{"id":"https://openalex.org/W4200626151","doi":"https://doi.org/10.1109/tnnls.2021.3131406","title":"Recursion Newton-Like Algorithm for <i>l</i> <sub>2,0</sub>-ReLU Deep Neural Networks","display_name":"Recursion Newton-Like Algorithm for <i>l</i> <sub>2,0</sub>-ReLU Deep Neural Networks","publication_year":2021,"publication_date":"2021-12-13","ids":{"openalex":"https://openalex.org/W4200626151","doi":"https://doi.org/10.1109/tnnls.2021.3131406","pmid":"https://pubmed.ncbi.nlm.nih.gov/34898441"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2021.3131406","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3131406","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/A5100626320","display_name":"Hui Zhang","orcid":"https://orcid.org/0000-0002-5699-9242"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hui Zhang","raw_affiliation_strings":["Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-5699-9242","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109246039","display_name":"Zhengpeng Yuan","orcid":null},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhengpeng Yuan","raw_affiliation_strings":["Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5071551240","display_name":"Naihua Xiu","orcid":"https://orcid.org/0000-0002-3129-2005"},"institutions":[{"id":"https://openalex.org/I21193070","display_name":"Beijing Jiaotong University","ror":"https://ror.org/01yj56c84","country_code":"CN","type":"education","lineage":["https://openalex.org/I21193070"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Naihua Xiu","raw_affiliation_strings":["Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China"],"raw_orcid":"https://orcid.org/0000-0002-3129-2005","affiliations":[{"raw_affiliation_string":"Department of Applied Mathematics, Beijing Jiaotong University, Beijing, China","institution_ids":["https://openalex.org/I21193070"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.7611,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.77015311,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":91,"max":97},"biblio":{"volume":"34","issue":"9","first_page":"5882","last_page":"5896"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10792","display_name":"Matrix Theory and Algorithms","score":0.9987000226974487,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9973000288009644,"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/T12303","display_name":"Tensor decomposition and applications","score":0.9936000108718872,"subfield":{"id":"https://openalex.org/subfields/2605","display_name":"Computational Mathematics"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.658312201499939},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5861421227455139},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.5503919124603271},{"id":"https://openalex.org/keywords/stationary-point","display_name":"Stationary point","score":0.5307552814483643},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.49298402667045593},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4654781222343445},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.45593661069869995},{"id":"https://openalex.org/keywords/minification","display_name":"Minification","score":0.42330342531204224},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.42091476917266846},{"id":"https://openalex.org/keywords/notation","display_name":"Notation","score":0.42045924067497253},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.408951073884964},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3247479796409607},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.2829790413379669},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23906561732292175},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.11665430665016174}],"concepts":[{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.658312201499939},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5861421227455139},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.5503919124603271},{"id":"https://openalex.org/C189237950","wikidata":"https://www.wikidata.org/wiki/Q2500758","display_name":"Stationary point","level":2,"score":0.5307552814483643},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.49298402667045593},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4654781222343445},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.45593661069869995},{"id":"https://openalex.org/C147764199","wikidata":"https://www.wikidata.org/wiki/Q6865248","display_name":"Minification","level":2,"score":0.42330342531204224},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42091476917266846},{"id":"https://openalex.org/C45357846","wikidata":"https://www.wikidata.org/wiki/Q2001982","display_name":"Notation","level":2,"score":0.42045924067497253},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.408951073884964},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3247479796409607},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2829790413379669},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23906561732292175},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.11665430665016174},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2021.3131406","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2021.3131406","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:34898441","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/34898441","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/G2363803437","display_name":null,"funder_award_id":"12131004","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G297500294","display_name":null,"funder_award_id":"Z190002","funder_id":"https://openalex.org/F4320322919","funder_display_name":"Natural Science Foundation of Beijing Municipality"},{"id":"https://openalex.org/G5111687257","display_name":null,"funder_award_id":"11971052","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"},{"id":"https://openalex.org/F4320322919","display_name":"Natural Science Foundation of Beijing Municipality","ror":null}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":79,"referenced_works":["https://openalex.org/W1525689276","https://openalex.org/W1533861849","https://openalex.org/W1673923490","https://openalex.org/W1677182931","https://openalex.org/W1836465849","https://openalex.org/W2101926813","https://openalex.org/W2107878631","https://openalex.org/W2112796928","https://openalex.org/W2119144962","https://openalex.org/W2121733388","https://openalex.org/W2194775991","https://openalex.org/W2460144244","https://openalex.org/W2499540656","https://openalex.org/W2749772809","https://openalex.org/W2758000438","https://openalex.org/W2769449302","https://openalex.org/W2795073474","https://openalex.org/W2799615326","https://openalex.org/W2805029945","https://openalex.org/W2885473730","https://openalex.org/W2886837499","https://openalex.org/W2890038638","https://openalex.org/W2892676835","https://openalex.org/W2900832763","https://openalex.org/W2901951655","https://openalex.org/W2910121883","https://openalex.org/W2911153392","https://openalex.org/W2919115771","https://openalex.org/W2950452769","https://openalex.org/W2962782102","https://openalex.org/W2962817490","https://openalex.org/W2963000224","https://openalex.org/W2963223345","https://openalex.org/W2963562721","https://openalex.org/W2980775160","https://openalex.org/W2981000869","https://openalex.org/W2981407587","https://openalex.org/W2983232253","https://openalex.org/W2994927236","https://openalex.org/W3000322757","https://openalex.org/W3006343684","https://openalex.org/W3011573341","https://openalex.org/W3020910274","https://openalex.org/W3036100489","https://openalex.org/W3080748381","https://openalex.org/W3083491356","https://openalex.org/W3100321043","https://openalex.org/W3101940057","https://openalex.org/W3102511045","https://openalex.org/W3127625569","https://openalex.org/W3132455321","https://openalex.org/W3136021864","https://openalex.org/W3194668998","https://openalex.org/W4243833218","https://openalex.org/W4287363917","https://openalex.org/W4293877733","https://openalex.org/W4294645744","https://openalex.org/W6631943919","https://openalex.org/W6637162671","https://openalex.org/W6638667902","https://openalex.org/W6677580257","https://openalex.org/W6677876225","https://openalex.org/W6694253912","https://openalex.org/W6705072498","https://openalex.org/W6724179616","https://openalex.org/W6725543821","https://openalex.org/W6729999211","https://openalex.org/W6745991264","https://openalex.org/W6752619511","https://openalex.org/W6753892653","https://openalex.org/W6754108890","https://openalex.org/W6755063874","https://openalex.org/W6757677476","https://openalex.org/W6766073595","https://openalex.org/W6771084760","https://openalex.org/W6774993453","https://openalex.org/W6783127570","https://openalex.org/W6788084180","https://openalex.org/W6790503700"],"related_works":["https://openalex.org/W1980381208","https://openalex.org/W1976679120","https://openalex.org/W2364594919","https://openalex.org/W2377519369","https://openalex.org/W2963177394","https://openalex.org/W3202311233","https://openalex.org/W2024638892","https://openalex.org/W2283037149","https://openalex.org/W2944731954","https://openalex.org/W2989495362"],"abstract_inverted_index":{"Rectified":[0],"linear":[1,157],"unit":[2],"(ReLU)":[3],"deep":[4,13],"neural":[5],"network":[6,102],"(DNN)":[7],"is":[8,26,196],"a":[9,54,67,94],"classical":[10],"model":[11,25,92],"in":[12,20,169],"learning":[14],"and":[15,75,140,177,187,198],"has":[16,52],"achieved":[17],"great":[18],"success":[19],"many":[21,30],"applications.":[22],"However,":[23],"this":[24,60,63],"characterized":[27],"by":[28,98,164],"too":[29],"parameters,":[31],"which":[32,154],"not":[33],"only":[34],"requires":[35],"huge":[36],"memory":[37],"but":[38],"also":[39],"imposes":[40],"unbearable":[41],"computation":[42],"burden.":[43],"The":[44],"<inline-formula":[45,79],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[46,80],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">":[47,81],"<tex-math":[48,82],"notation=\"LaTeX\">$l_{2,0}$":[49,83],"</tex-math></inline-formula>":[50,84],"regularization":[51],"become":[53],"useful":[55],"technique":[56],"to":[57,72,146],"cope":[58],"with":[59,78,173],"trouble.":[61],"In":[62],"article,":[64],"we":[65,87,118,126],"design":[66],"recursion":[68],"Newton-like":[69,167],"algorithm":[70],"(RNLA)":[71],"simultaneously":[73],"train":[74],"compress":[76],"ReLU-DNNs":[77],"regularization.":[85],"First,":[86],"reformulate":[88],"the":[89,101,105,108,112,116,128,137,165,188,192],"multicomposite":[90],"training":[91],"into":[93],"constrained":[95],"optimization":[96],"problem":[97],"explicitly":[99],"introducing":[100],"nodes":[103],"as":[104],"variables":[106],"of":[107,115,122,136,151],"optimization.":[109],"Based":[110],"on":[111,184],"penalty":[113],"function":[114],"reformulation,":[117],"obtain":[119],"two":[120,138,149],"types":[121],"minimization":[123],"subproblems.":[124],"Second,":[125],"build":[127],"first-order":[129],"optimality":[130],"conditions":[131],"for":[132],"acquiring":[133],"P-stationary":[134,142],"points":[135,143],"subproblems,":[139],"these":[141,162],"enable":[144],"us":[145],"equivalently":[147],"derive":[148],"sequences":[150],"stationary":[152],"equations,":[153],"are":[155,182],"piecewise":[156],"matrix":[158],"equations.":[159],"We":[160],"solve":[161],"equations":[163],"column":[166],"method":[168,194],"group":[170],"sparse":[171],"subspace":[172],"lower":[174],"computational":[175],"scale":[176],"cost.":[178],"Finally,":[179],"numerical":[180],"experiments":[181],"conducted":[183],"real":[185],"datasets,":[186],"results":[189],"demonstrate":[190],"that":[191],"proposed":[193],"RNLA":[195],"effective":[197],"applicable.":[199]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":3},{"year":2022,"cited_by_count":2}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2021-12-31T00:00:00"}