{"url":"/method/lsgan","slug":"lsgan","name":"LSGAN","full_name":"LSGAN","full_name_withheld":false,"description_markdown":"**LSGAN**, or **Least Squares GAN**, is a type of generative adversarial network that adopts the least squares loss function for the discriminator. Minimizing the objective function of LSGAN yields minimizing the Pearson $\\chi^{2}$ divergence. The objective function can be defined as:\r\n\r\n$$ \\min\\_{D}V\\_{LSGAN}\\left(D\\right) = \\frac{1}{2}\\mathbb{E}\\_{\\mathbf{x} \\sim p\\_{data}\\left(\\mathbf{x}\\right)}\\left[\\left(D\\left(\\mathbf{x}\\right) - b\\right)^{2}\\right] + \\frac{1}{2}\\mathbb{E}\\_{\\mathbf{z}\\sim p\\_{\\mathbf{z}}\\left(\\mathbf{z}\\right)}\\left[\\left(D\\left(G\\left(\\mathbf{z}\\right)\\right) - a\\right)^{2}\\right] $$\r\n\r\n$$ \\min\\_{G}V\\_{LSGAN}\\left(G\\right) = \\frac{1}{2}\\mathbb{E}\\_{\\mathbf{z} \\sim p\\_{\\mathbf{z}}\\left(\\mathbf{z}\\right)}\\left[\\left(D\\left(G\\left(\\mathbf{z}\\right)\\right) - c\\right)^{2}\\right] $$\r\n\r\nwhere $a$ and $b$ are the labels for fake data and real data and $c$ denotes the value that $G$ wants $D$ to believe for fake data.","description_state":"present","introduced_year":null,"introduced_by":{"title":"Least Squares Generative Adversarial Networks","paper":"/paper/least-squares-generative-adversarial-networks","first_author":"Xudong Mao","n_authors":6,"url_abs":null,"archive_paper_url":"https://paperswithcode.com/paper/least-squares-generative-adversarial-networks"},"source":{"url":"http://arxiv.org/abs/1611.04076v3","title":"Least Squares Generative Adversarial Networks","url_on_a_paper_host":true},"code_snippet_url":"https://github.com/eriklindernoren/PyTorch-GAN/blob/master/implementations/lsgan/lsgan.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":[]},{"area":"Computer Vision","area_id":"computer-vision","collection":"Generative Models","url":"/methods/category/generative-models","pwc_aliases":[]}],"n_papers_tagged":18,"archive_num_papers":18,"papers_newest_first":[{"paper":null,"title":"Low-light Enhancement Method Based on Attention Map Net","date":"2022-08-19","arxiv_id":"2208.09330","n_code_links":0,"syntology":null},{"paper":"/paper/gm-score-incorporating-inter-class-and-intra","title":"GM Score: Incorporating inter-class and intra-class generator diversity, discriminability of disentangled representation, and sample fidelity for evaluating GANs","date":"2021-12-13","arxiv_id":"2112.06431","n_code_links":1,"syntology":null},{"paper":null,"title":"Generative Adversarial Networks and Adversarial Autoencoders: Tutorial and Survey","date":"2021-11-26","arxiv_id":"2111.13282","n_code_links":0,"syntology":null},{"paper":"/paper/a-closer-look-at-fourier-spectrum","title":"A Closer Look at Fourier Spectrum Discrepancies for CNN-generated Images Detection","date":"2021-03-31","arxiv_id":"2103.17195","n_code_links":1,"syntology":{"ran":0,"of":8,"unverified":8,"pointer_only":0}},{"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":"/paper/priorgan-real-data-prior-for-generative","title":"PriorGAN: Real Data Prior for Generative Adversarial Nets","date":"2020-06-30","arxiv_id":"2006.16990","n_code_links":1,"syntology":null},{"paper":null,"title":"Towards a Neural Graphics Pipeline for Controllable Image Generation","date":"2020-06-18","arxiv_id":"2006.10569","n_code_links":0,"syntology":null},{"paper":"/paper/fastspeech-2-fast-and-high-quality-end-to-end","title":"FastSpeech 2: Fast and High-Quality End-to-End Text to Speech","date":"2020-06-08","arxiv_id":"2006.04558","n_code_links":37,"syntology":{"ran":73,"of":119,"unverified":46,"pointer_only":33}},{"paper":null,"title":"Least $k$th-Order and Rényi Generative Adversarial Networks","date":"2020-06-03","arxiv_id":"2006.02479","n_code_links":0,"syntology":null},{"paper":null,"title":"Identity-Preserving Realistic Talking Face Generation","date":"2020-05-25","arxiv_id":"2005.12318","n_code_links":0,"syntology":null},{"paper":"/paper/a-study-into-echocardiography-view-conversion","title":"A Study into Echocardiography View Conversion","date":"2019-12-05","arxiv_id":"1912.03120","n_code_links":1,"syntology":null},{"paper":"/paper/rankgan-a-maximum-margin-ranking-gan-for","title":"RankGAN: A Maximum Margin Ranking GAN for Generating Faces","date":"2018-12-19","arxiv_id":"1812.08196","n_code_links":1,"syntology":null},{"paper":"/paper/gans-beyond-divergence-minimization","title":"GANs beyond divergence minimization","date":"2018-09-06","arxiv_id":"1809.02145","n_code_links":1,"syntology":null},{"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}},{"paper":null,"title":"Tempered Adversarial Networks","date":"2018-02-12","arxiv_id":"1802.04374","n_code_links":0,"syntology":null},{"paper":"/paper/on-the-effectiveness-of-least-squares","title":"On the Effectiveness of Least Squares Generative Adversarial Networks","date":"2017-12-18","arxiv_id":"1712.06391","n_code_links":3,"syntology":{"ran":1,"of":1,"unverified":0,"pointer_only":1}},{"paper":"/paper/deep-generative-adversarial-networks-for","title":"Deep Generative Adversarial Networks for Compressed Sensing Automates MRI","date":"2017-05-31","arxiv_id":"1706.00051","n_code_links":2,"syntology":null},{"paper":"/paper/least-squares-generative-adversarial-networks","title":"Least Squares Generative Adversarial Networks","date":"2016-11-13","arxiv_id":"1611.04076","n_code_links":24,"syntology":{"ran":5,"of":9,"unverified":4,"pointer_only":0}}],"papers_shown":18,"tasks":[{"task":"/task/face-generation","name":"Face Generation","papers":3},{"task":"/task/image-generation","name":"Image Generation","papers":3},{"task":null,"name":"Generative Adversarial Network","papers":2},{"task":"/task/audio-visual-synchronization","name":"Audio-Visual Synchronization","papers":1},{"task":"/task/diagnostic","name":"Diagnostic","papers":1},{"task":"/task/dimensionality-reduction","name":"Dimensionality Reduction","papers":1},{"task":"/task/diversity","name":"Diversity","papers":1},{"task":"/task/fairness","name":"Fairness","papers":1},{"task":"/task/image-enhancement","name":"Image Enhancement","papers":1},{"task":"/task/image-reconstruction","name":"Image Reconstruction","papers":1},{"task":"/task/image-segmentation","name":"Image Segmentation","papers":1},{"task":"/task/image-to-image-translation","name":"Image-to-Image Translation","papers":1},{"task":"/task/knowledge-distillation","name":"Knowledge Distillation","papers":1},{"task":"/task/low-light-image-enhancement","name":"Low-Light Image Enhancement","papers":1},{"task":"/task/mri-reconstruction","name":"MRI Reconstruction","papers":1},{"task":"/task/neural-rendering","name":"Neural Rendering","papers":1},{"task":"/task/semantic-segmentation","name":"Semantic Segmentation","papers":1},{"task":"/task/speech-synthesis","name":"Speech Synthesis","papers":1},{"task":"/task/survey","name":"Survey","papers":1},{"task":"/task/synthetic-image-detection","name":"Synthetic Image Detection","papers":1}],"tasks_shown":20,"n_tasks":27,"usage_by_year":[{"year":"2016","papers":1},{"year":"2017","papers":2},{"year":"2018","papers":4},{"year":"2019","papers":1},{"year":"2020","papers":5},{"year":"2021","papers":4},{"year":"2022","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/lsgan"},"syntology_read_at":"2026-09-24T18:15:14+00:00"}