{"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/on-the-effectiveness-of-least-squares","title":"On the Effectiveness of Least Squares Generative Adversarial Networks","arxiv_id":"1712.06391","date":"2017-12-18","proceeding":null,"authors":["Xudong Mao","Qing Li","Haoran Xie","Raymond Y. K. Lau","Zhen Wang","Stephen Paul Smolley"],"abstract":"Unsupervised learning with generative adversarial networks (GANs) has proven\nto be hugely successful. Regular GANs hypothesize the discriminator as a\nclassifier with the sigmoid cross entropy loss function. However, we found that\nthis loss function may lead to the vanishing gradients problem during the\nlearning process. To overcome such a problem, we propose in this paper the\nLeast Squares Generative Adversarial Networks (LSGANs) which adopt the least\nsquares loss for both the discriminator and the generator. We show that\nminimizing the objective function of LSGAN yields minimizing the Pearson\n$\\chi^2$ divergence. We also show that the derived objective function that\nyields minimizing the Pearson $\\chi^2$ divergence performs better than the\nclassical one of using least squares for classification. There are two benefits\nof LSGANs over regular GANs. First, LSGANs are able to generate higher quality\nimages than regular GANs. Second, LSGANs perform more stably during the\nlearning process. For evaluating the image quality, we conduct both qualitative\nand quantitative experiments, and the experimental results show that LSGANs can\ngenerate higher quality images than regular GANs. Furthermore, we evaluate the\nstability of LSGANs in two groups. One is to compare between LSGANs and regular\nGANs without gradient penalty. We conduct three experiments, including Gaussian\nmixture distribution, difficult architectures, and a newly proposed method ---\ndatasets with small variability, to illustrate the stability of LSGANs. The\nother one is to compare between LSGANs with gradient penalty (LSGANs-GP) and\nWGANs with gradient penalty (WGANs-GP). The experimental results show that\nLSGANs-GP succeed in training for all the difficult architectures used in\nWGANs-GP, including 101-layer ResNet.","url_abs":"http://arxiv.org/abs/1712.06391v2","url_pdf":"http://arxiv.org/pdf/1712.06391v2.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":"on-the-effectiveness-of-least-squares","repo_url":"https://github.com/xudonmao/LSGAN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":{"status":"unanswered"}},{"paper_slug":"on-the-effectiveness-of-least-squares","repo_url":"https://github.com/xudonmao/improved_LSGAN","is_official":1,"mentioned_in_paper":1,"mentioned_in_github":1,"framework":"tf","reach":null},{"paper_slug":"on-the-effectiveness-of-least-squares","repo_url":"https://github.com/MindSpore-scientific/code-10/tree/main/Least_Generative","is_official":0,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"mindspore","reach":null}],"tasks":[],"methods":[{"method_slug":"1x1-convolution","method_name":"1x1 Convolution"},{"method_slug":"average-pooling","method_name":"Average Pooling"},{"method_slug":"batch-normalization","method_name":"Batch Normalization"},{"method_slug":"bottleneck-residual-block","method_name":"Bottleneck Residual Block"},{"method_slug":"convolution","method_name":"Convolution"},{"method_slug":"dense-connections","method_name":"Dense Connections"},{"method_slug":"gan-least-squares-loss","method_name":"GAN Least Squares Loss"},{"method_slug":"global-average-pooling","method_name":"Global Average Pooling"},{"method_slug":"kaiming-initialization","method_name":"Kaiming Initialization"},{"method_slug":"lsgan","method_name":"LSGAN"},{"method_slug":"max-pooling","method_name":"Max Pooling"},{"method_slug":"relu","method_name":"ReLU"},{"method_slug":"residual-block","method_name":"Residual Block"},{"method_slug":"residual-connection","method_name":"Residual Connection"}],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"syntology_url":"https://syntology.ai/paper/1712.06391","atlas_url":"https://app.syntology.ai/?focus=1712.06391","mcp":{"get_harvested_code_for_paper":{"arxiv_id":"1712.06391"}},"developers":"https://syntology.ai/developers","read_at":"2026-09-25T09:33:49+00:00","read_at_is":"when the build read Syntology's graph, not when any sample ran","claim":"Per-sample execution status on synthesized fixtures; not a correctness claim about the paper. 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