{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,19]],"date-time":"2026-04-19T19:58:15Z","timestamp":1776628695292,"version":"3.51.2"},"reference-count":34,"publisher":"MDPI AG","issue":"12","license":[{"start":{"date-parts":[[2023,12,13]],"date-time":"2023-12-13T00:00:00Z","timestamp":1702425600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>Generative Adversarial Nets (GANs) are a kind of transformative deep learning framework that has been frequently applied to a large variety of applications related to the processing of images, video, speech, and text. However, GANs still suffer from drawbacks such as mode collapse and training instability. To address these challenges, this paper proposes an Auto-Encoding GAN, which is composed of a set of generators, a discriminator, an encoder, and a decoder. The set of generators is responsible for learning diverse modes, and the discriminator is used to distinguish between real samples and generated ones. The encoder maps generated and real samples to the embedding space to encode distinguishable features, and the decoder determines from which generator the generated samples come and from which mode the real samples come. They are jointly optimized in training to enhance the feature representation. Moreover, a clustering algorithm is employed to perceive the distribution of real and generated samples, and an algorithm for cluster center matching is accordingly constructed to maintain the consistency of the distribution, thus preventing multiple generators from covering a certain mode. Extensive experiments are conducted on two classes of datasets, and the results visually and quantitatively demonstrate the preferable capability of the proposed model for reducing mode collapse and enhancing feature representation.<\/jats:p>","DOI":"10.3390\/e25121657","type":"journal-article","created":{"date-parts":[[2023,12,13]],"date-time":"2023-12-13T12:00:37Z","timestamp":1702468837000},"page":"1657","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":12,"title":["Auto-Encoding Generative Adversarial Networks towards Mode Collapse Reduction and Feature Representation Enhancement"],"prefix":"10.3390","volume":"25","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-3701-3185","authenticated-orcid":false,"given":"Yang","family":"Zou","sequence":"first","affiliation":[{"name":"Institute of Intelligence Science and Technology, School of Computer and Information, Hohai University, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yuxuan","family":"Wang","sequence":"additional","affiliation":[{"name":"Institute of Intelligence Science and Technology, School of Computer and Information, Hohai University, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Xiaoxiang","family":"Lu","sequence":"additional","affiliation":[{"name":"Institute of Intelligence Science and Technology, School of Computer and Information, Hohai University, Nanjing 211100, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2023,12,13]]},"reference":[{"key":"ref_1","unstructured":"Goodfellow, I., Pouget-Abadie, J., Mirza, M., Xu, B., Warde-Farley, D., Ozair, S., Courville, A., and Bengio, Y. (2014, January 8\u201313). Generative adversarial nets. Proceedings of the 27th International Conference on Neural Information Processing Systems (NIPS 2014), Montreal, QC, Canada."},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"139","DOI":"10.1145\/3422622","article-title":"Generative adversarial networks","volume":"63","author":"Goodfellow","year":"2020","journal-title":"Commun. ACM"},{"key":"ref_3","doi-asserted-by":"crossref","unstructured":"Zhu, J.Y., Park, T., Isola, P., and Efros, A.A. (2017, January 22\u201329). Unpaired image-to-image translation using cycle-consistent adversarial networks. Proceedings of the IEEE International Conference on Computer Vision (ICCV 2017), Venice, Italy.","DOI":"10.1109\/ICCV.2017.244"},{"key":"ref_4","doi-asserted-by":"crossref","unstructured":"Zhang, H., Xu, T., Li, H., Zhang, S., Wang, X., Huang, X., and Metaxas, D.N. (2017, January 22\u201329). Stackgan: Text to photo-realistic image synthesis with stacked generative adversarial networks. Proceedings of the IEEE International Conference on Computer Vision (ICCV 2017), Venice, Italy.","DOI":"10.1109\/ICCV.2017.629"},{"key":"ref_5","doi-asserted-by":"crossref","unstructured":"Karras, T., Laine, S., and Aila, T. (2019, January 15\u201320). A style-based generator architecture for generative adversarial networks. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR 2019), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00453"},{"key":"ref_6","doi-asserted-by":"crossref","unstructured":"Pathak, D., Krahenbuhl, P., Donahue, J., Darrell, T., and Efros, A.A. (2016, January 27\u201330). Context encoders: Feature learning by inpainting. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2016), Las Vegas, NV, USA.","DOI":"10.1109\/CVPR.2016.278"},{"key":"ref_7","doi-asserted-by":"crossref","unstructured":"Ledig, C., Theis, L., Husz\u00e1r, F., Caballero, J., Cunningham, A., Acosta, A., and Shi, W. (2017, January 21\u201326). Photo-realistic single image super-resolution using a generative adversarial network. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2017), Honolulu, HI, USA.","DOI":"10.1109\/CVPR.2017.19"},{"key":"ref_8","doi-asserted-by":"crossref","unstructured":"Wang, Y., Bilinski, P., Bremond, F., and Dantcheva, A. (2020, January 1\u20135). Imaginator: Conditional spatio-temporal gan for video generation. Proceedings of the IEEE Winter Conference on Applications of Computer Vision (WACV 2020), Snowmass, CO, USA.","DOI":"10.1109\/WACV45572.2020.9093492"},{"key":"ref_9","unstructured":"Xie, Q., Dai, Z., Hovy, E., Luong, T., and Le, Q. (2020, January 6\u201312). Unsupervised data augmentation for consistency training. Proceedings of the 34th International Conference on Neural Information Processing Systems (NIPS 2020), Vancouver, BC, Canada."},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"669","DOI":"10.1109\/TAI.2021.3115992","article-title":"A review of text style transfer using deep learning","volume":"3","author":"Toshevska","year":"2022","journal-title":"IEEE Trans. Artif. Intell."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"110585","DOI":"10.1016\/j.knosys.2023.110585","article-title":"M3gan: A masking strategy with a mutable filter for multidimensional anomaly detection","volume":"271","author":"Li","year":"2023","journal-title":"Knowl. Based Syst."},{"key":"ref_12","unstructured":"Arjovsky, M., and Bottou, L. (2017, January 24\u201326). Towards principled methods for training generative adversarial networks. Proceedings of the 5th International Conference on Learning Representations (ICLR 2017), Toulon, France."},{"key":"ref_13","unstructured":"Mescheder, L., Nowozin, S., and Geiger, A. (2017, January 4\u20139). The numerics of gans. Proceedings of the 31st Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA."},{"key":"ref_14","unstructured":"Mirza, M., and Osindero, S. (2014). Conditional generative adversarial nets. arXiv."},{"key":"ref_15","unstructured":"Chen, X., Duan, Y., and Houthooft, R. (2016, January 5\u201310). InfoGAN: Interpretable representation learning by information maximizing generative adversarial nets. Proceedings of the 30th International Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain."},{"key":"ref_16","doi-asserted-by":"crossref","unstructured":"Ghosh, A., Kulharia, V., Namboodiri, V., Namboodiri, V.P., Torr, P.H., and Dokania, P.K. (2018, January 18\u201323). Multi-agent diverse generative adversarial networks. Proceedings of the IEEE Conference on Computer Vision and Pattern Recognition (CVPR 2018), Salt Lake City, UT, USA.","DOI":"10.1109\/CVPR.2018.00888"},{"key":"ref_17","unstructured":"Hoang, Q., Nguyen, T.D., Le, T., and Phung, D. (May, January 30). MGAN: Training generative adversarial nets with multiple generators. Proceedings of the 6th International Conference on Learning Representations (ICLR 2018), Vancouver, BC, Canada."},{"key":"ref_18","unstructured":"Arjovsky, M., Chintala, S., and Bottou, L. (2017, January 6\u201311). Wasserstein generative adversarial networks. Proceedings of the 34th International Conference on Machine Learning (ICML 2017), Sydney, Australia."},{"key":"ref_19","unstructured":"Gulrajani, I., Ahmed, F., Arjovsky, M., Dumoulin, V., and Courville, A.C. (2017, January 4\u20139). Improved training of wasserstein GANs. Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA."},{"key":"ref_20","unstructured":"Radford, A., Metz, L., and Chintala, S. (2016, January 2\u20134). Unsupervised representation learning with deep convolutional generative adversarial networks. Proceedings of the 4th International Conference on Learning Representations (ICLR 2016), San Juan, Puerto Rico."},{"key":"ref_21","unstructured":"Salimans, T., Goodfellow, I., Zaremba, W., Cheung, V., Radford, A., and Chen, X. (2016, January 5\u201310). Improved techniques for training gans. Proceedings of the 30th International Conference on Neural Information Processing Systems (NIPS 2016), Barcelona, Spain."},{"key":"ref_22","unstructured":"Zhao, J., Mathieu, M., and LeCun, Y. (2017, January 24\u201326). Energy-based generative adversarial network. Proceedings of the 5th International Conference on Learning Representations (ICLR 2017), Toulon, France."},{"key":"ref_23","unstructured":"Berthelot, D., Schumm, T., and Metz, L. (2017). Began: Boundary equilibrium generative adversarial networks. arXiv."},{"key":"ref_24","unstructured":"Metz, L., Poole, B., Pfau, D., and Sohl-Dickstein, J. (2017, January 24\u201326). Unrolled generative adversarial networks. Proceedings of the 5th International Conference on Learning Representations (ICLR 2017), Toulon, France."},{"key":"ref_25","doi-asserted-by":"crossref","unstructured":"Eghbal-Zadeh, H., Zellinger, W., and Widmer, G. (2019, January 15\u201320). Mixture density generative adversarial networks. Proceedings of the IEEE\/CVF Conference on Computer Vision and Pattern Recognition (CVPR 2019), Long Beach, CA, USA.","DOI":"10.1109\/CVPR.2019.00597"},{"key":"ref_26","unstructured":"Srivastava, A., Valkoz, L., Russell, C., Gutmann, M.U., and Sutton, C. (2017, January 4\u20139). VEEGAN: Reducing mode collapse in gans using implicit variational learning. Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA."},{"key":"ref_27","unstructured":"Saatchi, Y., and Wilson, A.G. (2017, January 4\u20139). Bayesian GAN. Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA."},{"key":"ref_28","unstructured":"Durugkar, I., Gemp, I., and Mahadevan, S. (2017, January 24\u201326). Generative multi-adversarial networks. Proceedings of the 5th International Conference on Learning Representations (ICLR 2017), Toulon, France."},{"key":"ref_29","unstructured":"Guo, Y., An, D., and Qi, X. (2019). Mode collapse and regularity of optimal transportation maps. arXiv."},{"key":"ref_30","doi-asserted-by":"crossref","first-page":"2278","DOI":"10.1109\/5.726791","article-title":"Gradient-based learning applied to document recognition","volume":"86","author":"Lecun","year":"1998","journal-title":"Proc. IEEE"},{"key":"ref_31","unstructured":"Xiao, H., Rasul, K., and Vollgraf, R. (2017). Fashion-mnist: A novel image dataset for benchmarking machine learning algorithms. arXiv."},{"key":"ref_32","unstructured":"Nene, S.A., Nayar, S.K., and Murase, H. (2023, December 11). Columbia Object Image Library (Coil-20). Technical Report. CUCS-005-96. Available online: https:\/\/www.cs.columbia.edu\/CAVE\/software\/softlib\/coil-20.php."},{"key":"ref_33","unstructured":"Krizhevsky, A. (2023, December 11). Learning Multiple Layers of Features from Tiny Images. Available online: https:\/\/api.semanticscholar.org\/CorpusID:18268744."},{"key":"ref_34","unstructured":"Heusel, M., Ramsauer, H., Unterthiner, T., Nessler, B., and Hochreiter, S. (2017, January 4\u20139). Gans trained by a two time-scale update rule converge to a local nash equilibrium. Proceedings of the 31st International Conference on Neural Information Processing Systems (NIPS 2017), Long Beach, CA, USA."}],"container-title":["Entropy"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/12\/1657\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T21:38:17Z","timestamp":1760132297000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/1099-4300\/25\/12\/1657"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,12,13]]},"references-count":34,"journal-issue":{"issue":"12","published-online":{"date-parts":[[2023,12]]}},"alternative-id":["e25121657"],"URL":"https:\/\/doi.org\/10.3390\/e25121657","relation":{},"ISSN":["1099-4300"],"issn-type":[{"value":"1099-4300","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,12,13]]}}}