{"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/hyperbolic-generative-adversarial-network","title":"Hyperbolic Generative Adversarial Network","arxiv_id":"2102.05567","date":"2021-02-10","proceeding":null,"authors":["Diego Lazcano","Nicolás Fredes","Werner Creixell"],"abstract":"Recently, Hyperbolic Spaces in the context of Non-Euclidean Deep Learning have gained popularity because of their ability to represent hierarchical data. We propose that it is possible to take advantage of the hierarchical characteristic present in the images by using hyperbolic neural networks in a GAN architecture. In this study, different configurations using fully connected hyperbolic layers in the GAN, CGAN, and WGAN are tested, in what we call the HGAN, HCGAN, and HWGAN, respectively. The results are measured using the Inception Score (IS) and the Fr\\'echet Inception Distance (FID) on the MNIST dataset. Depending on the configuration and space curvature, better results are achieved for each proposed hyperbolic versions than their euclidean counterpart.","url_abs":"https://arxiv.org/abs/2102.05567v1","url_pdf":"https://arxiv.org/pdf/2102.05567v1.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":[],"tasks":[{"task_slug":null,"task_name":"Generative Adversarial Network"},{"task_slug":"image-generation","task_name":"Image Generation"}],"methods":[{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"wgan","method_name":"WGAN"}],"datasets_introduced":[],"methods_introduced":[],"results":[{"leaderboard":"/sota/image-generation-on-mnist","task":"Image Generation","dataset":"MNIST","model":"HypGAN","rank_in_archive_order":9,"of":15,"metrics":{"FID":"7.87"},"uses_additional_data":false}],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}