{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,2,28]],"date-time":"2026-02-28T04:22:14Z","timestamp":1772252534268,"version":"3.50.1"},"reference-count":46,"publisher":"MDPI AG","issue":"5","license":[{"start":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T00:00:00Z","timestamp":1619049600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["1623190"],"award-info":[{"award-number":["1623190"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["HRD-1834620"],"award-info":[{"award-number":["HRD-1834620"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"DOI":"10.13039\/100000001","name":"National Science Foundation","doi-asserted-by":"publisher","award":["HRD-2034030"],"award-info":[{"award-number":["HRD-2034030"]}],"id":[{"id":"10.13039\/100000001","id-type":"DOI","asserted-by":"publisher"}]},{"name":"program of the development of the Scientific-Educational Mathematical Center of Volga Federal District","award":["075-02-2020-1478"],"award-info":[{"award-number":["075-02-2020-1478"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Entropy"],"abstract":"<jats:p>As a system becomes more complex, at first, its description and analysis becomes more complicated. However, a further increase in the system\u2019s complexity often makes this analysis simpler. A classical example is Central Limit Theorem: when we have a few independent sources of uncertainty, the resulting uncertainty is very difficult to describe, but as the number of such sources increases, the resulting distribution gets close to an easy-to-analyze normal one\u2014and indeed, normal distributions are ubiquitous. We show that such limit theorems often make analysis of complex systems easier\u2014i.e., lead to blessing of dimensionality phenomenon\u2014for all the aspects of these systems: the corresponding transformation, the system\u2019s uncertainty, and the desired result of the system\u2019s analysis.<\/jats:p>","DOI":"10.3390\/e23050501","type":"journal-article","created":{"date-parts":[[2021,4,22]],"date-time":"2021-04-22T13:59:14Z","timestamp":1619099954000},"page":"501","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Limit Theorems as Blessing of Dimensionality: Neural-Oriented Overview"],"prefix":"10.3390","volume":"23","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-1244-1650","authenticated-orcid":false,"given":"Vladik","family":"Kreinovich","sequence":"first","affiliation":[{"name":"Departments of Computer Science (V.K.) and Teacher Education (O.K.), University of Texas at El Paso, El Paso, TX 79968, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2587-4209","authenticated-orcid":false,"given":"Olga","family":"Kosheleva","sequence":"additional","affiliation":[{"name":"Departments of Computer Science (V.K.) and Teacher Education (O.K.), University of Texas at El Paso, El Paso, TX 79968, USA"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2021,4,22]]},"reference":[{"key":"ref_1","unstructured":"Warwick, K., and K\u00e1rn\u00fd, M.M. 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