{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T10:53:35Z","timestamp":1782125615753,"version":"3.54.5"},"reference-count":59,"publisher":"Elsevier BV","license":[{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/tdm\/userlicense\/1.0\/"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/www.elsevier.com\/legal\/tdmrep-license"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-017"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-037"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-012"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-029"},{"start":{"date-parts":[[2026,10,1]],"date-time":"2026-10-01T00:00:00Z","timestamp":1790812800000},"content-version":"stm-asf","delay-in-days":0,"URL":"https:\/\/doi.org\/10.15223\/policy-004"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":["elsevier.com","sciencedirect.com"],"crossmark-restriction":true},"short-container-title":["Applied Soft Computing"],"published-print":{"date-parts":[[2026,10]]},"DOI":"10.1016\/j.asoc.2026.115769","type":"journal-article","created":{"date-parts":[[2026,6,16]],"date-time":"2026-06-16T23:22:09Z","timestamp":1781652129000},"page":"115769","update-policy":"https:\/\/doi.org\/10.1016\/elsevier_cm_policy","source":"Crossref","is-referenced-by-count":0,"special_numbering":"PA","title":["GNS-GAN: A novel GAN model based on gradient noise suppression"],"prefix":"10.1016","volume":"202","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-5486-5128","authenticated-orcid":false,"given":"Hongyou","family":"Chen","sequence":"first","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-2544-4324","authenticated-orcid":false,"given":"Lingfeng","family":"Qu","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-1109-958X","authenticated-orcid":false,"given":"Baodan","family":"Tian","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yutong","family":"He","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Yong","family":"Fan","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-9853-1720","authenticated-orcid":false,"given":"Hadi","family":"Amirpour","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0031-5243","authenticated-orcid":false,"given":"Christian","family":"Timmerer","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-6495-081X","authenticated-orcid":false,"given":"Yao","family":"Xin","sequence":"additional","affiliation":[],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"78","reference":[{"issue":"7995","key":"10.1016\/j.asoc.2026.115769_bib0005","doi-asserted-by":"crossref","first-page":"476","DOI":"10.1038\/s41586-023-06747-5","article-title":"Solving olympiad geometry without human demonstrations","volume":"625","author":"Trinh","year":"2024","journal-title":"Nature"},{"key":"10.1016\/j.asoc.2026.115769_bib0010","first-page":"2672","article-title":"Generative adversarial nets","author":"Goodfellow","year":"2014","journal-title":"Adv. Neural Inf. Process. Syst. (neurips)"},{"issue":"8","key":"10.1016\/j.asoc.2026.115769_bib0015","doi-asserted-by":"crossref","first-page":"1","DOI":"10.1145\/3463475","article-title":"A survey on generative adversarial networks: variants, applications, and training","volume":"54","author":"Jabbar","year":"2021","journal-title":"ACM Comput. Surv."},{"key":"10.1016\/j.asoc.2026.115769_bib0020","series-title":"IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","first-page":"24142","article-title":"Generative image dynamics","author":"Li","year":"2024"},{"issue":"4","key":"10.1016\/j.asoc.2026.115769_bib0025","doi-asserted-by":"crossref","first-page":"3313","DOI":"10.1109\/TKDE.2021.3130191","article-title":"A review on generative adversarial networks: algorithms, theory, and applications","volume":"35","author":"Gui","year":"2021","journal-title":"IEEE Trans. Knowl. Data Eng."},{"key":"10.1016\/j.asoc.2026.115769_bib0030","series-title":"International Conference on Learning Representations (ICLR)","article-title":"Unsupervised representation learning with deep convolutional generative adversarial networks","author":"Radford","year":"2016"},{"key":"10.1016\/j.asoc.2026.115769_bib0035","first-page":"2670","article-title":"Dual discriminator generative adversarial nets","author":"Nguyen","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst. (neurips)"},{"key":"10.1016\/j.asoc.2026.115769_bib0040","series-title":"IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","first-page":"16219","article-title":"AdaptiveMix: improving GAN training via feature space shrinkage","author":"Liu","year":"2023"},{"key":"10.1016\/j.asoc.2026.115769_bib0045","series-title":"IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","first-page":"4401","article-title":"A style-based generator architecture for generative adversarial networks","author":"Karras","year":"2019"},{"key":"10.1016\/j.asoc.2026.115769_bib0050","first-page":"14745","article-title":"TransGAN: two pure transformers can make one strong GAN, and that can scale up","author":"Jiang","year":"2021","journal-title":"Adv. Neural Inf. Process. Syst. (neurips)"},{"key":"10.1016\/j.asoc.2026.115769_bib0055","series-title":"International Conference on Machine Learning (ICML)","first-page":"214","article-title":"Wasserstein generative adversarial networks","author":"Arjovsky","year":"2017"},{"key":"10.1016\/j.asoc.2026.115769_bib0060","doi-asserted-by":"crossref","first-page":"415","DOI":"10.1016\/j.knosys.2018.08.004","article-title":"LP-WGAN: using LP-norm normalization to stabilize Wasserstein generative adversarial networks","volume":"161","author":"Zhou","year":"2018","journal-title":"Knowl.-based Syst."},{"key":"10.1016\/j.asoc.2026.115769_bib0065","first-page":"5767","article-title":"Improved training of Wasserstein GANs","author":"Gulrajani","year":"2017","journal-title":"Adv. Neural Inf. Process. Syst. (neurips)"},{"key":"10.1016\/j.asoc.2026.115769_bib0070","author":"Berthelot"},{"key":"10.1016\/j.asoc.2026.115769_bib0075","series-title":"European Conference on Computer Vision (ECCV)","first-page":"673","article-title":"Wasserstein divergence for GANs","author":"Wu","year":"2018"},{"key":"10.1016\/j.asoc.2026.115769_bib0080","series-title":"IEEE International Conference on Computer Vision (ICCV)","first-page":"2813","article-title":"Least squares generative adversarial networks","author":"Mao","year":"2017"},{"key":"10.1016\/j.asoc.2026.115769_bib0085","author":"Lim"},{"key":"10.1016\/j.asoc.2026.115769_bib0090","series-title":"International Conference on Learning Representations (ICLR)","article-title":"Spectral normalization for generative adversarial networks","author":"Miyato","year":"2018"},{"key":"10.1016\/j.asoc.2026.115769_bib0095","series-title":"International Conference on Learning Representations (ICLR)","article-title":"Real or not real, that is the question","author":"Xiangli","year":"2020"},{"key":"10.1016\/j.asoc.2026.115769_bib0100","doi-asserted-by":"crossref","first-page":"177","DOI":"10.1016\/j.ins.2022.01.073","article-title":"\u03b1\u03b2-GAN: robust generative adversarial networks","volume":"593","author":"Gnanha","year":"2022","journal-title":"Inf. Sci."},{"issue":"11","key":"10.1016\/j.asoc.2026.115769_bib0105","doi-asserted-by":"crossref","DOI":"10.1142\/S0218001421520182","article-title":"SSC-GAN: a novel GAN based on the same solution constraints of first-order ODES","volume":"35","author":"Chen","year":"2021","journal-title":"Int. J. Pattern Recognit. Artif. Intell."},{"key":"10.1016\/j.asoc.2026.115769_bib0110","series-title":"International Conference on Artificial Intelligence and Security (ICAIS)","first-page":"14","article-title":"Multi-penalty functions GANs via multi-task learning","author":"Chen","year":"2021"},{"issue":"110086","key":"10.1016\/j.asoc.2026.115769_bib0115","article-title":"Training generative adversarial networks by auxiliary adversarial example regulator","volume":"136","author":"Gan","year":"2023","journal-title":"Appl. Soft Comput."},{"key":"10.1016\/j.asoc.2026.115769_bib0120","doi-asserted-by":"crossref","first-page":"44177","DOI":"10.52202\/079017-1402","article-title":"Generative adversarial nets: a modern baseline","author":"Huang","year":"2024","journal-title":"Adv. Neural Inf. Process. Syst. (neurips)"},{"key":"10.1016\/j.asoc.2026.115769_bib0125","author":"Su"},{"key":"10.1016\/j.asoc.2026.115769_bib0130","series-title":"International Conference on Learning Representations (ICLR)","article-title":"Variational discriminator bottleneck: improving imitation learning, inverse RL, and GANs by constraining information flow","author":"Peng","year":"2019"},{"key":"10.1016\/j.asoc.2026.115769_bib0135","series-title":"International Conference on Learning Representations (ICLR)","article-title":"The relativistic discriminator: a key element missing from standard GAN","author":"Jolicoeur-Martineau","year":"2019"},{"issue":"1","key":"10.1016\/j.asoc.2026.115769_bib0140","doi-asserted-by":"crossref","DOI":"10.1142\/S0218001422520012","article-title":"Antinoise learning and coalitional game GAN","volume":"36","author":"Chen","year":"2022","journal-title":"Int. J. Pattern Recognit. Artif. Intell."},{"key":"10.1016\/j.asoc.2026.115769_bib0145","series-title":"International Conference on Machine Learning (ICML)","first-page":"7354","article-title":"Self-attention generative adversarial networks","author":"Zhang","year":"2019"},{"key":"10.1016\/j.asoc.2026.115769_bib0150","first-page":"5599","article-title":"Training generative adversarial networks by solving ordinary differential equations","author":"Qin","year":"2020","journal-title":"Adv. Neural Inf. Process. Syst. (neurips)"},{"key":"10.1016\/j.asoc.2026.115769_bib0155","series-title":"International Joint Conference on Neural Networks (IJCNN)","first-page":"1","article-title":"A Gauss-Newton approach for min-max optimization in generative adversarial networks","author":"Mishra","year":"2024"},{"key":"10.1016\/j.asoc.2026.115769_bib0160","series-title":"IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","first-page":"7796","article-title":"MSG-GAN: multi-scale gradients for generative adversarial networks","author":"Karnewar","year":"2020"},{"key":"10.1016\/j.asoc.2026.115769_bib0165","author":"Xiong"},{"key":"10.1016\/j.asoc.2026.115769_bib0170","series-title":"In International Conference on Learning Representations (ICLR)","article-title":"Diffusion-GAN: training GANs with diffusion","author":"Wang","year":"2023"},{"key":"10.1016\/j.asoc.2026.115769_bib0175","author":"Xia"},{"key":"10.1016\/j.asoc.2026.115769_bib0180","series-title":"International Conference on Machine Learning (ICML)","first-page":"23140","article-title":"Stabilizing GANs\u2019 training with brownian motion controller","author":"Luo","year":"2023"},{"key":"10.1016\/j.asoc.2026.115769_bib0185","series-title":"IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","first-page":"2233","article-title":"Making deep neural networks robust to label noise: a loss correction approach","author":"Patrini","year":"2017"},{"key":"10.1016\/j.asoc.2026.115769_bib0190","series-title":"AAAI Conference on Artificial Intelligence (AAAI)","first-page":"1919","article-title":"Robust loss functions under label noise for deep neural networks","author":"Ghosh","year":"2017"},{"key":"10.1016\/j.asoc.2026.115769_bib0195","series-title":"International Conference on Machine Learning (ICML)","first-page":"3361","article-title":"Dimensionality-driven learning with noisy labels","author":"Ma","year":"2018"},{"issue":"11","key":"10.1016\/j.asoc.2026.115769_bib0200","doi-asserted-by":"crossref","first-page":"8135","DOI":"10.1109\/TNNLS.2022.3152527","article-title":"Learning from noisy labels with deep neural networks: a survey","volume":"34","author":"Song","year":"2022","journal-title":"IEEE Trans. Neural Netw. Learn. Syst."},{"key":"10.1016\/j.asoc.2026.115769_bib0205","series-title":"International Conference on Machine Learning (ICML)","first-page":"5827","article-title":"A tail-index analysis of stochastic gradient noise in deep neural networks","author":"Simsekli","year":"2019"},{"key":"10.1016\/j.asoc.2026.115769_bib0210","first-page":"273","article-title":"First exit time analysis of stochastic gradient descent under heavy-tailed gradient noise","author":"Nguyen","year":"2019","journal-title":"Adv. Neural Inf. Process. Syst. (neurips)"},{"key":"10.1016\/j.asoc.2026.115769_bib0215","series-title":"International Conference on Machine Learning (ICML)","first-page":"8970","article-title":"Fractional underdamped langevin dynamics: retargeting SGD with momentum under heavy-tailed gradient noise","author":"Simsekli","year":"2020"},{"key":"10.1016\/j.asoc.2026.115769_bib0220","series-title":"International Conference on Machine Learning (ICML)","first-page":"28578","article-title":"Algorithmic stability of heavy-tailed SGD with general loss functions","author":"Raj","year":"2023"},{"key":"10.1016\/j.asoc.2026.115769_bib0225","author":"Wu"},{"issue":"2017","key":"10.1016\/j.asoc.2026.115769_bib0230","first-page":"1","article-title":"Stochastic gradient descent as approximate Bayesian inference","volume":"18","author":"Mandt","year":"2017","journal-title":"J. Mach. Learn. Res."},{"key":"10.1016\/j.asoc.2026.115769_bib0235","author":"Jastrzebski"},{"key":"10.1016\/j.asoc.2026.115769_bib0240","series-title":"IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","first-page":"770","article-title":"Deep residual learning for image recognition","author":"He","year":"2016"},{"key":"10.1016\/j.asoc.2026.115769_bib0245","series-title":"International Conference on Machine Learning (ICML)","first-page":"9276","article-title":"Momentum residual neural networks","author":"Sander","year":"2021"},{"key":"10.1016\/j.asoc.2026.115769_bib0250","series-title":"International Conference on Machine Learning (ICML)","first-page":"3276","article-title":"Beyond finite layer neural networks: bridging deep architectures and numerical differential equations","author":"Lu","year":"2018"},{"key":"10.1016\/j.asoc.2026.115769_bib0255","series-title":"International Conference on Learning Representations (ICLR)","article-title":"FractalNet: ultra-deep neural networks without residuals","author":"Larsson","year":"2017"},{"key":"10.1016\/j.asoc.2026.115769_bib0260","first-page":"6572","article-title":"Neural ordinary differential equations","author":"Chen","year":"2018","journal-title":"Adv. Neural Inf. Process. Syst. (neurips)"},{"key":"10.1016\/j.asoc.2026.115769_bib0265","series-title":"IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR)","first-page":"3900","article-title":"PolyNet: a pursuit of structural diversity in very deep networks","author":"Zhang","year":"2017"},{"key":"10.1016\/j.asoc.2026.115769_bib0270","series-title":"Probability and Statistics","author":"Chen","year":"2017"},{"key":"10.1016\/j.asoc.2026.115769_bib0275","series-title":"An Introduction to Stochastic Differential Equations","author":"Evans","year":"2021"},{"issue":"5","key":"10.1016\/j.asoc.2026.115769_bib0280","doi-asserted-by":"crossref","first-page":"810","DOI":"10.1214\/aop\/1176996847","article-title":"Limiting behavior of weighted sums of independent random variables","volume":"1","author":"Chow","year":"1973","journal-title":"Ann. Probab."},{"key":"10.1016\/j.asoc.2026.115769_bib0285","series-title":"European Conference on Computer Vision (ECCV)","first-page":"218","article-title":"How good is my GAN?","author":"Shmelkov","year":"2018"},{"key":"10.1016\/j.asoc.2026.115769_bib0290","author":"Xu"},{"issue":"2021","key":"10.1016\/j.asoc.2026.115769_bib0295","doi-asserted-by":"crossref","first-page":"2587","DOI":"10.1109\/TIP.2020.3048632","article-title":"SFace: sigmoid-constrained hypersphere loss for robust face recognition","volume":"30","author":"Zhong","year":"2021","journal-title":"IEEE Trans. Image Process."}],"container-title":["Applied Soft Computing"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1568494626012172?httpAccept=text\/xml","content-type":"text\/xml","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/api.elsevier.com\/content\/article\/PII:S1568494626012172?httpAccept=text\/plain","content-type":"text\/plain","content-version":"vor","intended-application":"text-mining"}],"deposited":{"date-parts":[[2026,6,22]],"date-time":"2026-06-22T10:35:07Z","timestamp":1782124507000},"score":1,"resource":{"primary":{"URL":"https:\/\/linkinghub.elsevier.com\/retrieve\/pii\/S1568494626012172"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2026,10]]},"references-count":59,"alternative-id":["S1568494626012172"],"URL":"https:\/\/doi.org\/10.1016\/j.asoc.2026.115769","relation":{},"ISSN":["1568-4946"],"issn-type":[{"value":"1568-4946","type":"print"}],"subject":[],"published":{"date-parts":[[2026,10]]},"assertion":[{"value":"Elsevier","name":"publisher","label":"This article is maintained by"},{"value":"GNS-GAN: A novel GAN model based on gradient noise suppression","name":"articletitle","label":"Article Title"},{"value":"Applied Soft Computing","name":"journaltitle","label":"Journal Title"},{"value":"https:\/\/doi.org\/10.1016\/j.asoc.2026.115769","name":"articlelink","label":"CrossRef DOI link to publisher maintained version"},{"value":"article","name":"content_type","label":"Content Type"},{"value":"\u00a9 2026 Elsevier B.V. All rights are reserved, including those for text and data mining, AI training, and similar technologies.","name":"copyright","label":"Copyright"}],"article-number":"115769"}}