{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,2]],"date-time":"2026-05-02T06:56:02Z","timestamp":1777704962073,"version":"3.51.4"},"reference-count":1,"publisher":"SAGE Publications","issue":"6","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IFS"],"published-print":{"date-parts":[[2022,11,11]]},"abstract":"<jats:p>Neural networks \u2013 specifically, deep neural networks \u2013 are, at present, the most effective machine learning techniques. There are reasonable explanations of why deep neural networks work better than traditional \u201cshallow\u201d ones, but the question remains: why neural networks in the first place? why not networks consisting of non-linear functions from some other family of functions? In this paper, we provide a possible theoretical answer to this question: namely, we show that of all families with the smallest possible number of parameters, families corresponding to neurons are indeed optimal \u2013 for all optimality criteria that satisfy some reasonable requirements: namely, for all optimality criteria which are final and invariant with respect to coordinate changes, changes of measuring units, and similar linear transformations.<\/jats:p>","DOI":"10.3233\/jifs-212009","type":"journal-article","created":{"date-parts":[[2022,8,2]],"date-time":"2022-08-02T11:53:48Z","timestamp":1659441228000},"page":"6947-6951","source":"Crossref","is-referenced-by-count":1,"title":["Why neural networks in the first place: a theoretical explanation"],"prefix":"10.1177","volume":"43","author":[{"given":"Jonatan","family":"Contreras","sequence":"first","affiliation":[{"name":"Department of Computer Science, University of Texas at El Paso, TX, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Martine","family":"Ceberio","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at El Paso, TX, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Olga","family":"Kosheleva","sequence":"additional","affiliation":[{"name":"Department of Teacher Education, University of Texas at El Paso, TX, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Vladik","family":"Kreinovich","sequence":"additional","affiliation":[{"name":"Department of Computer Science, University of Texas at El Paso, TX, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","reference":[{"key":"10.3233\/JIFS-212009_ref2","unstructured":"Goodfellow I. , Bengio Y. , Courville A. Deep Learning, MIT Press, Cambridge, Massachusetts, 2016."}],"container-title":["Journal of Intelligent &amp; Fuzzy Systems"],"original-title":[],"link":[{"URL":"https:\/\/content.iospress.com\/download?id=10.3233\/JIFS-212009","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T09:42:32Z","timestamp":1777455752000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/full\/10.3233\/JIFS-212009"}},"subtitle":[],"editor":[{"given":"Ildar","family":"Batyrshin","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Fernando","family":"Gomide","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Vladik","family":"Kreinovich","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]},{"given":"Shahnaz","family":"Shahbazova","sequence":"additional","affiliation":[],"role":[{"role":"editor","vocabulary":"crossref"}]}],"short-title":[],"issued":{"date-parts":[[2022,11,11]]},"references-count":1,"journal-issue":{"issue":"6"},"URL":"https:\/\/doi.org\/10.3233\/jifs-212009","relation":{},"ISSN":["1064-1246","1875-8967"],"issn-type":[{"value":"1064-1246","type":"print"},{"value":"1875-8967","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,11,11]]}}}