{"id":"https:\/\/openalex.org\/W4324326676","doi":"https:\/\/doi.org\/10.48550\/arxiv.2303.06726","title":"Global Optimality of Elman-type RNN in the Mean-Field Regime","display_name":"Global Optimality of Elman-type RNN in the Mean-Field Regime","publication_year":2023,"publication_date":"2023-03-12","ids":{"openalex":"https:\/\/openalex.org\/W4324326676","doi":"https:\/\/doi.org\/10.48550\/arxiv.2303.06726"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2303.06726","is_oa":true,"landing_page_url":"http:\/\/arxiv.org\/abs\/2303.06726","pdf_url":"https:\/\/arxiv.org\/pdf\/2303.06726","source":{"id":"https:\/\/openalex.org\/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https:\/\/openalex.org\/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https:\/\/openalex.org\/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https:\/\/arxiv.org\/pdf\/2303.06726","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https:\/\/openalex.org\/A5046714529","display_name":"Andr\u00e9a Agazzi","orcid":"https:\/\/orcid.org\/0000-0001-7498-6034"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Agazzi, Andrea","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https:\/\/openalex.org\/A5061472917","display_name":"Jianfeng Lu","orcid":"https:\/\/orcid.org\/0000-0001-6255-5165"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lu, Jianfeng","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https:\/\/openalex.org\/A5036208626","display_name":"Sayan Mukherjee","orcid":"https:\/\/orcid.org\/0000-0002-2032-2707"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mukherjee, Sayan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":3,"corresponding_author_ids":["https:\/\/openalex.org\/A5046714529"],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"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":0.9882000088691711,"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":0.9882000088691711,"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\/T12676","display_name":"Machine Learning and ELM","score":0.9832000136375427,"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\/T11206","display_name":"Model Reduction and Neural Networks","score":0.9811000227928162,"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\/initialization","display_name":"Initialization","score":0.8086966872215271},{"id":"https:\/\/openalex.org\/keywords\/recurrent-neural-network","display_name":"Recurrent neural network","score":0.782386302947998},{"id":"https:\/\/openalex.org\/keywords\/convergence","display_name":"Convergence (economics)","score":0.7338035106658936},{"id":"https:\/\/openalex.org\/keywords\/limit","display_name":"Limit (mathematics)","score":0.6193487644195557},{"id":"https:\/\/openalex.org\/keywords\/gradient-descent","display_name":"Gradient descent","score":0.5469118356704712},{"id":"https:\/\/openalex.org\/keywords\/limiting","display_name":"Limiting","score":0.5413411259651184},{"id":"https:\/\/openalex.org\/keywords\/feature","display_name":"Feature (linguistics)","score":0.5249231457710266},{"id":"https:\/\/openalex.org\/keywords\/computer-science","display_name":"Computer science","score":0.47039565443992615},{"id":"https:\/\/openalex.org\/keywords\/mean-field-theory","display_name":"Mean field theory","score":0.46663886308670044},{"id":"https:\/\/openalex.org\/keywords\/type","display_name":"Type (biology)","score":0.4235367178916931},{"id":"https:\/\/openalex.org\/keywords\/field","display_name":"Field (mathematics)","score":0.42132464051246643},{"id":"https:\/\/openalex.org\/keywords\/mathematics","display_name":"Mathematics","score":0.38361290097236633},{"id":"https:\/\/openalex.org\/keywords\/mathematical-optimization","display_name":"Mathematical optimization","score":0.3431435525417328},{"id":"https:\/\/openalex.org\/keywords\/artificial-neural-network","display_name":"Artificial neural network","score":0.3181006908416748},{"id":"https:\/\/openalex.org\/keywords\/artificial-intelligence","display_name":"Artificial intelligence","score":0.2805226445198059},{"id":"https:\/\/openalex.org\/keywords\/physics","display_name":"Physics","score":0.11331754922866821},{"id":"https:\/\/openalex.org\/keywords\/mathematical-analysis","display_name":"Mathematical analysis","score":0.08056363463401794},{"id":"https:\/\/openalex.org\/keywords\/engineering","display_name":"Engineering","score":0.06410112977027893}],"concepts":[{"id":"https:\/\/openalex.org\/C114466953","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q6034165","display_name":"Initialization","level":2,"score":0.8086966872215271},{"id":"https:\/\/openalex.org\/C147168706","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.782386302947998},{"id":"https:\/\/openalex.org\/C2777303404","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q759757","display_name":"Convergence (economics)","level":2,"score":0.7338035106658936},{"id":"https:\/\/openalex.org\/C151201525","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6193487644195557},{"id":"https:\/\/openalex.org\/C153258448","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q1199743","display_name":"Gradient descent","level":3,"score":0.5469118356704712},{"id":"https:\/\/openalex.org\/C188198153","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q1613840","display_name":"Limiting","level":2,"score":0.5413411259651184},{"id":"https:\/\/openalex.org\/C2776401178","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.5249231457710266},{"id":"https:\/\/openalex.org\/C41008148","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q21198","display_name":"Computer science","level":0,"score":0.47039565443992615},{"id":"https:\/\/openalex.org\/C202213908","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q626011","display_name":"Mean field theory","level":2,"score":0.46663886308670044},{"id":"https:\/\/openalex.org\/C2777299769","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q3707858","display_name":"Type (biology)","level":2,"score":0.4235367178916931},{"id":"https:\/\/openalex.org\/C9652623","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q190109","display_name":"Field (mathematics)","level":2,"score":0.42132464051246643},{"id":"https:\/\/openalex.org\/C33923547","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q395","display_name":"Mathematics","level":0,"score":0.38361290097236633},{"id":"https:\/\/openalex.org\/C126255220","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3431435525417328},{"id":"https:\/\/openalex.org\/C50644808","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q192776","display_name":"Artificial neural network","level":2,"score":0.3181006908416748},{"id":"https:\/\/openalex.org\/C154945302","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2805226445198059},{"id":"https:\/\/openalex.org\/C121332964","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q413","display_name":"Physics","level":0,"score":0.11331754922866821},{"id":"https:\/\/openalex.org\/C134306372","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q7754","display_name":"Mathematical analysis","level":1,"score":0.08056363463401794},{"id":"https:\/\/openalex.org\/C127413603","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q11023","display_name":"Engineering","level":0,"score":0.06410112977027893},{"id":"https:\/\/openalex.org\/C86803240","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q420","display_name":"Biology","level":0,"score":0},{"id":"https:\/\/openalex.org\/C50522688","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q189833","display_name":"Economic growth","level":1,"score":0},{"id":"https:\/\/openalex.org\/C138885662","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q5891","display_name":"Philosophy","level":0,"score":0},{"id":"https:\/\/openalex.org\/C78519656","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q101333","display_name":"Mechanical engineering","level":1,"score":0},{"id":"https:\/\/openalex.org\/C162324750","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q8134","display_name":"Economics","level":0,"score":0},{"id":"https:\/\/openalex.org\/C41895202","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q8162","display_name":"Linguistics","level":1,"score":0},{"id":"https:\/\/openalex.org\/C62520636","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q944","display_name":"Quantum mechanics","level":1,"score":0},{"id":"https:\/\/openalex.org\/C18903297","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q7150","display_name":"Ecology","level":1,"score":0},{"id":"https:\/\/openalex.org\/C202444582","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q837863","display_name":"Pure mathematics","level":1,"score":0},{"id":"https:\/\/openalex.org\/C199360897","wikidata":"https:\/\/www.wikidata.org\/wiki\/Q9143","display_name":"Programming language","level":1,"score":0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2303.06726","is_oa":true,"landing_page_url":"http:\/\/arxiv.org\/abs\/2303.06726","pdf_url":"https:\/\/arxiv.org\/pdf\/2303.06726","source":{"id":"https:\/\/openalex.org\/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https:\/\/openalex.org\/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https:\/\/openalex.org\/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},{"id":"pmh:oai:arpi.unipi.it:11568\/1174105","is_oa":true,"landing_page_url":"https:\/\/hdl.handle.net\/11568\/1174105","pdf_url":"https:\/\/arpi.unipi.it\/bitstream\/11568\/1174105\/1\/2303.06726.pdf","source":{"id":"https:\/\/openalex.org\/S4377196265","display_name":"CINECA IRIS Institutial research information system (University of Pisa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https:\/\/openalex.org\/I108290504","host_organization_name":"University of Pisa","host_organization_lineage":["https:\/\/openalex.org\/I108290504"],"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":null,"raw_type":"info:eu-repo\/semantics\/conferenceObject"},{"id":"doi:10.48550\/arxiv.2303.06726","is_oa":true,"landing_page_url":"https:\/\/doi.org\/10.48550\/arxiv.2303.06726","pdf_url":null,"source":{"id":"https:\/\/openalex.org\/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https:\/\/openalex.org\/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https:\/\/openalex.org\/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2303.06726","is_oa":true,"landing_page_url":"http:\/\/arxiv.org\/abs\/2303.06726","pdf_url":"https:\/\/arxiv.org\/pdf\/2303.06726","source":{"id":"https:\/\/openalex.org\/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"host_organization":"https:\/\/openalex.org\/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https:\/\/openalex.org\/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":null},"sustainable_development_goals":[],"awards":[{"id":"https:\/\/openalex.org\/G1151036099","display_name":null,"funder_award_id":"2016-IDG-1013","funder_id":"https:\/\/openalex.org\/F4320308571","funder_display_name":"North Carolina Biotechnology Center"},{"id":"https:\/\/openalex.org\/G1257848790","display_name":null,"funder_award_id":"DBI 1661386","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G1840908629","display_name":null,"funder_award_id":"CCF-193496","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G2038615950","display_name":null,"funder_award_id":"PRA_2022_8","funder_id":"https:\/\/openalex.org\/F4320324499","funder_display_name":"Universit\u00e0 di Pisa"},{"id":"https:\/\/openalex.org\/G2449561906","display_name":null,"funder_award_id":"PRA_2022_85","funder_id":"https:\/\/openalex.org\/F4320324499","funder_display_name":"Universit\u00e0 di Pisa"},{"id":"https:\/\/openalex.org\/G2615244064","display_name":null,"funder_award_id":"PRA 2022 85","funder_id":"https:\/\/openalex.org\/F4320324499","funder_display_name":"Universit\u00e0 di Pisa"},{"id":"https:\/\/openalex.org\/G4293858528","display_name":null,"funder_award_id":"2016-IDG-1013","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G4508289328","display_name":null,"funder_award_id":"PE00000013","funder_id":"https:\/\/openalex.org\/F4320320300","funder_display_name":"European Commission"},{"id":"https:\/\/openalex.org\/G5518200836","display_name":"HDR TRIPODS: Innovations in Data Science: Integrating Stochastic Modeling, Data Representations, and Algorithms","funder_award_id":"1934964","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G5865894165","display_name":null,"funder_award_id":"DMS 16-13261","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G6203420807","display_name":null,"funder_award_id":"TRIPODS","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G6623739242","display_name":"CAREER: Evolution of Morphological Diversity in Primates as revealed by 3D Digital Data, Comprehensive Datasets, and Automated Phenotyping","funder_award_id":"1552848","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G6707714828","display_name":null,"funder_award_id":"DMS-2012286","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G7062312830","display_name":null,"funder_award_id":"2012286","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G7452998910","display_name":null,"funder_award_id":"00000","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G7525462396","display_name":null,"funder_award_id":"CCF-1934964","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G7785050591","display_name":null,"funder_award_id":"BCS 1552848","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G7926010854","display_name":"ABI Development: Collaborative Research: The first open access digital archive for high fidelity 3D data on morphological phenomes","funder_award_id":"1661386","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G8201318391","display_name":null,"funder_award_id":"DMS 17-13012","funder_id":"https:\/\/openalex.org\/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https:\/\/openalex.org\/G8409961469","display_name":null,"funder_award_id":"Spoke 1","funder_id":"https:\/\/openalex.org\/F4320320300","funder_display_name":"European Commission"},{"id":"https:\/\/openalex.org\/G8893660128","display_name":null,"funder_award_id":"PE0000001","funder_id":"https:\/\/openalex.org\/F4320320300","funder_display_name":"European Commission"},{"id":"https:\/\/openalex.org\/G940023585","display_name":null,"funder_award_id":"-IDG-","funder_id":"https:\/\/openalex.org\/F4320308571","funder_display_name":"North Carolina Biotechnology Center"}],"funders":[{"id":"https:\/\/openalex.org\/F4320306076","display_name":"National Science Foundation","ror":"https:\/\/ror.org\/021nxhr62"},{"id":"https:\/\/openalex.org\/F4320308571","display_name":"North Carolina Biotechnology Center","ror":"https:\/\/ror.org\/03hj4jr80"},{"id":"https:\/\/openalex.org\/F4320320300","display_name":"European Commission","ror":"https:\/\/ror.org\/00k4n6c32"},{"id":"https:\/\/openalex.org\/F4320324499","display_name":"Universit\u00e0 di Pisa","ror":"https:\/\/ror.org\/03ad39j10"},{"id":"https:\/\/openalex.org\/F4320327897","display_name":"Max-Planck-Institut f\u00fcr Mathematik in den Naturwissenschaften","ror":"https:\/\/ror.org\/00ez2he07"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https:\/\/openalex.org\/W3204184292","https:\/\/openalex.org\/W3176564347","https:\/\/openalex.org\/W1985458517","https:\/\/openalex.org\/W2355833770","https:\/\/openalex.org\/W2805949325","https:\/\/openalex.org\/W4300536205","https:\/\/openalex.org\/W4226299596","https:\/\/openalex.org\/W4309434778","https:\/\/openalex.org\/W3214759249","https:\/\/openalex.org\/W4283773090"],"abstract_inverted_index":{"We":[0,36],"analyze":[1],"Elman-type":[2],"Recurrent":[3],"Reural":[4],"Networks":[5],"(RNNs)":[6],"and":[7],"their":[8],"training":[9,21],"in":[10,31,69],"the":[11,24,27,32,40,44,55,58,70],"mean-field":[12,29,71],"regime.":[13],"Specifically,":[14],"we":[15],"show":[16,38],"convergence":[17],"of":[18,23,43,57],"gradient":[19],"descent":[20],"dynamics":[22,47],"RNN":[25],"to":[26],"corresponding":[28],"formulation":[30],"large":[33],"width":[34],"limit.":[35],"also":[37],"that":[39],"fixed":[41],"points":[42],"limiting":[45],"infinite-width":[46],"are":[48],"globally":[49],"optimal,":[50],"under":[51],"some":[52],"assumptions":[53],"on":[54],"initialization":[56],"weights.":[59],"Our":[60],"results":[61],"establish":[62],"optimality":[63],"for":[64],"feature-learning":[65],"with":[66],"wide":[67],"RNNs":[68],"regime":[72]},"counts_by_year":[],"updated_date":"2026-04-21T08:09:41.155169","created_date":"2025-10-10T00:00:00"}