{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,7,6]],"date-time":"2026-07-06T15:04:06Z","timestamp":1783350246530,"version":"3.54.6"},"reference-count":47,"publisher":"MDPI AG","issue":"9","license":[{"start":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T00:00:00Z","timestamp":1600646400000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100001809","name":"National Natural Science Foundation of China","doi-asserted-by":"publisher","award":["61772188"],"award-info":[{"award-number":["61772188"]}],"id":[{"id":"10.13039\/501100001809","id-type":"DOI","asserted-by":"publisher"}]},{"name":"National Key R&amp;D Program of China","award":["2018YFC0831800"],"award-info":[{"award-number":["2018YFC0831800"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Generative adversarial networks (GANs), which are a promising type of deep generative network, have recently drawn considerable attention and made impressive progress. However, GAN models suffer from the well-known problem of mode collapse. This study focuses on this challenge and introduces a new model design, called the encoded multi-agent generative adversarial network (E-MGAN), which tackles the mode collapse problem by introducing the variational latent representations learned from a variable auto-encoder (VAE) to a multi-agent GAN. The variational latent representations are extracted from training data to replace the random noise input of the general multi-agent GANs. The generator in E-MGAN employs multiple generators and is penalized by a classifier. This integration guarantees that the proposed model not only enhances the quality of generated samples but also improves the diversity of generated samples to avoid the mode collapse problem. Moreover, extensive experiments are conducted on both a synthetic dataset and two large-scale real-world datasets. The generated samples are visualized for qualitative evaluation. The inception score (IS) and Fr\u00e9chet inception distance (FID) are adopted to measure the performance of the model for quantitative assessment. The results confirmed that the proposed model achieves outstanding performances compared to other state-of-the-art GAN variants.<\/jats:p>","DOI":"10.3390\/e22091055","type":"journal-article","created":{"date-parts":[[2020,9,21]],"date-time":"2020-09-21T21:01:21Z","timestamp":1600722081000},"page":"1055","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":9,"title":["Improving Multi-Agent Generative Adversarial Nets with Variational Latent Representation"],"prefix":"10.3390","volume":"22","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-6286-5868","authenticated-orcid":false,"given":"Huan","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Information Science and Engineering, Hunan University, Changsha 410082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-7433-9945","authenticated-orcid":false,"given":"Tingting","family":"Li","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Hunan University, Changsha 410082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-0199-1681","authenticated-orcid":false,"given":"Yufeng","family":"Xiao","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Hunan University, Changsha 410082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-7780-6593","authenticated-orcid":false,"given":"Yu","family":"Wang","sequence":"additional","affiliation":[{"name":"School of Information Science and Engineering, Hunan University, Changsha 410082, China"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,9,21]]},"reference":[{"key":"ref_1","unstructured":"Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. 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