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The main result is that the least amount of training data for a bandlimited task signal corresponds to a sampling rate which is larger than the Nyquist rate. Some numerical experiments are carried out to show the comparison between the learning process and the signal recovery, which demonstrates our result. Based on the equivalence between supervised learning and signal recovery, some spectral methods can be used to reveal underlying mechanisms of various supervised learning models, especially those \u201cblack-box\u201d neural networks.<\/jats:p>","DOI":"10.3233\/jifs-211024","type":"journal-article","created":{"date-parts":[[2022,8,26]],"date-time":"2022-08-26T11:11:53Z","timestamp":1661512313000},"page":"4891-4906","source":"Crossref","is-referenced-by-count":1,"title":["On the least amount of training data for a machine learning model"],"prefix":"10.1177","volume":"44","author":[{"given":"Dazhi","family":"Zhao","sequence":"first","affiliation":[{"name":"School of Sciences, Southwest Petroleum University, Chengdu, China"},{"name":"Institute for Artificial Intelligence, Southwest Petroleum University, Chengdu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Yunquan","family":"Hao","sequence":"additional","affiliation":[{"name":"School of Sciences, Southwest Petroleum University, Chengdu, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Weibin","family":"Li","sequence":"additional","affiliation":[{"name":"China Aerodynamics Research and Development Center, Mianyang, China"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Zhe","family":"Tu","sequence":"additional","affiliation":[{"name":"College of Big Data and Software Engineering, Zhejiang Wanli University, Ningbo, China"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-211024_ref2","doi-asserted-by":"crossref","first-page":"436","DOI":"10.1038\/nature14539","article-title":"Deep learning","volume":"521","author":"LeCun","year":"2015","journal-title":"Nature"},{"key":"10.3233\/JIFS-211024_ref4","doi-asserted-by":"crossref","first-page":"484","DOI":"10.1038\/nature16961","article-title":"Mastering the game of go with deep neural networks and tree search","volume":"529","author":"Silver","year":"2016","journal-title":"Nature"},{"issue":"3","key":"10.3233\/JIFS-211024_ref5","doi-asserted-by":"crossref","first-page":"2150071","DOI":"10.1142\/S0218348X21500717","article-title":"Diffusion on Fractal Objects Modeling and its Physics-Informed Neural Network Solution","volume":"29","author":"Zhao","year":"2021","journal-title":"Fractals"},{"issue":"4","key":"10.3233\/JIFS-211024_ref6","doi-asserted-by":"crossref","first-page":"60","DOI":"10.4018\/IJEHMC.20210701.oa4","article-title":"Performance analysis of machine learning algorithms for big data classification: Ml and ai-based algorithms for big data analysis","volume":"12","author":"Punia","year":"2021","journal-title":"International Journal of E-Health and Medical Communications"},{"key":"10.3233\/JIFS-211024_ref7","doi-asserted-by":"crossref","first-page":"82","DOI":"10.1016\/j.neunet.2019.03.013","article-title":"Equivalence between dropout and data augmentation: A mathematical check","volume":"115","author":"Zhao","year":"2019","journal-title":"Neural Networks"},{"key":"10.3233\/JIFS-211024_ref8","doi-asserted-by":"crossref","first-page":"143","DOI":"10.1017\/S0962492900002919","article-title":"Approximation theory of the MLP model in neural networks","volume":"8","author":"Pinkus","year":"1999","journal-title":"Acta numerica"},{"key":"10.3233\/JIFS-211024_ref9","doi-asserted-by":"crossref","unstructured":"Shalev-Shwartz S. , Ben-David S. . 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