{"id":"https://openalex.org/W4386695561","doi":"https://doi.org/10.1142/s2972335323500011","title":"Asymptotic Edge of Chaos as Guiding Principle for Neural Network Training","display_name":"Asymptotic Edge of Chaos as Guiding Principle for Neural Network Training","publication_year":2023,"publication_date":"2023-09-13","ids":{"openalex":"https://openalex.org/W4386695561","doi":"https://doi.org/10.1142/s2972335323500011"},"language":"en","primary_location":{"id":"doi:10.1142/s2972335323500011","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s2972335323500011","pdf_url":null,"source":{"id":"https://openalex.org/S5407039934","display_name":"International Journal of Artificial Intelligence and Robotics Research","issn_l":"2972-3353","issn":["2972-3353","2972-3361"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Artificial Intelligence and Robotics Research","raw_type":"journal-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/A5101742585","display_name":"Lin Zhang","orcid":"https://orcid.org/0009-0003-4398-3430"},"institutions":[{"id":"https://openalex.org/I115228651","display_name":"Agency for Science, Technology and Research","ror":"https://ror.org/036wvzt09","country_code":"SG","type":"government","lineage":["https://openalex.org/I115228651"]},{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I3004594783","display_name":"Institute of High Performance Computing","ror":"https://ror.org/02n0ejh50","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I3004594783","https://openalex.org/I91275662"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Lin Zhang","raw_affiliation_strings":["Department of Physics, Faculty of Science, National University of Singapore, Singapore 117551, Singapore","Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore 138632, Singapore"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Faculty of Science, National University of Singapore, Singapore 117551, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore 138632, Singapore","institution_ids":["https://openalex.org/I3004594783","https://openalex.org/I115228651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042150866","display_name":"Ling Feng","orcid":"https://orcid.org/0000-0001-6578-2558"},"institutions":[{"id":"https://openalex.org/I115228651","display_name":"Agency for Science, Technology and Research","ror":"https://ror.org/036wvzt09","country_code":"SG","type":"government","lineage":["https://openalex.org/I115228651"]},{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]},{"id":"https://openalex.org/I3004594783","display_name":"Institute of High Performance Computing","ror":"https://ror.org/02n0ejh50","country_code":"SG","type":"facility","lineage":["https://openalex.org/I115228651","https://openalex.org/I3004594783","https://openalex.org/I91275662"]}],"countries":["SG"],"is_corresponding":true,"raw_author_name":"Ling Feng","raw_affiliation_strings":["Department of Physics, Faculty of Science, National University of Singapore, Singapore 117551, Singapore","IHPC, Agency for Science, Technology and Research, Singapore, Singapore 138632, Singapore","Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore 138632, Singapore"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Faculty of Science, National University of Singapore, Singapore 117551, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"IHPC, Agency for Science, Technology and Research, Singapore, Singapore 138632, Singapore","institution_ids":["https://openalex.org/I115228651"]},{"raw_affiliation_string":"Institute of High Performance Computing, Agency for Science, Technology and Research (A*STAR), Singapore 138632, Singapore","institution_ids":["https://openalex.org/I3004594783","https://openalex.org/I115228651"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100636629","display_name":"Kan Chen","orcid":"https://orcid.org/0000-0002-4002-7297"},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Kan Chen","raw_affiliation_strings":["Department of Mathematics, Faculty of Science, National University of Singapore, Singapore 119076, Singapore","Risk Management Institute, National University of Singapore, Singapore 119613, Singapore"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, Faculty of Science, National University of Singapore, Singapore 119076, Singapore","institution_ids":["https://openalex.org/I165932596"]},{"raw_affiliation_string":"Risk Management Institute, National University of Singapore, Singapore 119613, Singapore","institution_ids":["https://openalex.org/I165932596"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101742823","display_name":"Choy Heng Lai","orcid":null},"institutions":[{"id":"https://openalex.org/I165932596","display_name":"National University of Singapore","ror":"https://ror.org/01tgyzw49","country_code":"SG","type":"education","lineage":["https://openalex.org/I165932596"]}],"countries":["SG"],"is_corresponding":false,"raw_author_name":"Choy Heng Lai","raw_affiliation_strings":["Department of Physics, Faculty of Science, National University of Singapore, Singapore 117551, Singapore"],"affiliations":[{"raw_affiliation_string":"Department of Physics, Faculty of Science, National University of Singapore, Singapore 117551, Singapore","institution_ids":["https://openalex.org/I165932596"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5042150866"],"corresponding_institution_ids":["https://openalex.org/I115228651","https://openalex.org/I165932596","https://openalex.org/I3004594783"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.11644545,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"01","issue":"01","first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9968000054359436,"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":0.9968000054359436,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.9736999869346619,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9401000142097473,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/edge-of-chaos","display_name":"Edge of chaos","score":0.7046958208084106},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.6505131721496582},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.6258893013000488},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5737938284873962},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5164744853973389},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.5013959407806396},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.44145476818084717},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.4203639626502991},{"id":"https://openalex.org/keywords/enhanced-data-rates-for-gsm-evolution","display_name":"Enhanced Data Rates for GSM Evolution","score":0.41265127062797546},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.377651184797287},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.35143452882766724},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.33721059560775757},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.33111363649368286}],"concepts":[{"id":"https://openalex.org/C2780713532","wikidata":"https://www.wikidata.org/wiki/Q93158","display_name":"Edge of chaos","level":2,"score":0.7046958208084106},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6505131721496582},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.6258893013000488},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5737938284873962},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5164744853973389},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.5013959407806396},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.44145476818084717},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.4203639626502991},{"id":"https://openalex.org/C162307627","wikidata":"https://www.wikidata.org/wiki/Q204833","display_name":"Enhanced Data Rates for GSM Evolution","level":2,"score":0.41265127062797546},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.377651184797287},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.35143452882766724},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.33721059560775757},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.33111363649368286},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"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/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1142/s2972335323500011","is_oa":false,"landing_page_url":"https://doi.org/10.1142/s2972335323500011","pdf_url":null,"source":{"id":"https://openalex.org/S5407039934","display_name":"International Journal of Artificial Intelligence and Robotics Research","issn_l":"2972-3353","issn":["2972-3353","2972-3361"],"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":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Artificial Intelligence and Robotics Research","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G4779386528","display_name":null,"funder_award_id":"ACADEMIC RESEARCH FUND (AcRF) R-144-000-415-114","funder_id":"https://openalex.org/F4320320709","funder_display_name":"National Research Foundation Singapore"}],"funders":[{"id":"https://openalex.org/F4320320709","display_name":"National Research Foundation Singapore","ror":"https://ror.org/03cpyc314"}],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":22,"referenced_works":["https://openalex.org/W1527520754","https://openalex.org/W1991904924","https://openalex.org/W2022820481","https://openalex.org/W2027802883","https://openalex.org/W2042489792","https://openalex.org/W2064512219","https://openalex.org/W2074683236","https://openalex.org/W2079166245","https://openalex.org/W2087327526","https://openalex.org/W2116621978","https://openalex.org/W2160815625","https://openalex.org/W2177218873","https://openalex.org/W2257979135","https://openalex.org/W2529714286","https://openalex.org/W2559655401","https://openalex.org/W2598912124","https://openalex.org/W2604272474","https://openalex.org/W2919115771","https://openalex.org/W2959995783","https://openalex.org/W2998483963","https://openalex.org/W3083720136","https://openalex.org/W4207074716"],"related_works":["https://openalex.org/W2373629362","https://openalex.org/W2371138613","https://openalex.org/W2023463163","https://openalex.org/W2048963458","https://openalex.org/W43109613","https://openalex.org/W2359952343","https://openalex.org/W2080152487","https://openalex.org/W2239445980","https://openalex.org/W2995553446","https://openalex.org/W2952585100"],"abstract_inverted_index":{"It":[0],"has":[1],"been":[2],"recently":[3],"demonstrated":[4],"that":[5,81,111,161],"optimal":[6,106],"neural":[7,19,78],"networks":[8],"operate":[9],"near":[10],"the":[11,29,44,53,59,63,88,93,105,112,117,128,132,140,143,151,166,170,178],"asymptotic":[12,33],"edge":[13,118,144],"of":[14,32,67,87,119,145,155,184],"chaos":[15,120,146],"for":[16,138],"state-of-the-art":[17],"feed-forward":[18],"networks,":[20],"where":[21],"its":[22,148],"generalization":[23],"power":[24],"is":[25,147],"maximal":[26],"due":[27],"to":[28,38,42,58,103,130,177],"highest":[30,133],"number":[31],"metastable":[34],"states.":[35],"However,":[36],"how":[37],"leverage":[39],"this":[40],"principle":[41],"improve":[43],"model":[45,54,69,80,113,129,141],"training":[46,57,86,94,171],"process":[47],"remains":[48],"open.":[49],"Here,":[50],"by":[51],"mapping":[52],"evolution":[55],"during":[56,121],"phase":[60],"diagram":[61],"in":[62,70,169],"classic":[64],"analytic":[65],"result":[66],"Sherrington\u2013Kirkpatrick":[68],"spin":[71],"glasses,":[72],"we":[73,98,159],"illustrate":[74],"on":[75,188],"a":[76,100],"simple":[77,182],"network":[79,89],"one":[82],"can":[83],"provide":[84,99],"principled":[85],"without":[90,191],"manually":[91],"tuning":[92],"hyper-parameters.":[95],"In":[96],"particular,":[97],"semi-analytical":[101],"method":[102],"set":[104],"weight":[107],"decay":[108],"strength,":[109],"such":[110,124],"will":[114],"converge":[115],"toward":[116],"training.":[122],"Consequently,":[123],"hyper-parameter":[125],"setting":[126],"leads":[127],"achieve":[131],"test":[134],"accuracy.":[135],"Another":[136],"benefit":[137],"restricting":[139],"at":[142],"robustness":[149],"against":[150],"common":[152],"practical":[153],"problem":[154],"label":[156],"noise,":[157],"as":[158],"find":[160],"it":[162],"automatically":[163],"avoids":[164],"fitting":[165,176],"shuffled":[167],"labels":[168,190],"samples":[172],"while":[173],"maintaining":[174],"good":[175,186],"correct":[179],"labels,":[180],"providing":[181],"means":[183],"achieving":[185],"performance":[187],"noisy":[189],"any":[192],"additional":[193],"treatment.":[194]},"counts_by_year":[],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
