{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,30]],"date-time":"2026-05-30T05:03:23Z","timestamp":1780117403843,"version":"3.54.0"},"reference-count":26,"publisher":"MDPI AG","issue":"4","license":[{"start":{"date-parts":[[2020,4,13]],"date-time":"2020-04-13T00:00:00Z","timestamp":1586736000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100003725","name":"National Research Foundation of Korea","doi-asserted-by":"publisher","award":["NRF-2017R1E1A1A03070311"],"award-info":[{"award-number":["NRF-2017R1E1A1A03070311"]}],"id":[{"id":"10.13039\/501100003725","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>This paper analyzes the operation principle and predicted value of the recurrent-neural-network (RNN) structure, which is the most basic and suitable for the change of time in the structure of a neural network for various types of artificial intelligence (AI). In particular, an RNN in which all connections are symmetric guarantees that it will converge. The operating principle of a RNN is based on linear data combinations and is composed through the synthesis of nonlinear activation functions. Linear combined data are similar to the autoregressive-moving average (ARMA) method of statistical processing. However, distortion due to the nonlinear activation function in RNNs causes the predicted value to be different from the predicted ARMA value. Through this, we know the limit of the predicted value of an RNN and the range of prediction that changes according to the learning data. In addition to mathematical proofs, numerical experiments confirmed our claims.<\/jats:p>","DOI":"10.3390\/sym12040615","type":"journal-article","created":{"date-parts":[[2020,4,14]],"date-time":"2020-04-14T03:10:01Z","timestamp":1586833801000},"page":"615","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":34,"title":["Analysis of Recurrent Neural Network and Predictions"],"prefix":"10.3390","volume":"12","author":[{"given":"Jieun","family":"Park","sequence":"first","affiliation":[{"name":"Seongsan Liberal Arts College, Daegu University, Kyungsan 38453, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Dokkyun","family":"Yi","sequence":"additional","affiliation":[{"name":"Seongsan Liberal Arts College, Daegu University, Kyungsan 38453, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-3930-985X","authenticated-orcid":false,"given":"Sangmin","family":"Ji","sequence":"additional","affiliation":[{"name":"Department of Mathematics, College of Natural Sciences, Chungnam National University, Daejeon 34134, Korea"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"1968","published-online":{"date-parts":[[2020,4,13]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"533","DOI":"10.1038\/323533a0","article-title":"Learning representations by back-propagating errors","volume":"323","author":"Rumelhart","year":"1986","journal-title":"Nature"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"339","DOI":"10.1016\/0893-6080(88)90007-X","article-title":"Generalization of backpropagation with application to a recurrent gas market model","volume":"1","author":"Werbos","year":"1988","journal-title":"Neural Netw."},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"403","DOI":"10.1080\/09540098908915650","article-title":"A Local Learning Algorithm for Dynamic Feedforward and Recurrent Networks","volume":"1","author":"Schmidhuber","year":"1989","journal-title":"Connect. 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