{"url":"/method/relativistic-gan","slug":"relativistic-gan","name":"Relativistic GAN","full_name":"Relativistic GAN","full_name_withheld":false,"description_markdown":"A **Relativistic GAN** is a type of generative adversarial network. It has a relativistic discriminator which estimates the probability that the given real data is more realistic than a randomly sampled fake data. The idea is to endow GANs with the property that the probability of real data being real ($D\\left(x\\_{r}\\right)$) should decrease as the probability of fake data being real ($D\\left(x\\_{f}\\right)$) increases.\r\n\r\nWith a standard [GAN](https://paperswithcode.com/method/gan), we can achieve this as follows. The standard GAN discriminator can be defined, in term of the non-transformed layer $C\\left(x\\right)$, as $D\\left(x\\right) = \\text{sigmoid}\\left(C\\left(x\\right)\\right)$. A simple way to make discriminator relativistic - having the output of $D$ depend on both real and fake data - is to sample from real/fake data pairs $\\tilde{x} = \\left(x\\_{r}, x\\_{f}\\right)$ and define it as $D\\left(\\tilde{x}\\right) = \\text{sigmoid}\\left(C\\left(x\\_{r}\\right) − C\\left(x\\_{f}\\right)\\right)$. The modification can be interpreted as: the discriminator estimates the probability\r\nthat the given real data is more realistic than a randomly sampled fake data.\r\n\r\nMore generally a Relativistic GAN can be interpreted as having a discriminator of the form $a\\left(C\\left(x\\_{r}\\right)−C\\left(x\\_{f}\\right)\\right)$, where $a$ is the activation function, to be relativistic.","description_state":"present","introduced_year":null,"introduced_by":{"title":"The relativistic discriminator: a key element missing from standard GAN","paper":"/paper/the-relativistic-discriminator-a-key-element","first_author":"Alexia Jolicoeur-Martineau","n_authors":1,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/the-relativistic-discriminator-a-key-element"},"source":{"url":"http://arxiv.org/abs/1807.00734v3","title":"The relativistic discriminator: a key element missing from standard GAN","url_on_a_paper_host":true},"code_snippet_url":"https://github.com/eriklindernoren/PyTorch-GAN/blob/master/implementations/relativistic_gan/relativistic_gan.py","code_snippet_url_on_a_code_host":true,"categories":[{"area":"Computer Vision","area_id":"computer-vision","collection":"Generative Adversarial Networks","url":"/methods/category/generative-adversarial-networks","pwc_aliases":[]}],"n_papers_tagged":6,"archive_num_papers":6,"papers_newest_first":[{"paper":"/paper/the-gan-is-dead-long-live-the-gan-a-modern","title":"The GAN is dead; long live the GAN! A Modern GAN Baseline","date":"2025-01-09","arxiv_id":"2501.05441","n_code_links":1,"syntology":{"ran":9,"of":11,"unverified":2,"pointer_only":11}},{"paper":null,"title":"A Three-Player GAN for Super-Resolution in Magnetic Resonance Imaging","date":"2023-03-24","arxiv_id":"2303.13900","n_code_links":0,"syntology":null},{"paper":null,"title":"Improve GAN-based Neural Vocoder using Pointwise Relativistic LeastSquare GAN","date":"2021-03-26","arxiv_id":"2103.14245","n_code_links":0,"syntology":null},{"paper":null,"title":"UU-Nets Connecting Discriminator and Generator for Image to Image Translation","date":"2019-04-04","arxiv_id":"1904.02675","n_code_links":0,"syntology":null},{"paper":"/paper/esrgan-enhanced-super-resolution-generative","title":"ESRGAN: Enhanced Super-Resolution Generative Adversarial Networks","date":"2018-09-01","arxiv_id":"1809.00219","n_code_links":46,"syntology":{"ran":8,"of":44,"unverified":36,"pointer_only":0}},{"paper":"/paper/the-relativistic-discriminator-a-key-element","title":"The relativistic discriminator: a key element missing from standard GAN","date":"2018-07-02","arxiv_id":"1807.00734","n_code_links":10,"syntology":{"ran":1,"of":9,"unverified":8,"pointer_only":2}}],"papers_shown":6,"tasks":[{"task":"/task/image-generation","name":"Image Generation","papers":3},{"task":null,"name":"Generative Adversarial Network","papers":2},{"task":"/task/image-super-resolution","name":"Image Super-Resolution","papers":2},{"task":"/task/super-resolution","name":"Super-Resolution","papers":2},{"task":"/task/decoder","name":"Decoder","papers":1},{"task":"/task/face-hallucination","name":"Face Hallucination","papers":1},{"task":"/task/image-to-image-translation","name":"Image-to-Image Translation","papers":1},{"task":"/task/translation","name":"Translation","papers":1},{"task":"/task/video-super-resolution","name":"Video Super-Resolution","papers":1}],"tasks_shown":9,"n_tasks":9,"usage_by_year":[{"year":"2018","papers":2},{"year":"2019","papers":1},{"year":"2021","papers":1},{"year":"2023","papers":1},{"year":"2025","papers":1}],"row_source":"methods_table","archive":{"source":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","archive_url":"https://paperswithcode.com/method/relativistic-gan"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}