{"id":"https://openalex.org/W2739160792","doi":"https://doi.org/10.1109/tit.2018.2854560","title":"Theoretical Insights Into the Optimization Landscape of Over-Parameterized Shallow Neural Networks","display_name":"Theoretical Insights Into the Optimization Landscape of Over-Parameterized Shallow Neural Networks","publication_year":2018,"publication_date":"2018-07-10","ids":{"openalex":"https://openalex.org/W2739160792","doi":"https://doi.org/10.1109/tit.2018.2854560","mag":"2739160792"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2018.2854560","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2854560","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":"preprint","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1707.04926.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046962187","display_name":"Mahdi Soltanolkotabi","orcid":"https://orcid.org/0000-0003-2101-6418"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Mahdi Soltanolkotabi","raw_affiliation_strings":["Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","[Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA]"],"affiliations":[{"raw_affiliation_string":"Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]},{"raw_affiliation_string":"[Ming Hsieh Department of Electrical Engineering, University of Southern California, Los Angeles, CA, USA]","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010342958","display_name":"Adel Javanmard","orcid":"https://orcid.org/0000-0003-1934-8747"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Adel Javanmard","raw_affiliation_strings":["Department of Data Science and Operations Research, University of Southern California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Data Science and Operations Research, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5059740024","display_name":"Jason D. Lee","orcid":"https://orcid.org/0000-0003-0064-7800"},"institutions":[{"id":"https://openalex.org/I1174212","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60","country_code":"US","type":"education","lineage":["https://openalex.org/I1174212"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jason D. Lee","raw_affiliation_strings":["Department of Data Science and Operations Research, University of Southern California, Los Angeles, CA, USA"],"affiliations":[{"raw_affiliation_string":"Department of Data Science and Operations Research, University of Southern California, Los Angeles, CA, USA","institution_ids":["https://openalex.org/I1174212"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5046962187"],"corresponding_institution_ids":["https://openalex.org/I1174212"],"apc_list":null,"apc_paid":null,"fwci":1.3538,"has_fulltext":false,"cited_by_count":15,"citation_normalized_percentile":{"value":0.85322178,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"65","issue":"2","first_page":"742","last_page":"769"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9995999932289124,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9995999932289124,"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/T12676","display_name":"Machine Learning and ELM","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/T10057","display_name":"Face and Expression Recognition","score":0.9991000294685364,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parameterized-complexity","display_name":"Parameterized complexity","score":0.8575682640075684},{"id":"https://openalex.org/keywords/heuristics","display_name":"Heuristics","score":0.7412028908729553},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6935734748840332},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.6502772569656372},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.5796274542808533},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.5625466108322144},{"id":"https://openalex.org/keywords/set","display_name":"Set (abstract data type)","score":0.5320257544517517},{"id":"https://openalex.org/keywords/quadratic-equation","display_name":"Quadratic equation","score":0.5318626165390015},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5248406529426575},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5234148502349854},{"id":"https://openalex.org/keywords/variety","display_name":"Variety (cybernetics)","score":0.4627630114555359},{"id":"https://openalex.org/keywords/optimization-problem","display_name":"Optimization problem","score":0.44574111700057983},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4348789155483246},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.31508463621139526},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.29846882820129395}],"concepts":[{"id":"https://openalex.org/C165464430","wikidata":"https://www.wikidata.org/wiki/Q1570441","display_name":"Parameterized complexity","level":2,"score":0.8575682640075684},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.7412028908729553},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6935734748840332},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.6502772569656372},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.5796274542808533},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.5625466108322144},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5320257544517517},{"id":"https://openalex.org/C129844170","wikidata":"https://www.wikidata.org/wiki/Q41299","display_name":"Quadratic equation","level":2,"score":0.5318626165390015},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5248406529426575},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5234148502349854},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.4627630114555359},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.44574111700057983},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4348789155483246},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31508463621139526},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.29846882820129395},{"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/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tit.2018.2854560","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2018.2854560","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"},{"id":"mag:2739160792","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1707.04926.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null}],"best_oa_location":{"id":"mag:2739160792","is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1707.04926.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G56678839","display_name":null,"funder_award_id":"#1813877","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G8097725666","display_name":null,"funder_award_id":"FA9550-18-1-0078","funder_id":"https://openalex.org/F4320338279","funder_display_name":"Air Force Office of Scientific Research"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320308204","display_name":"Northrop Grumman","ror":"https://ror.org/05kewds18"},{"id":"https://openalex.org/F4320308668","display_name":"University of Southern California","ror":"https://ror.org/03taz7m60"},{"id":"https://openalex.org/F4320309327","display_name":"Google","ror":"https://ror.org/00njsd438"},{"id":"https://openalex.org/F4320338279","display_name":"Air Force Office of Scientific Research","ror":"https://ror.org/011e9bt93"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":58,"referenced_works":["https://openalex.org/W178986290","https://openalex.org/W653925602","https://openalex.org/W813605148","https://openalex.org/W1573820523","https://openalex.org/W1839868949","https://openalex.org/W1899249567","https://openalex.org/W1903051497","https://openalex.org/W1966897734","https://openalex.org/W1969891152","https://openalex.org/W1987635176","https://openalex.org/W1993882792","https://openalex.org/W1995842804","https://openalex.org/W2009941369","https://openalex.org/W2066544664","https://openalex.org/W2117130368","https://openalex.org/W2133656711","https://openalex.org/W2142949395","https://openalex.org/W2221366174","https://openalex.org/W2281746805","https://openalex.org/W2283214199","https://openalex.org/W2398500126","https://openalex.org/W2399994860","https://openalex.org/W2514392868","https://openalex.org/W2560848383","https://openalex.org/W2561193401","https://openalex.org/W2587741277","https://openalex.org/W2592651140","https://openalex.org/W2593299318","https://openalex.org/W2593709294","https://openalex.org/W2608422103","https://openalex.org/W2613481513","https://openalex.org/W2618003483","https://openalex.org/W2618398196","https://openalex.org/W2625063094","https://openalex.org/W2709553318","https://openalex.org/W2777256551","https://openalex.org/W2949086226","https://openalex.org/W2949978219","https://openalex.org/W2949979820","https://openalex.org/W2950220847","https://openalex.org/W2951773851","https://openalex.org/W2952318479","https://openalex.org/W2953243802","https://openalex.org/W2963446085","https://openalex.org/W2964106499","https://openalex.org/W2965497096","https://openalex.org/W4236966694","https://openalex.org/W6607280820","https://openalex.org/W6608025168","https://openalex.org/W6623399679","https://openalex.org/W6639736602","https://openalex.org/W6681017033","https://openalex.org/W6684191040","https://openalex.org/W6685292845","https://openalex.org/W6713348437","https://openalex.org/W6720643467","https://openalex.org/W6734728544","https://openalex.org/W6764210312"],"related_works":["https://openalex.org/W2964161337","https://openalex.org/W3165421101","https://openalex.org/W2970443625","https://openalex.org/W2802031777","https://openalex.org/W3042684314","https://openalex.org/W2591714514","https://openalex.org/W2952469083","https://openalex.org/W2971055146","https://openalex.org/W3035424311","https://openalex.org/W2765701314","https://openalex.org/W2965025199","https://openalex.org/W3020911106","https://openalex.org/W3008268030","https://openalex.org/W2917744435","https://openalex.org/W3118500814","https://openalex.org/W2975322687","https://openalex.org/W2925468389","https://openalex.org/W2952132225","https://openalex.org/W2617119588","https://openalex.org/W2071332068"],"abstract_inverted_index":{"In":[0],"this":[1,23],"paper,":[2],"we":[3,95],"study":[4,22],"the":[5,26,30,37,42,48,51,122,132],"problem":[6,24],"of":[7,32,39,54,76,88],"learning":[8],"a":[9,17,74,106,110,118,128],"shallow":[10,57],"artificial":[11],"neural":[12,58],"network":[13],"that":[14,46,64,98],"best":[15],"fits":[16],"training":[18,86],"data":[19,87],"set.":[20],"We":[21,44],"in":[25,41],"over-parameterized":[27],"regime":[28],"where":[29,121],"numbers":[31],"observations":[33],"are":[34,124,134],"fewer":[35],"than":[36],"number":[38],"parameters":[40],"model.":[43,113],"show":[45,97],"with":[47],"quadratic":[49],"activations,":[50],"optimization":[52],"landscape":[53],"training,":[55],"such":[56],"networks,":[59],"has":[60],"certain":[61],"favorable":[62],"characteristics":[63],"allow":[65],"globally":[66,111],"optimal":[67,112],"models":[68],"to":[69,109,137],"be":[70],"found":[71],"efficiently":[72],"using":[73],"variety":[75],"local":[77],"search":[78],"heuristics.":[79],"This":[80,114],"result":[81,115],"holds":[82],"for":[83],"an":[84],"arbitrary":[85],"input/output":[89],"pairs.":[90],"For":[91],"differentiable":[92],"activation":[93],"functions,":[94],"also":[96],"gradient":[99],"descent,":[100],"when":[101],"suitably":[102],"initialized,":[103],"converges":[104],"at":[105],"linear":[107],"rate":[108],"focuses":[116],"on":[117],"realizable":[119],"model":[120],"inputs":[123],"chosen":[125],"i.i.d.":[126],"from":[127],"Gaussian":[129],"distribution":[130],"and":[131],"labels":[133],"generated":[135],"according":[136],"planted":[138],"weight":[139],"coefficients.":[140]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":3},{"year":2021,"cited_by_count":3},{"year":2019,"cited_by_count":1},{"year":2018,"cited_by_count":4},{"year":2017,"cited_by_count":3}],"updated_date":"2026-04-09T08:11:56.329763","created_date":"2025-10-10T00:00:00"}