{"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/f-gans-in-an-information-geometric-nutshell","title":"f-GANs in an Information Geometric Nutshell","arxiv_id":"1707.04385","date":"2017-07-14","proceeding":"NeurIPS 2017 12","authors":["Richard Nock","Zac Cranko","Aditya Krishna Menon","Lizhen Qu","Robert C. Williamson"],"abstract":"Nowozin \\textit{et al} showed last year how to extend the GAN\n\\textit{principle} to all $f$-divergences. The approach is elegant but falls\nshort of a full description of the supervised game, and says little about the\nkey player, the generator: for example, what does the generator actually\nconverge to if solving the GAN game means convergence in some space of\nparameters? How does that provide hints on the generator's design and compare\nto the flourishing but almost exclusively experimental literature on the\nsubject?\n  In this paper, we unveil a broad class of distributions for which such\nconvergence happens --- namely, deformed exponential families, a wide superset\nof exponential families --- and show tight connections with the three other key\nGAN parameters: loss, game and architecture. In particular, we show that\ncurrent deep architectures are able to factorize a very large number of such\ndensities using an especially compact design, hence displaying the power of\ndeep architectures and their concinnity in the $f$-GAN game. This result holds\ngiven a sufficient condition on \\textit{activation functions} --- which turns\nout to be satisfied by popular choices. The key to our results is a variational\ngeneralization of an old theorem that relates the KL divergence between regular\nexponential families and divergences between their natural parameters. We\ncomplete this picture with additional results and experimental insights on how\nthese results may be used to ground further improvements of GAN architectures,\nvia (i) a principled design of the activation functions in the generator and\n(ii) an explicit integration of proper composite losses' link function in the\ndiscriminator.","url_abs":"http://arxiv.org/abs/1707.04385v1","url_pdf":"http://arxiv.org/pdf/1707.04385v1.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":"f-gans-in-an-information-geometric-nutshell","repo_url":"https://github.com/qulizhen/fgan_info_geometric","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":0,"framework":"pytorch","reach":{"status":"unanswered"}}],"tasks":[],"methods":[{"method_slug":"convolution","method_name":"Convolution"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":"https://app.syntology.ai/?focus=1707.04385","mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}