{"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/understanding-the-effectiveness-of-lipschitz","title":"Understanding the Effectiveness of Lipschitz-Continuity in Generative Adversarial Nets","arxiv_id":"1807.00751","date":"2018-07-02","proceeding":null,"authors":["Zhiming Zhou","Yuxuan Song","Lantao Yu","Hongwei Wang","Jiadong Liang","Wei-Nan Zhang","Zhihua Zhang","Yong Yu"],"abstract":"In this paper, we investigate the underlying factor that leads to failure and\nsuccess in the training of GANs. We study the property of the optimal\ndiscriminative function and show that in many GANs, the gradient from the\noptimal discriminative function is not reliable, which turns out to be the\nfundamental cause of failure in training of GANs. We further demonstrate that a\nwell-defined distance metric does not necessarily guarantee the convergence of\nGANs. Finally, we prove in this paper that Lipschitz-continuity condition is a\ngeneral solution to make the gradient of the optimal discriminative function\nreliable, and characterized the necessary condition where Lipschitz-continuity\nensures the convergence, which leads to a broad family of valid GAN objectives\nunder Lipschitz-continuity condition, where Wasserstein distance is one special\ncase. We experiment with several new objectives, which are sound according to\nour theorems, and we found that, compared with Wasserstein distance, the\noutputs of the discriminator with new objectives are more stable and the final\nqualities of generated samples are also consistently higher than those produced\nby Wasserstein distance.","url_abs":"http://arxiv.org/abs/1807.00751v6","url_pdf":"http://arxiv.org/pdf/1807.00751v6.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":"understanding-the-effectiveness-of-lipschitz","repo_url":"https://github.com/ZhimingZhou/AM-GAN2","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":1,"framework":"tf","reach":{"status":"ok"}}],"tasks":[{"task_slug":null,"task_name":"valid"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1807.00751","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}