{"id":"https://openalex.org/W2800287482","doi":"https://doi.org/10.1109/icassp.2018.8462001","title":"A Random Matrix and Concentration Inequalities Framework for Neural Networks Analysis","display_name":"A Random Matrix and Concentration Inequalities Framework for Neural Networks Analysis","publication_year":2018,"publication_date":"2018-04-01","ids":{"openalex":"https://openalex.org/W2800287482","doi":"https://doi.org/10.1109/icassp.2018.8462001","mag":"2800287482"},"language":"en","primary_location":{"id":"doi:10.1109/icassp.2018.8462001","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2018.8462001","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://hal.science/hal-01962077","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5045532672","display_name":"Cosme Louart","orcid":null},"institutions":[{"id":"https://openalex.org/I2738703131","display_name":"Commissariat \u00e0 l'\u00c9nergie Atomique et aux \u00c9nergies Alternatives","ror":"https://ror.org/00jjx8s55","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131"]},{"id":"https://openalex.org/I4210085861","display_name":"Laboratoire d'Int\u00e9gration des Syst\u00e8mes et des Technologies","ror":"https://ror.org/000dbcc61","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210085861","https://openalex.org/I4210117989"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4210124956","display_name":"GIPSA-Lab","ror":"https://ror.org/02wrme198","country_code":"FR","type":"facility","lineage":["https://openalex.org/I106785703","https://openalex.org/I1294671590","https://openalex.org/I4210124956","https://openalex.org/I899635006","https://openalex.org/I899635006"]},{"id":"https://openalex.org/I4210128565","display_name":"CEA Paris-Saclay","ror":"https://ror.org/03n15ch10","country_code":"FR","type":"government","lineage":["https://openalex.org/I2738703131","https://openalex.org/I277688954","https://openalex.org/I4210128565"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Cosme Louart","raw_affiliation_strings":["CentraleSup\u00b4elec, Gif-sur-Yvette, France","GIPSA-CICS - GIPSA - Communication Information and Complex Systems (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)","LVIC - Laboratoire Vision et Ing\u00e9nierie des Contenus (CEA Saclay Nano-INNOV Institut CEA LIST Point courrier n\u00b0173 91 191 Gif sur Yvette CEDEX - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CentraleSup\u00b4elec, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210107720"]},{"raw_affiliation_string":"GIPSA-CICS - GIPSA - Communication Information and Complex Systems (GIPSA-lab, 11 rue des Math\u00e9matiques, Grenoble Campus BP46, F-38402 SAINT MARTIN D'HERES CEDEX - France)","institution_ids":["https://openalex.org/I4210124956"]},{"raw_affiliation_string":"LVIC - Laboratoire Vision et Ing\u00e9nierie des Contenus (CEA Saclay Nano-INNOV Institut CEA LIST Point courrier n\u00b0173 91 191 Gif sur Yvette CEDEX - France)","institution_ids":["https://openalex.org/I2738703131","https://openalex.org/I4210085861","https://openalex.org/I4210128565"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5021257434","display_name":"Romain Couillet","orcid":"https://orcid.org/0000-0001-5755-2090"},"institutions":[{"id":"https://openalex.org/I4210097418","display_name":"Laboratoire des signaux et syst\u00e8mes","ror":"https://ror.org/00skw9v43","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I277688954","https://openalex.org/I277688954","https://openalex.org/I4210097418","https://openalex.org/I4210107720"]},{"id":"https://openalex.org/I4210107720","display_name":"CentraleSup\u00e9lec","ror":"https://ror.org/019tcpt25","country_code":"FR","type":"facility","lineage":["https://openalex.org/I277688954","https://openalex.org/I4210107720"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"Romain Couillet","raw_affiliation_strings":["CentraleSup\u00b4elec, Gif-sur-Yvette, France","L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"CentraleSup\u00b4elec, Gif-sur-Yvette, France","institution_ids":["https://openalex.org/I4210107720"]},{"raw_affiliation_string":"L2S - Laboratoire des signaux et syst\u00e8mes (Plateau de Moulon 3 rue Joliot Curie 91192 GIF SUR YVETTE CEDEX - France)","institution_ids":["https://openalex.org/I4210097418"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":6,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":"132","issue":null,"first_page":"4214","last_page":"4218"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11716","display_name":"Random Matrices and Applications","score":0.9993000030517578,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.9984999895095825,"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"}},{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9977999925613403,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.7048916816711426},{"id":"https://openalex.org/keywords/lipschitz-continuity","display_name":"Lipschitz continuity","score":0.6390863060951233},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6351280808448792},{"id":"https://openalex.org/keywords/random-matrix","display_name":"Random matrix","score":0.5715531706809998},{"id":"https://openalex.org/keywords/stochastic-neural-network","display_name":"Stochastic neural network","score":0.5158966779708862},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5080745220184326},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.5063115358352661},{"id":"https://openalex.org/keywords/limiting","display_name":"Limiting","score":0.4886665642261505},{"id":"https://openalex.org/keywords/concentration-inequality","display_name":"Concentration inequality","score":0.466727614402771},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4301188290119171},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4226638078689575},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37011289596557617},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3212512135505676},{"id":"https://openalex.org/keywords/time-delay-neural-network","display_name":"Time delay neural network","score":0.17645809054374695},{"id":"https://openalex.org/keywords/pure-mathematics","display_name":"Pure mathematics","score":0.09132122993469238}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7048916816711426},{"id":"https://openalex.org/C22324862","wikidata":"https://www.wikidata.org/wiki/Q652707","display_name":"Lipschitz continuity","level":2,"score":0.6390863060951233},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6351280808448792},{"id":"https://openalex.org/C64812099","wikidata":"https://www.wikidata.org/wiki/Q176604","display_name":"Random matrix","level":3,"score":0.5715531706809998},{"id":"https://openalex.org/C86582703","wikidata":"https://www.wikidata.org/wiki/Q7617824","display_name":"Stochastic neural network","level":4,"score":0.5158966779708862},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5080745220184326},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.5063115358352661},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.4886665642261505},{"id":"https://openalex.org/C2777169571","wikidata":"https://www.wikidata.org/wiki/Q5158328","display_name":"Concentration inequality","level":2,"score":0.466727614402771},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4301188290119171},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4226638078689575},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37011289596557617},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3212512135505676},{"id":"https://openalex.org/C175202392","wikidata":"https://www.wikidata.org/wiki/Q2434543","display_name":"Time delay neural network","level":3,"score":0.17645809054374695},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.09132122993469238},{"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/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C78519656","wikidata":"https://www.wikidata.org/wiki/Q101333","display_name":"Mechanical engineering","level":1,"score":0.0},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.0},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","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}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/icassp.2018.8462001","is_oa":false,"landing_page_url":"https://doi.org/10.1109/icassp.2018.8462001","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2018 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP)","raw_type":"proceedings-article"},{"id":"pmh:oai:HAL:hal-01962077v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01962077","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ICASSP 2018 - IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2018, Calgary, Canada. &#x27E8;10.1109/ICASSP.2018.8462001&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"}],"best_oa_location":{"id":"pmh:oai:HAL:hal-01962077v1","is_oa":true,"landing_page_url":"https://hal.science/hal-01962077","pdf_url":null,"source":{"id":"https://openalex.org/S4306402512","display_name":"HAL (Le Centre pour la Communication Scientifique Directe)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1294671590","host_organization_name":"Centre National de la Recherche Scientifique","host_organization_lineage":["https://openalex.org/I1294671590"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ICASSP 2018 - IEEE International Conference on Acoustics, Speech and Signal Processing, Apr 2018, Calgary, Canada. &#x27E8;10.1109/ICASSP.2018.8462001&#x27E9;","raw_type":"info:eu-repo/semantics/conferenceObject"},"sustainable_development_goals":[{"score":0.46000000834465027,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"},{"score":0.4099999964237213,"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W602904462","https://openalex.org/W615589970","https://openalex.org/W1573820523","https://openalex.org/W1586554030","https://openalex.org/W1596717185","https://openalex.org/W1644055776","https://openalex.org/W1829169350","https://openalex.org/W1899249567","https://openalex.org/W2111072639","https://openalex.org/W2125930537","https://openalex.org/W2132657058","https://openalex.org/W2136341714","https://openalex.org/W2577176882","https://openalex.org/W2618381130","https://openalex.org/W2710361134","https://openalex.org/W2963586744","https://openalex.org/W2963650649","https://openalex.org/W2963971929","https://openalex.org/W4250954493","https://openalex.org/W6639736602","https://openalex.org/W6681804681","https://openalex.org/W6734074438","https://openalex.org/W6738685885","https://openalex.org/W6739901026"],"related_works":["https://openalex.org/W3185235544","https://openalex.org/W4297791327","https://openalex.org/W2897842840","https://openalex.org/W2911623553","https://openalex.org/W2397777611","https://openalex.org/W1502031429","https://openalex.org/W2318923278","https://openalex.org/W2417585376","https://openalex.org/W3194228126","https://openalex.org/W4322825348"],"abstract_inverted_index":{"This":[0,23,45],"article":[1],"provides":[2],"a":[3,11,18,29],"theoretical":[4],"analysis":[5,54],"of":[6,10,42,48,87],"the":[7,33,40,62,66,84,88],"asymptotic":[8],"performance":[9],"regression":[12],"or":[13],"classification":[14],"task":[15],"performed":[16],"by":[17,27,65],"simple":[19],"random":[20,36,89],"neural":[21,52,90],"network.":[22],"result":[24],"is":[25,47],"obtained":[26,99],"leveraging":[28],"new":[30],"framework":[31],"at":[32,55],"crossroads":[34],"between":[35],"matrix":[37],"theory":[38],"and":[39,93],"concentration":[41],"measure":[43],"theory.":[44],"approach":[46],"utmost":[49],"interest":[50],"for":[51,83],"network":[53,91],"large":[56],"in":[57],"that":[58,72],"it":[59],"naturally":[60],"dismisses":[61],"difficulty":[63],"induced":[64],"non-linear":[67],"activation":[68],"functions,":[69],"so":[70],"long":[71],"these":[73],"are":[74],"Lipschitz":[75],"functions.":[76],"As":[77],"an":[78],"application,":[79],"we":[80],"provide":[81],"formulas":[82],"limiting":[85],"law":[86],"output":[92],"compare":[94],"them":[95],"conclusively":[96],"to":[97],"those":[98],"practically":[100],"on":[101],"handwritten":[102],"digits":[103],"databases.":[104]},"counts_by_year":[],"updated_date":"2026-07-25T15:57:00.446498","created_date":"2025-10-10T00:00:00"}
