{"id":"https://openalex.org/W3184062643","doi":"https://doi.org/10.1109/tit.2022.3199601","title":"Neural Network Approximation of Refinable Functions","display_name":"Neural Network Approximation of Refinable Functions","publication_year":2022,"publication_date":"2022-08-17","ids":{"openalex":"https://openalex.org/W3184062643","doi":"https://doi.org/10.1109/tit.2022.3199601","mag":"3184062643"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3199601","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3199601","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5107519484","display_name":"Ingrid Daubechies","orcid":"https://orcid.org/0000-0002-6472-1056"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ingrid Daubechies","raw_affiliation_strings":["Department of Mathematics, and Rhodes Information Initiative, Duke University, Durham, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, and Rhodes Information Initiative, Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110385534","display_name":"Ronald DeVore","orcid":"https://orcid.org/0009-0005-1105-5925"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ronald DeVore","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086417185","display_name":"Nadav Dym","orcid":null},"institutions":[{"id":"https://openalex.org/I174306211","display_name":"Technion \u2013 Israel Institute of Technology","ror":"https://ror.org/03qryx823","country_code":"IL","type":"education","lineage":["https://openalex.org/I174306211"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Nadav Dym","raw_affiliation_strings":["Faculty of Mathematics, Technion—Israel Institute of Technology, Haifa, Israel"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Mathematics, Technion—Israel Institute of Technology, Haifa, Israel","institution_ids":["https://openalex.org/I174306211"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068471566","display_name":"Shira Faigenbaum-Golovin","orcid":"https://orcid.org/0000-0003-0320-9726"},"institutions":[{"id":"https://openalex.org/I170897317","display_name":"Duke University","ror":"https://ror.org/00py81415","country_code":"US","type":"education","lineage":["https://openalex.org/I170897317"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shira Faigenbaum-Golovin","raw_affiliation_strings":["Department of Mathematics, and Rhodes Information Initiative, Duke University, Durham, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, and Rhodes Information Initiative, Duke University, Durham, NC, USA","institution_ids":["https://openalex.org/I170897317"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074707764","display_name":"Shahar Z. Kovalsky","orcid":"https://orcid.org/0000-0001-8924-5538"},"institutions":[{"id":"https://openalex.org/I114027177","display_name":"University of North Carolina at Chapel Hill","ror":"https://ror.org/0130frc33","country_code":"US","type":"education","lineage":["https://openalex.org/I114027177"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Shahar Z. Kovalsky","raw_affiliation_strings":["Department of Mathematics, The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The University of North Carolina at Chapel Hill, Chapel Hill, NC, USA","institution_ids":["https://openalex.org/I114027177"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112666351","display_name":"Kung-Chin Lin","orcid":"https://orcid.org/0009-0004-3008-8864"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kung-Chin Lin","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067871294","display_name":"Josiah Park","orcid":"https://orcid.org/0000-0002-0075-8917"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Josiah Park","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101696095","display_name":"Guergana Petrova","orcid":"https://orcid.org/0000-0002-8873-4150"},"institutions":[{"id":"https://openalex.org/I91045830","display_name":"Texas A&M University","ror":"https://ror.org/01f5ytq51","country_code":"US","type":"education","lineage":["https://openalex.org/I91045830"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Guergana Petrova","raw_affiliation_strings":["Department of Mathematics, Texas A&M University, College Station, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Texas A&M University, College Station, TX, USA","institution_ids":["https://openalex.org/I91045830"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5074615861","display_name":"Barak Sober","orcid":"https://orcid.org/0000-0001-5090-5551"},"institutions":[{"id":"https://openalex.org/I197251160","display_name":"Hebrew University of Jerusalem","ror":"https://ror.org/03qxff017","country_code":"IL","type":"education","lineage":["https://openalex.org/I197251160"]}],"countries":["IL"],"is_corresponding":false,"raw_author_name":"Barak Sober","raw_affiliation_strings":["Department of Statistics and Data Science and Digital Humanities, The Hebrew University of Jerusalem, Jerusalem, Israel"],"raw_orcid":"https://orcid.org/0000-0001-5090-5551","affiliations":[{"raw_affiliation_string":"Department of Statistics and Data Science and Digital Humanities, The Hebrew University of Jerusalem, Jerusalem, Israel","institution_ids":["https://openalex.org/I197251160"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":5,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.2698,"has_fulltext":false,"cited_by_count":10,"citation_normalized_percentile":{"value":0.73350923,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"69","issue":"1","first_page":"482","last_page":"495"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11245","display_name":"Advanced Numerical Analysis Techniques","score":0.9997000098228455,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10188","display_name":"Advanced machining processes and optimization","score":0.9923999905586243,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11138","display_name":"Tribology and Lubrication Engineering","score":0.97079998254776,"subfield":{"id":"https://openalex.org/subfields/2210","display_name":"Mechanical Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6259707808494568},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5420596599578857},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5372815728187561},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.5105615854263306},{"id":"https://openalex.org/keywords/transfer-function","display_name":"Transfer function","score":0.45987576246261597},{"id":"https://openalex.org/keywords/wavelet","display_name":"Wavelet","score":0.4441221058368683},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4318605065345764},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.4275570809841156},{"id":"https://openalex.org/keywords/function-approximation","display_name":"Function approximation","score":0.4155206084251404},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.35601386427879333},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.34416893124580383},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.30354005098342896},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.2106904685497284},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.15847855806350708}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6259707808494568},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5420596599578857},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5372815728187561},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.5105615854263306},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.45987576246261597},{"id":"https://openalex.org/C47432892","wikidata":"https://www.wikidata.org/wiki/Q831390","display_name":"Wavelet","level":2,"score":0.4441221058368683},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4318605065345764},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.4275570809841156},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.4155206084251404},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.35601386427879333},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.34416893124580383},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.30354005098342896},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.2106904685497284},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.15847855806350708},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.0},{"id":"https://openalex.org/C119599485","wikidata":"https://www.wikidata.org/wiki/Q43035","display_name":"Electrical engineering","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tit.2022.3199601","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3199601","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Information Theory","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G3153538429","display_name":null,"funder_award_id":"DMS 18-17603","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5130348904","display_name":null,"funder_award_id":"N00014-20-1-278","funder_id":"https://openalex.org/F4320337345","funder_display_name":"Office of Naval Research"},{"id":"https://openalex.org/G8277604305","display_name":null,"funder_award_id":"DMS 21-34077","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320337345","display_name":"Office of Naval Research","ror":"https://ror.org/00rk2pe57"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":26,"referenced_works":["https://openalex.org/W204546099","https://openalex.org/W1980149518","https://openalex.org/W1980947251","https://openalex.org/W2003989039","https://openalex.org/W2030934791","https://openalex.org/W2062024414","https://openalex.org/W2119682789","https://openalex.org/W2158581396","https://openalex.org/W2162870748","https://openalex.org/W2341241031","https://openalex.org/W2528305538","https://openalex.org/W2612218357","https://openalex.org/W2963172624","https://openalex.org/W3005363104","https://openalex.org/W3022862919","https://openalex.org/W3133816032","https://openalex.org/W3161792008","https://openalex.org/W3194828218","https://openalex.org/W4231428347","https://openalex.org/W4297562995","https://openalex.org/W4388250268","https://openalex.org/W6688256371","https://openalex.org/W6691187937","https://openalex.org/W6695533872","https://openalex.org/W6718212895","https://openalex.org/W6762290775"],"related_works":["https://openalex.org/W4285277090","https://openalex.org/W4327738859","https://openalex.org/W2348722996","https://openalex.org/W2334570605","https://openalex.org/W3181683615","https://openalex.org/W4286826125","https://openalex.org/W1633485514","https://openalex.org/W1980454230","https://openalex.org/W2300851791","https://openalex.org/W2152067846"],"abstract_inverted_index":{"In":[0,115],"the":[1,5,29,66,80,100,108,121,144,175],"desire":[2],"to":[3,120,171,183],"quantify":[4],"success":[6],"of":[7,31,40,48,68,79,82,124,146,163,166,178],"neural":[8,32,149],"networks":[9,150],"in":[10,21,161,174,189],"deep":[11,147],"learning":[12],"and":[13,95,155],"other":[14,101],"applications,":[15],"there":[16,36],"is":[17,63,112],"a":[18,38,45,152],"great":[19],"interest":[20],"understanding":[22],"which":[23,42,111],"functions":[24,49,69,91,97,105,126,140,172,184],"are":[25,141],"efficiently":[26],"approximated":[27,52,73,142],"by":[28,57,127,143],"outputs":[30,145],"networks.":[33],"By":[34],"now,":[35],"exists":[37],"variety":[39],"results":[41,169],"show":[43,137],"that":[44,65,70,129,138],"wide":[46],"range":[47],"can":[50,71],"be":[51,72],"with":[53,74,151,158],"sometimes":[54],"surprising":[55],"accuracy":[56,76,159],"these":[58],"outputs.":[59],"For":[60],"example,":[61],"it":[62,130],"known":[64],"set":[67],"exponential":[75,160],"(in":[77],"terms":[78,162],"number":[81,165],"parameters":[83],"used)":[84],"includes,":[85],"on":[86,99],"one":[87],"hand,":[88,102],"very":[89,103],"smooth":[90],"such":[92,106],"as":[93,107,180,182],"polynomials":[94],"analytic":[96],"and,":[98],"rough":[104,125],"Weierstrass":[109],"function,":[110],"nowhere":[113],"differentiable.":[114],"this":[116],"paper,":[117],"we":[118,136],"add":[119],"latter":[122],"class":[123],"showing":[128],"also":[131],"includes":[132],"refinable":[133,139],"functions.":[134],"Namely,":[135],"ReLU":[148],"fixed":[153],"width":[154],"increasing":[156],"depth":[157],"their":[164],"parameters.":[167],"Our":[168],"apply":[170],"used":[173],"standard":[176],"construction":[177],"wavelets":[179],"well":[181],"constructed":[185],"via":[186],"subdivision":[187],"algorithms":[188],"Computer":[190],"Aided":[191],"Geometric":[192],"Design.":[193]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}