{"status":"public","quality_controlled":"1","title":"Fundamental limits of two-layer autoencoders, and achieving them with gradient methods","alternative_title":["PMLR"],"date_created":"2023-10-29T23:01:17Z","user_id":"2DF688A6-F248-11E8-B48F-1D18A9856A87","oa_version":"Preprint","oa":1,"scopus_import":"1","publisher":"ML Research Press","publication_status":"published","date_published":"2023-07-30T00:00:00Z","abstract":[{"text":"Autoencoders are a popular model in many branches of machine learning and lossy data compression. However, their fundamental limits, the performance of gradient methods and the features learnt during optimization remain poorly understood, even in the two-layer setting. In fact, earlier work has considered either linear autoencoders or specific training regimes (leading to vanishing or diverging compression rates). Our paper addresses this gap by focusing on non-linear two-layer autoencoders trained in the challenging proportional regime in which the input dimension scales linearly with the size of the representation. Our results characterize the minimizers of the population risk, and show that such minimizers are achieved by gradient methods; their structure is also unveiled, thus leading to a concise description of the features obtained via training. For the special case of a sign activation function, our analysis establishes the fundamental limits for the lossy compression of Gaussian sources via (shallow) autoencoders. Finally, while the results are proved for Gaussian data, numerical simulations on standard datasets display the universality of the theoretical predictions.","lang":"eng"}],"main_file_link":[{"open_access":"1","url":"https://doi.org/10.48550/arXiv.2212.13468"}],"department":[{"_id":"MaMo"},{"_id":"DaAl"}],"day":"30","type":"conference","date_updated":"2024-09-10T13:03:19Z","month":"07","article_processing_charge":"No","acknowledgement":"Aleksandr Shevchenko, Kevin Kogler and Marco Mondelli are supported by the 2019 Lopez-Loreta Prize. Hamed Hassani acknowledges the support by the NSF CIF award (1910056) and the NSF Institute for CORE Emerging Methods in Data Science (EnCORE).","project":[{"_id":"059876FA-7A3F-11EA-A408-12923DDC885E","name":"Prix Lopez-Loretta 2019 - Marco Mondelli"}],"volume":202,"intvolume":"       202","year":"2023","citation":{"short":"A. Shevchenko, K. Kögler, H. Hassani, M. Mondelli, in:, Proceedings of the 40th International Conference on Machine Learning, ML Research Press, 2023, pp. 31151–31209.","ista":"Shevchenko A, Kögler K, Hassani H, Mondelli M. 2023. Fundamental limits of two-layer autoencoders, and achieving them with gradient methods. Proceedings of the 40th International Conference on Machine Learning. ICML: International Conference on Machine Learning, PMLR, vol. 202, 31151–31209.","chicago":"Shevchenko, Aleksandr, Kevin Kögler, Hamed Hassani, and Marco Mondelli. “Fundamental Limits of Two-Layer Autoencoders, and Achieving Them with Gradient Methods.” In <i>Proceedings of the 40th International Conference on Machine Learning</i>, 202:31151–209. ML Research Press, 2023.","apa":"Shevchenko, A., Kögler, K., Hassani, H., &#38; Mondelli, M. (2023). Fundamental limits of two-layer autoencoders, and achieving them with gradient methods. In <i>Proceedings of the 40th International Conference on Machine Learning</i> (Vol. 202, pp. 31151–31209). Honolulu, Hawaii, HI, United States: ML Research Press.","ama":"Shevchenko A, Kögler K, Hassani H, Mondelli M. Fundamental limits of two-layer autoencoders, and achieving them with gradient methods. In: <i>Proceedings of the 40th International Conference on Machine Learning</i>. Vol 202. ML Research Press; 2023:31151-31209.","ieee":"A. Shevchenko, K. Kögler, H. Hassani, and M. Mondelli, “Fundamental limits of two-layer autoencoders, and achieving them with gradient methods,” in <i>Proceedings of the 40th International Conference on Machine Learning</i>, Honolulu, Hawaii, HI, United States, 2023, vol. 202, pp. 31151–31209.","mla":"Shevchenko, Aleksandr, et al. “Fundamental Limits of Two-Layer Autoencoders, and Achieving Them with Gradient Methods.” <i>Proceedings of the 40th International Conference on Machine Learning</i>, vol. 202, ML Research Press, 2023, pp. 31151–209."},"conference":{"name":"ICML: International Conference on Machine Learning","start_date":"2023-07-23","location":"Honolulu, Hawaii, HI, United States","end_date":"2023-07-29"},"_id":"14459","language":[{"iso":"eng"}],"author":[{"id":"F2B06EC2-C99E-11E9-89F0-752EE6697425","full_name":"Shevchenko, Aleksandr","first_name":"Aleksandr","last_name":"Shevchenko"},{"last_name":"Kögler","first_name":"Kevin","id":"94ec913c-dc85-11ea-9058-e5051ab2428b","full_name":"Kögler, Kevin"},{"first_name":"Hamed","last_name":"Hassani","full_name":"Hassani, Hamed"},{"id":"27EB676C-8706-11E9-9510-7717E6697425","full_name":"Mondelli, Marco","last_name":"Mondelli","first_name":"Marco","orcid":"0000-0002-3242-7020"}],"publication":"Proceedings of the 40th International Conference on Machine Learning","page":"31151-31209","publication_identifier":{"eissn":["2640-3498"]},"external_id":{"arxiv":["2212.13468"]}}