{"id":"https://openalex.org/W7133243783","doi":"https://doi.org/10.52202/068431-2336","title":"Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide Neural Networks","display_name":"Self-Consistent Dynamical Field Theory of Kernel Evolution in Wide Neural Networks","publication_year":2022,"publication_date":"2022-01-01","ids":{"openalex":"https://openalex.org/W7133243783","doi":"https://doi.org/10.52202/068431-2336"},"language":"en","primary_location":{"id":"doi:10.52202/068431-2336","doi":"https://doi.org/10.52202/068431-2336","is_oa":false,"landing_page_url":"https://doi.org/10.52202/068431-2336","pdf_url":null,"source":{"id":"https://openalex.org/S4363606243","display_name":"neural information processing systems","issn_l":"1049-5258","issn":["1049-5258"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Neural Information Processing Systems 35","raw_type":"proceedings-article"},"volume":null,"type":"conference-paper","indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2205.09653","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5039282308","display_name":"Blake Bordelon","orcid":"https://orcid.org/0000-0003-0455-9445","observed_orcids":["https://orcid.org/0000-0003-0455-9445"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Blake Bordelon","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5023195984","display_name":"Cengiz Pehlevan","orcid":"https://orcid.org/0000-0001-9767-6063","observed_orcids":["https://orcid.org/0000-0001-9767-6063"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cengiz Pehlevan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.4881,"has_fulltext":false,"cited_by_count":19,"citation_normalized_percentile":{"value":0.92029154,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":93,"max":98},"biblio":{"volume":null,"issue":null,"first_page":"32240","last_page":"32256"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9301999807357788,"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":0.9301999807357788,"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/T10581","display_name":"Neural dynamics and brain function","score":0.014700000174343586,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T12676","display_name":"Machine Learning and ELM","score":0.00860000029206276,"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/wide-neural-networks","display_name":"wide neural networks","score":0.8389999866485596},{"id":"https://openalex.org/keywords/self-consistent-field-theory","display_name":"self-consistent field theory","score":0.7749999761581421},{"id":"https://openalex.org/keywords/neural-network-training-dynamics","display_name":"neural network training dynamics","score":0.6129999756813049},{"id":"https://openalex.org/keywords/kernel-methods","display_name":"kernel methods","score":0.4300000071525574},{"id":"https://openalex.org/keywords/neural-tangent-kernel","display_name":"neural tangent kernel","score":0.4269999861717224}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.492900013923645},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4927000105381012},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.43070000410079956},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.41190001368522644},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4113999903202057},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4016999900341034},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3698999881744385},{"id":"https://openalex.org/C79379906","wikidata":"https://www.wikidata.org/wiki/Q3174497","display_name":"Dynamical systems theory","level":2,"score":0.3296999931335449},{"id":"https://openalex.org/C2776401178","wikidata":"https://www.wikidata.org/wiki/Q12050496","display_name":"Feature (linguistics)","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.265500009059906},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.2619999945163727},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2587999999523163},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.25699999928474426},{"id":"https://openalex.org/C33962884","wikidata":"https://www.wikidata.org/wiki/Q378637","display_name":"Dynamical system (definition)","level":3,"score":0.25609999895095825}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.52202/068431-2336","doi":"https://doi.org/10.52202/068431-2336","is_oa":false,"landing_page_url":"https://doi.org/10.52202/068431-2336","pdf_url":null,"source":{"id":"https://openalex.org/S4363606243","display_name":"neural information processing systems","issn_l":"1049-5258","issn":["1049-5258"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","norway-2"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Advances in Neural Information Processing Systems 35","raw_type":"proceedings-article"},{"id":"pmh:oai:arXiv.org:2205.09653","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2205.09653","pdf_url":"https://arxiv.org/pdf/2205.09653","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2205.09653","doi":"https://doi.org/10.48550/arxiv.2205.09653","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2205.09653","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2205.09653","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2205.09653","pdf_url":"https://arxiv.org/pdf/2205.09653","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"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":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7133246981","https://openalex.org/W4303438727","https://openalex.org/W3110116503","https://openalex.org/W4224675625","https://openalex.org/W4398157310","https://openalex.org/W4416159177","https://openalex.org/W4407569646","https://openalex.org/W4409922941","https://openalex.org/W7133446673","https://openalex.org/W7133224629"],"abstract_inverted_index":{"We":[0,18,76,133],"analyze":[1],"feature":[2,90,197],"learning":[3,91,198],"in":[4,37,166,181],"infinite-width":[5,89],"neural":[6,69],"networks":[7,92],"trained":[8],"with":[9,99],"gradient":[10,149],"flow":[11],"through":[12,52],"a":[13,20,46,110,206],"self-consistent":[14,138,170],"dynamical":[15,24],"field":[16,80],"theory.":[17],"construct":[19],"collection":[21],"of":[22,42,49,67,88,112,136,160,193],"deterministic":[23],"order":[25,56,131,154],"parameters":[26,57],"which":[27,185],"are":[28],"inner-product":[29],"kernels":[30,108],"for":[31,128],"hidden":[32,61],"unit":[33],"activations":[34],"and":[35,72,96,152,190],"gradients":[36],"each":[38,159],"layer":[39,62],"at":[40,195],"pairs":[41],"time":[43],"points,":[44],"providing":[45],"reduced":[47],"description":[48],"network":[50],"activity":[51],"training.":[53],"These":[54],"kernel":[55,130,191],"collectively":[58],"define":[59],"the":[60,65,68,79,84,129,137,145,188],"activation":[63],"distribution,":[64],"evolution":[66],"tangent":[70],"kernel,":[71],"consequently":[73],"output":[74],"predictions.":[75],"show":[77],"that":[78,158,187],"theory":[81],"derivation":[82],"recovers":[83],"recursive":[85],"stochastic":[86],"process":[87],"obtained":[93],"from":[94],"Yang":[95],"Hu":[97],"(2021)":[98],"Tensor":[100],"Programs":[101],".":[102],"For":[103,116],"deep":[104],"linear":[105],"networks,":[106,118],"these":[107,161],"satisfy":[109],"set":[111],"algebraic":[113],"matrix":[114],"equations.":[115],"nonlinear":[117],"we":[119,178],"provide":[120,134,173,179],"an":[121,174],"alternating":[122],"sampling":[123],"procedure":[124],"to":[125,140],"self-consistently":[126],"solve":[127],"parameters.":[132],"comparisons":[135],"solution":[139],"various":[141],"approximation":[142],"schemes":[143],"including":[144],"static":[146],"NTK":[147],"approximation,":[148],"independence":[150],"assumption,":[151],"leading":[153],"perturbation":[155],"theory,":[156],"showing":[157],"approximations":[162],"can":[163],"break":[164],"down":[165],"regimes":[167],"where":[168],"general":[169],"solutions":[171],"still":[172],"accurate":[175],"description.":[176],"Lastly,":[177],"experiments":[180],"more":[182],"realistic":[183],"settings":[184],"demonstrate":[186],"loss":[189],"dynamics":[192],"CNNs":[194],"fixed":[196],"strength":[199],"is":[200],"preserved":[201],"across":[202],"different":[203],"widths":[204],"on":[205],"CIFAR":[207],"classification":[208],"task.":[209]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":6},{"year":2022,"cited_by_count":3}],"updated_date":"2026-10-12T09:40:04.860316","created_date":"2026-03-03T00:00:00"}
