{"id":"https://openalex.org/W3018505745","doi":"https://doi.org/10.3390/sym12040660","title":"A Novel Learning Rate Schedule in Optimization for Neural Networks and It\u2019s Convergence","display_name":"A Novel Learning Rate Schedule in Optimization for Neural Networks and It\u2019s Convergence","publication_year":2020,"publication_date":"2020-04-22","ids":{"openalex":"https://openalex.org/W3018505745","doi":"https://doi.org/10.3390/sym12040660","mag":"3018505745"},"language":"en","primary_location":{"id":"doi:10.3390/sym12040660","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040660","pdf_url":"https://www.mdpi.com/2073-8994/12/4/660/pdf?version=1587554200","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/2073-8994/12/4/660/pdf?version=1587554200","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100710876","display_name":"Ji\u2010Eun Park","orcid":"https://orcid.org/0000-0001-5698-9565"},"institutions":[{"id":"https://openalex.org/I9323808","display_name":"Daegu University","ror":"https://ror.org/01zqccq48","country_code":"KR","type":"education","lineage":["https://openalex.org/I9323808"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Jieun Park","raw_affiliation_strings":["Seongsan Liberal Arts College, Daegu University, Kyungsan 38453, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Seongsan Liberal Arts College, Daegu University, Kyungsan 38453, Korea","institution_ids":["https://openalex.org/I9323808"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035754746","display_name":"Dokkyun Yi","orcid":null},"institutions":[{"id":"https://openalex.org/I9323808","display_name":"Daegu University","ror":"https://ror.org/01zqccq48","country_code":"KR","type":"education","lineage":["https://openalex.org/I9323808"]}],"countries":["KR"],"is_corresponding":false,"raw_author_name":"Dokkyun Yi","raw_affiliation_strings":["Seongsan Liberal Arts College, Daegu University, Kyungsan 38453, Korea"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Seongsan Liberal Arts College, Daegu University, Kyungsan 38453, Korea","institution_ids":["https://openalex.org/I9323808"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5052851457","display_name":"Sangmin Ji","orcid":"https://orcid.org/0000-0003-3930-985X"},"institutions":[{"id":"https://openalex.org/I196345858","display_name":"Chungnam National University","ror":"https://ror.org/0227as991","country_code":"KR","type":"education","lineage":["https://openalex.org/I196345858"]}],"countries":["KR"],"is_corresponding":true,"raw_author_name":"Sangmin Ji","raw_affiliation_strings":["Department of Mathematics, College of Natural Sciences, Chungnam National University, Daejeon 34134, Korea"],"raw_orcid":"https://orcid.org/0000-0003-3930-985X","affiliations":[{"raw_affiliation_string":"Department of Mathematics, College of Natural Sciences, Chungnam National University, Daejeon 34134, Korea","institution_ids":["https://openalex.org/I196345858"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5052851457"],"corresponding_institution_ids":["https://openalex.org/I196345858"],"apc_list":{"value":2000,"currency":"CHF","value_usd":2165},"apc_paid":{"value":2000,"currency":"CHF","value_usd":2165},"fwci":3.5363,"has_fulltext":false,"cited_by_count":43,"citation_normalized_percentile":{"value":0.939939,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":99},"biblio":{"volume":"12","issue":"4","first_page":"660","last_page":"660"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998999834060669,"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":0.9998999834060669,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9993000030517578,"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/T12072","display_name":"Machine Learning and Algorithms","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"}}],"keywords":[{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.7053148746490479},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6863878965377808},{"id":"https://openalex.org/keywords/schedule","display_name":"Schedule","score":0.6515527963638306},{"id":"https://openalex.org/keywords/monotonic-function","display_name":"Monotonic function","score":0.6418050527572632},{"id":"https://openalex.org/keywords/rate-of-convergence","display_name":"Rate of convergence","score":0.6384992003440857},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.5989459753036499},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.5862325429916382},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5191368460655212},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.46427008509635925},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.31634846329689026},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.24387133121490479},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.07034125924110413}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7053148746490479},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6863878965377808},{"id":"https://openalex.org/C68387754","wikidata":"https://www.wikidata.org/wiki/Q7271585","display_name":"Schedule","level":2,"score":0.6515527963638306},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.6418050527572632},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.6384992003440857},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.5989459753036499},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.5862325429916382},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5191368460655212},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.46427008509635925},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.31634846329689026},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24387133121490479},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.07034125924110413},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","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},{"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/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/sym12040660","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040660","pdf_url":"https://www.mdpi.com/2073-8994/12/4/660/pdf?version=1587554200","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:1a54bcf3652d40ef810a3243e878465e","is_oa":true,"landing_page_url":"https://doaj.org/article/1a54bcf3652d40ef810a3243e878465e","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Symmetry, Vol 12, Iss 4, p 660 (2020)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/sym12040660","is_oa":true,"landing_page_url":"https://doi.org/10.3390/sym12040660","pdf_url":"https://www.mdpi.com/2073-8994/12/4/660/pdf?version=1587554200","source":{"id":"https://openalex.org/S190787756","display_name":"Symmetry","issn_l":"2073-8994","issn":["2073-8994"],"is_oa":true,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Symmetry","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G500070973","display_name":null,"funder_award_id":"NRF-2017R1E1A1A03070311","funder_id":"https://openalex.org/F4320322120","funder_display_name":"National Research Foundation of Korea"}],"funders":[{"id":"https://openalex.org/F4320322120","display_name":"National Research Foundation of Korea","ror":"https://ror.org/013aysd81"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":28,"referenced_works":["https://openalex.org/W6908809","https://openalex.org/W19621276","https://openalex.org/W104184427","https://openalex.org/W648446685","https://openalex.org/W1491468723","https://openalex.org/W1498436455","https://openalex.org/W1806891645","https://openalex.org/W1844261860","https://openalex.org/W1904365287","https://openalex.org/W1970789124","https://openalex.org/W2123224804","https://openalex.org/W2124541940","https://openalex.org/W2143476164","https://openalex.org/W2146502635","https://openalex.org/W2160815625","https://openalex.org/W2163605009","https://openalex.org/W2168231600","https://openalex.org/W2951650375","https://openalex.org/W2951651062","https://openalex.org/W2963433607","https://openalex.org/W2980844465","https://openalex.org/W2990219166","https://openalex.org/W3004917840","https://openalex.org/W4206097460","https://openalex.org/W6631190155","https://openalex.org/W6635753154","https://openalex.org/W6681435938","https://openalex.org/W6684859321"],"related_works":["https://openalex.org/W2077314575","https://openalex.org/W4315701745","https://openalex.org/W1990290471","https://openalex.org/W4380682190","https://openalex.org/W2005710836","https://openalex.org/W2102386043","https://openalex.org/W2945307361","https://openalex.org/W1987764909","https://openalex.org/W2116636209","https://openalex.org/W2053698688"],"abstract_inverted_index":{"The":[0],"process":[1,39],"of":[2,40,139,180],"machine":[3],"learning":[4,16,74,112,133,151,191,199],"is":[5,20,76,83,108,148,152,192],"to":[6,47,60,86,102,109,124,136,168],"find":[7,125],"parameters":[8,25,33,55,128,157],"that":[9,27,163,174,190],"minimize":[10],"the":[11,17,24,31,38,42,49,54,62,65,73,79,103,111,116,126,132,137,140,145,150,155,164,169,181,197],"cost":[12,141,146,182],"function":[13,147,183],"constructed":[14],"by":[15],"data.":[18],"This":[19,160,172],"called":[21,30],"optimization":[22,51],"and":[23,154],"at":[26,97],"time":[28,81],"are":[29,92,158],"optimal":[32,63,127,156,170],"in":[34,58,71,202],"neural":[35],"networks.":[36],"In":[37],"finding":[41],"optimization,":[43],"there":[44],"were":[45],"attempts":[46],"solve":[48],"symmetric":[50],"or":[52,82],"initialize":[53],"symmetrically.":[56],"Furthermore,":[57],"order":[59],"obtain":[61],"parameters,":[64],"existing":[66],"methods":[67,70,91],"have":[68],"used":[69],"which":[72,129],"rate":[75,100,113,134,200],"decreased":[77],"over":[78],"iteration":[80,104],"changed":[84],"according":[85,101,135],"a":[87,93,98,122,178],"certain":[88],"ratio.":[89],"These":[90],"monotonically":[94,117],"decreasing":[95,118],"method":[96,123,165,176],"constant":[99],"time.":[105],"Our":[106],"idea":[107],"make":[110],"changeable":[114],"unlike":[115],"method.":[119],"We":[120],"introduce":[121],"adaptively":[130],"changes":[131],"value":[138],"function.":[142],"Therefore,":[143],"when":[144,195],"optimized,":[149],"complete":[153],"obtained.":[159],"paper":[161],"proves":[162],"ensures":[166],"convergence":[167],"parameters.":[171],"means":[173],"our":[175],"achieves":[177],"minimum":[179],"(or":[184],"effective":[185,194],"learning).":[186],"Numerical":[187],"experiments":[188],"demonstrate":[189],"good":[193],"using":[196],"proposed":[198],"schedule":[201],"various":[203],"situations.":[204]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":7},{"year":2024,"cited_by_count":9},{"year":2023,"cited_by_count":5},{"year":2022,"cited_by_count":9},{"year":2021,"cited_by_count":9},{"year":2020,"cited_by_count":3}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}