descent-gan-optimization-is-locally","repo_url":"https://github.com/locuslab/gradient_regularized_gan","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}}],"tasks":[],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1706.04156","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}