{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,3]],"date-time":"2026-04-03T04:18:57Z","timestamp":1775189937399,"version":"3.50.1"},"reference-count":43,"publisher":"Institute of Electrical and Electronics Engineers (IEEE)","issue":"7","license":[{"start":{"date-parts":[[2022,7,1]],"date-time":"2022-07-01T00:00:00Z","timestamp":1656633600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by-nc-nd\/4.0\/"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["IEEE Trans. Neural Netw. Learning Syst."],"published-print":{"date-parts":[[2022,7]]},"DOI":"10.1109\/tnnls.2021.3049719","type":"journal-article","created":{"date-parts":[[2021,1,29]],"date-time":"2021-01-29T20:44:22Z","timestamp":1611953062000},"page":"3079-3093","source":"Crossref","is-referenced-by-count":24,"title":["Efficient Approximation of High-Dimensional Functions With Neural Networks"],"prefix":"10.1109","volume":"33","author":[{"ORCID":"https:\/\/orcid.org\/0000-0001-9074-7295","authenticated-orcid":false,"given":"Patrick","family":"Cheridito","sequence":"first","affiliation":[{"name":"Department of Mathematics, ETH Zurich, Zurich, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-9840-3339","authenticated-orcid":false,"given":"Arnulf","family":"Jentzen","sequence":"additional","affiliation":[{"name":"Department of Mathematics, ETH Zurich, Zurich, Switzerland"}]},{"ORCID":"https:\/\/orcid.org\/0000-0001-5772-5086","authenticated-orcid":false,"given":"Florian","family":"Rossmannek","sequence":"additional","affiliation":[{"name":"Department of Mathematics, ETH Zurich, Zurich, Switzerland"}]}],"member":"263","reference":[{"key":"ref1","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(89)90003-8"},{"key":"ref2","doi-asserted-by":"publisher","DOI":"10.1007\/bf02551274"},{"key":"ref3","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(89)90020-8"},{"key":"ref4","doi-asserted-by":"publisher","DOI":"10.1016\/0893-6080(91)90009-T"},{"key":"ref5","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(05)80131-5"},{"key":"ref6","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2017.12.007"},{"key":"ref7","doi-asserted-by":"publisher","DOI":"10.1214\/aos\/1176348546"},{"key":"ref8","doi-asserted-by":"publisher","DOI":"10.1109\/18.256500"},{"key":"ref9","doi-asserted-by":"publisher","DOI":"10.1007\/bf02678464"},{"key":"ref10","first-page":"97","article-title":"Rates of convergence for radial basis functions and neural networks","volume-title":"Artificial Neural Networks for Speech and Vision","author":"Girosi","year":"1993"},{"key":"ref11","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2008.2006383"},{"key":"ref12","first-page":"69","article-title":"Neural net approximation","volume-title":"Proc. 7th Yale Workshop Adapt. Learn. Syst.","author":"Barron"},{"key":"ref13","doi-asserted-by":"publisher","DOI":"10.1007\/bf00993164"},{"key":"ref14","doi-asserted-by":"publisher","DOI":"10.1006\/jcss.1997.1506"},{"key":"ref15","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2018.2874447"},{"key":"ref16","doi-asserted-by":"publisher","DOI":"10.1016\/S0893-6080(97)00028-2"},{"key":"ref17","doi-asserted-by":"publisher","DOI":"10.1109\/18.971754"},{"key":"ref18","doi-asserted-by":"publisher","DOI":"10.1162\/neco.2008.20.1.252"},{"key":"ref19","doi-asserted-by":"publisher","DOI":"10.1016\/j.jco.2008.08.001"},{"key":"ref20","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2011.2169531"},{"key":"ref21","doi-asserted-by":"publisher","DOI":"10.1038\/nature14539"},{"key":"ref22","volume-title":"Deep Learning","author":"Goodfellow","year":"2016"},{"key":"ref23","first-page":"907","article-title":"The power of depth for feedforward neural networks","volume-title":"Proc. 29th Annu. Conf. Learn. Theory","author":"Eldan"},{"key":"ref24","first-page":"2979","article-title":"Depth-width tradeoffs in approximating natural functions with neural networks","volume-title":"Proc. 34th Int. Conf. Mach. Learn.","author":"Safran"},{"key":"ref25","first-page":"690","article-title":"Depth separation for neural networks","volume-title":"Proc. 2017 Conf. Learn. Theory","author":"Daniely"},{"key":"ref26","doi-asserted-by":"publisher","DOI":"10.1017\/s0962492900002919"},{"key":"ref27","doi-asserted-by":"publisher","DOI":"10.1016\/S0925-2312(98)00111-8"},{"key":"ref28","doi-asserted-by":"publisher","DOI":"10.1016\/j.neucom.2018.07.075"},{"key":"ref29","doi-asserted-by":"publisher","DOI":"10.1137\/18m118709x"},{"key":"ref30","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2018.08.019"},{"key":"ref31","doi-asserted-by":"publisher","DOI":"10.1007\/bf02070821"},{"key":"ref32","article-title":"Approximation in $\\text{L}^{p}$\n($\\mu$\n) with deep ReLU neural networks","author":"Voigtlaender","year":"2019","journal-title":"arXiv:1904.04789"},{"key":"ref33","doi-asserted-by":"publisher","DOI":"10.1137\/20m134695x"},{"key":"ref34","doi-asserted-by":"publisher","DOI":"10.1016\/j.neunet.2017.07.002"},{"key":"ref35","doi-asserted-by":"publisher","DOI":"10.1147\/rd.383.0277"},{"key":"ref36","doi-asserted-by":"publisher","DOI":"10.1142\/s0219530518500203"},{"key":"ref37","doi-asserted-by":"publisher","DOI":"10.1090\/memo\/1410"},{"key":"ref38","doi-asserted-by":"publisher","DOI":"10.4310\/cms.2021.v19.n5.a1"},{"key":"ref39","doi-asserted-by":"publisher","DOI":"10.1007\/s42985-019-0006-9"},{"key":"ref40","first-page":"1271","article-title":"On the ability of neural nets to express distributions","volume-title":"Proc. Conf. Learn. Theory","volume":"65","author":"Lee"},{"key":"ref41","doi-asserted-by":"publisher","DOI":"10.1109\/TIT.2021.3062161"},{"key":"ref42","doi-asserted-by":"publisher","DOI":"10.1007\/s10444-022-09970-2"},{"key":"ref43","doi-asserted-by":"publisher","DOI":"10.1007\/s10955-017-1836-5"}],"container-title":["IEEE Transactions on Neural Networks and Learning Systems"],"original-title":[],"link":[{"URL":"http:\/\/xplorestaging.ieee.org\/ielx7\/5962385\/9816060\/09340559.pdf?arnumber=9340559","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,1,9]],"date-time":"2024-01-09T23:33:51Z","timestamp":1704843231000},"score":1,"resource":{"primary":{"URL":"https:\/\/ieeexplore.ieee.org\/document\/9340559\/"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2022,7]]},"references-count":43,"journal-issue":{"issue":"7"},"URL":"https:\/\/doi.org\/10.1109\/tnnls.2021.3049719","relation":{},"ISSN":["2162-237X","2162-2388"],"issn-type":[{"value":"2162-237X","type":"print"},{"value":"2162-2388","type":"electronic"}],"subject":[],"published":{"date-parts":[[2022,7]]}}}