{"id":"https://openalex.org/W2963482148","doi":"https://doi.org/10.1109/tnnls.2018.2868980","title":"Generalization and Expressivity for Deep Nets","display_name":"Generalization and Expressivity for Deep Nets","publication_year":2018,"publication_date":"2018-09-27","ids":{"openalex":"https://openalex.org/W2963482148","doi":"https://doi.org/10.1109/tnnls.2018.2868980","mag":"2963482148","pmid":"https://pubmed.ncbi.nlm.nih.gov/30281491"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2018.2868980","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2018.2868980","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5022287632","display_name":"Shao-Bo Lin","orcid":"https://orcid.org/0000-0001-5122-9153"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":true,"raw_author_name":"Shao-Bo Lin","raw_affiliation_strings":["Department of Mathematics, City University of Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5022287632"],"corresponding_institution_ids":["https://openalex.org/I168719708"],"apc_list":null,"apc_paid":null,"fwci":4.3976,"has_fulltext":false,"cited_by_count":59,"citation_normalized_percentile":{"value":0.95592755,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":99},"biblio":{"volume":"30","issue":"5","first_page":"1392","last_page":"1406"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9994000196456909,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9962000250816345,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.8283294439315796},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.7512549161911011},{"id":"https://openalex.org/keywords/expressivity","display_name":"Expressivity","score":0.6832766532897949},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6535124778747559},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.5978305339813232},{"id":"https://openalex.org/keywords/variance","display_name":"Variance (accounting)","score":0.507098913192749},{"id":"https://openalex.org/keywords/net","display_name":"Net (polyhedron)","score":0.4863038957118988},{"id":"https://openalex.org/keywords/empirical-research","display_name":"Empirical research","score":0.41193628311157227},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.37106651067733765},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3584032654762268},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.34218093752861023},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2567506432533264},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.11903709173202515},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.08248528838157654}],"concepts":[{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.8283294439315796},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.7512549161911011},{"id":"https://openalex.org/C92811239","wikidata":"https://www.wikidata.org/wiki/Q20998670","display_name":"Expressivity","level":2,"score":0.6832766532897949},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6535124778747559},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5978305339813232},{"id":"https://openalex.org/C196083921","wikidata":"https://www.wikidata.org/wiki/Q7915758","display_name":"Variance (accounting)","level":2,"score":0.507098913192749},{"id":"https://openalex.org/C14166107","wikidata":"https://www.wikidata.org/wiki/Q253829","display_name":"Net (polyhedron)","level":2,"score":0.4863038957118988},{"id":"https://openalex.org/C120936955","wikidata":"https://www.wikidata.org/wiki/Q2155640","display_name":"Empirical research","level":2,"score":0.41193628311157227},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.37106651067733765},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3584032654762268},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.34218093752861023},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2567506432533264},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.11903709173202515},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.08248528838157654},{"id":"https://openalex.org/C121955636","wikidata":"https://www.wikidata.org/wiki/Q4116214","display_name":"Accounting","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C144133560","wikidata":"https://www.wikidata.org/wiki/Q4830453","display_name":"Business","level":0,"score":0.0},{"id":"https://openalex.org/C54355233","wikidata":"https://www.wikidata.org/wiki/Q7162","display_name":"Genetics","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2018.2868980","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2018.2868980","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:30281491","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/30281491","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G2405491850","display_name":null,"funder_award_id":"61502342","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G2641593616","display_name":null,"funder_award_id":"11771012","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G651730104","display_name":null,"funder_award_id":"61876133","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":57,"referenced_works":["https://openalex.org/W136946273","https://openalex.org/W597932189","https://openalex.org/W913685725","https://openalex.org/W1484867920","https://openalex.org/W1963616278","https://openalex.org/W1971909566","https://openalex.org/W1978581090","https://openalex.org/W1979234952","https://openalex.org/W1985700052","https://openalex.org/W1989006755","https://openalex.org/W1994642189","https://openalex.org/W1996388931","https://openalex.org/W2006240266","https://openalex.org/W2017332415","https://openalex.org/W2018166535","https://openalex.org/W2021676252","https://openalex.org/W2033137841","https://openalex.org/W2044675413","https://openalex.org/W2052100548","https://openalex.org/W2056763477","https://openalex.org/W2072128103","https://openalex.org/W2085481869","https://openalex.org/W2089947415","https://openalex.org/W2105464873","https://openalex.org/W2109999160","https://openalex.org/W2112531253","https://openalex.org/W2125569215","https://openalex.org/W2133665775","https://openalex.org/W2136922672","https://openalex.org/W2141473882","https://openalex.org/W2152593035","https://openalex.org/W2158581396","https://openalex.org/W2161388792","https://openalex.org/W2253400648","https://openalex.org/W2267573953","https://openalex.org/W2511261638","https://openalex.org/W2513671774","https://openalex.org/W2595315035","https://openalex.org/W2605622124","https://openalex.org/W2609900968","https://openalex.org/W2615421548","https://openalex.org/W2734819659","https://openalex.org/W2951603627","https://openalex.org/W2952108874","https://openalex.org/W2962742960","https://openalex.org/W2962949242","https://openalex.org/W2962990163","https://openalex.org/W2963694768","https://openalex.org/W2963982496","https://openalex.org/W3105432754","https://openalex.org/W3105890793","https://openalex.org/W3157685993","https://openalex.org/W4231109964","https://openalex.org/W4242686374","https://openalex.org/W4245558064","https://openalex.org/W6678500653","https://openalex.org/W6680850120"],"related_works":["https://openalex.org/W2048138016","https://openalex.org/W2408998960","https://openalex.org/W2739995301","https://openalex.org/W4285275252","https://openalex.org/W2144961711","https://openalex.org/W1460228849","https://openalex.org/W2067704480","https://openalex.org/W2052009157","https://openalex.org/W2005924229","https://openalex.org/W2943567877"],"abstract_inverted_index":{"Along":[0],"with":[1,49,112],"the":[2,57,78,95,128,135,155,185],"rapid":[3],"development":[4],"of":[5,29,52,101,121,157,181],"deep":[6,30,40,69,85,102,110,140,174,182],"learning":[7,66,166,186],"in":[8,119],"practice,":[9],"theoretical":[10,27,99],"explanations":[11],"for":[12,68,168],"its":[13],"success":[14],"become":[15],"urgent.":[16],"Generalization":[17],"and":[18,123,149],"expressivity":[19,33,89,118],"are":[20],"two":[21,113],"widely":[22],"used":[23],"measurements":[24],"to":[25,76,97,133],"quantify":[26],"behaviors":[28],"nets.":[31,70,103,159,175],"The":[32,60],"focuses":[34],"on":[35,84,173],"finding":[36],"functions":[37],"expressible":[38],"by":[39,46,147],"nets":[41,48,141,183],"but":[42],"cannot":[43],"be":[44],"approximated":[45],"shallow":[47,158],"similar":[50],"number":[51,132],"neurons.":[53],"It":[54,71],"usually":[55,72],"implies":[56],"large":[58],"capacity.":[59],"generalization":[61],"aims":[62],"at":[63],"deriving":[64],"fast":[65],"rate":[67],"requires":[73],"small":[74],"capacity":[75,156],"reduce":[77],"variance.":[79],"Different":[80],"from":[81,184],"previous":[82],"studies":[83],"nets,":[86],"pursuing":[87],"either":[88],"or":[90],"generalization,":[91],"we":[92,107,137,163],"consider":[93],"both":[94],"factors":[96],"explore":[98],"advantages":[100,180],"For":[104],"this":[105],"purpose,":[106],"construct":[108],"a":[109,161],"net":[111],"hidden":[114],"layers":[115],"possessing":[116],"excellent":[117,143],"terms":[120],"localized":[122,148],"sparse":[124,150],"approximation.":[125],"Then,":[126],"utilizing":[127],"well":[129],"known":[130],"covering":[131],"measure":[134],"capacity,":[136],"find":[138],"that":[139],"possess":[142],"expressive":[144],"power":[145],"(measured":[146],"approximation)":[151],"without":[152],"essentially":[153],"enlarging":[154],"As":[160],"consequence,":[162],"derive":[164],"near-optimal":[165],"rates":[167],"implementing":[169],"empirical":[170],"risk":[171],"minimization":[172],"These":[176],"results":[177],"theoretically":[178],"exhibit":[179],"theory":[187],"viewpoint.":[188]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":8},{"year":2022,"cited_by_count":7},{"year":2021,"cited_by_count":11},{"year":2020,"cited_by_count":6},{"year":2019,"cited_by_count":10}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}