{"id":"https://openalex.org/W2005520864","doi":"https://doi.org/10.1109/ijcnn.2013.6706832","title":"Convergence of a neural network for sparse approximation using the nonsmooth Łojasiewicz inequality","display_name":"Convergence of a neural network for sparse approximation using the nonsmooth Łojasiewicz inequality","publication_year":2013,"publication_date":"2013-08-01","ids":{"openalex":"https://openalex.org/W2005520864","doi":"https://doi.org/10.1109/ijcnn.2013.6706832","mag":"2005520864"},"language":"en","primary_location":{"id":"doi:10.1109/ijcnn.2013.6706832","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2013.6706832","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 2013 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-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/A5066882577","display_name":"Aur\u00e8le Balavoine","orcid":null},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Aurele Balavoine","raw_affiliation_strings":["School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA","Sch. of Electr. & Comput. Eng.,, Georgia Inst. of Technol., Atlanta, GA, USA"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Sch. of Electr. & Comput. Eng.,, Georgia Inst. of Technol., Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5011481913","display_name":"Christopher J. Rozell","orcid":"https://orcid.org/0000-0001-5173-1661"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Christopher J. Rozell","raw_affiliation_strings":["School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA","Sch. of Electr. & Comput. Eng.,, Georgia Inst. of Technol., Atlanta, GA, USA"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Sch. of Electr. & Comput. Eng.,, Georgia Inst. of Technol., Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041443633","display_name":"Justin Romberg","orcid":"https://orcid.org/0000-0002-6616-197X"},"institutions":[{"id":"https://openalex.org/I130701444","display_name":"Georgia Institute of Technology","ror":"https://ror.org/01zkghx44","country_code":"US","type":"education","lineage":["https://openalex.org/I130701444"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Justin Romberg","raw_affiliation_strings":["School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA","Sch. of Electr. & Comput. Eng.,, Georgia Inst. of Technol., Atlanta, GA, USA"],"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, Georgia Institute of Technology, Atlanta, GA","institution_ids":["https://openalex.org/I130701444"]},{"raw_affiliation_string":"Sch. of Electr. & Comput. Eng.,, Georgia Inst. of Technol., Atlanta, GA, USA","institution_ids":["https://openalex.org/I130701444"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5066882577"],"corresponding_institution_ids":["https://openalex.org/I130701444"],"apc_list":null,"apc_paid":null,"fwci":1.0249596,"has_fulltext":false,"cited_by_count":6,"citation_normalized_percentile":{"value":0.76418492,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":96},"biblio":{"volume":"317","issue":null,"first_page":"1","last_page":"8"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.9998999834060669,"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/T10320","display_name":"Neural Networks and Applications","score":0.9990000128746033,"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/T11233","display_name":"Advanced Adaptive Filtering 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"}}],"keywords":[{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.7285650372505188},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5749551057815552},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.564717710018158},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5600371956825256},{"id":"https://openalex.org/keywords/state","display_name":"State (computer science)","score":0.472968727350235},{"id":"https://openalex.org/keywords/approximation-algorithm","display_name":"Approximation algorithm","score":0.4196484088897705},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.23963838815689087},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.22841876745224},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.12407499551773071}],"concepts":[{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7285650372505188},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5749551057815552},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.564717710018158},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5600371956825256},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.472968727350235},{"id":"https://openalex.org/C148764684","wikidata":"https://www.wikidata.org/wiki/Q621751","display_name":"Approximation algorithm","level":2,"score":0.4196484088897705},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.23963838815689087},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.22841876745224},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.12407499551773071},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/ijcnn.2013.6706832","is_oa":false,"landing_page_url":"https://doi.org/10.1109/ijcnn.2013.6706832","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"The 2013 International Joint Conference on Neural Networks (IJCNN)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":12,"referenced_works":["https://openalex.org/W66442755","https://openalex.org/W1551360398","https://openalex.org/W1991693778","https://openalex.org/W2010141219","https://openalex.org/W2021361347","https://openalex.org/W2050745689","https://openalex.org/W2078204800","https://openalex.org/W2100543212","https://openalex.org/W2107306109","https://openalex.org/W2112246162","https://openalex.org/W2156564598","https://openalex.org/W2169273485"],"related_works":["https://openalex.org/W1517908938","https://openalex.org/W2391251536","https://openalex.org/W2362198218","https://openalex.org/W2019521278","https://openalex.org/W1984922432","https://openalex.org/W2375008505","https://openalex.org/W1982750869","https://openalex.org/W2085756966","https://openalex.org/W2350679292","https://openalex.org/W2086348228"],"abstract_inverted_index":{"Sparse":[0],"approximation":[1,53],"is":[2,25,42,67],"an":[3],"optimization":[4,127],"program":[5,128],"that":[6,89,101],"produces":[7],"state-of-the-art":[8],"results":[9,77,117],"in":[10,13,22,35,55,63],"many":[11,131],"applications":[12],"signal":[14],"processing":[15],"and":[16,104,132],"engineering.":[17],"To":[18],"deploy":[19],"this":[20,61],"approach":[21],"real-time,":[23],"it":[24,66],"necessary":[26],"to":[27,47,69,108,121],"develop":[28],"faster":[29],"solvers":[30],"than":[31],"are":[32],"currently":[33],"available":[34],"digital.":[36],"The":[37],"Locally":[38],"Competitive":[39],"Algorithm":[40],"(LCA)":[41],"a":[43,109,122],"dynamical":[44],"system":[45],"designed":[46],"solve":[48],"the":[49,79,82,93,102,126],"class":[50],"of":[51,81,92],"sparse":[52],"problems":[54],"continuous":[56],"time.":[57],"But":[58],"before":[59],"implementing":[60],"network":[62],"analog":[64],"VLSI,":[65],"essential":[68],"provide":[70],"performance":[71],"guarantees.":[72],"This":[73,113],"paper":[74],"presents":[75],"new":[76],"on":[78,115],"convergence":[80,120],"LCA":[83],"neural":[84],"network.":[85],"Using":[86],"recently-developed":[87],"methods":[88],"make":[90],"use":[91],"\u0141ojasiewicz":[94],"inequality":[95],"for":[96],"nonsmooth":[97],"functions,":[98],"we":[99],"prove":[100],"output":[103],"state":[105],"trajectories":[106],"converge":[107],"single":[110],"fixed":[111],"point.":[112],"improves":[114],"previous":[116],"by":[118],"guaranteeing":[119],"singleton":[123],"even":[124],"when":[125],"has":[129],"infinitely":[130],"non-isolated":[133],"solution":[134],"points.":[135]},"counts_by_year":[{"year":2022,"cited_by_count":2},{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":2},{"year":2014,"cited_by_count":1}],"updated_date":"2025-11-06T03:46:38.306776","created_date":"2025-10-10T00:00:00"}