{"id":"https://openalex.org/W7214768121","doi":"https://doi.org/10.48550/arxiv.2609.35029","title":"Fast Learning Rate Transfer in Shallow Linear Networks at Growing Training Horizons","display_name":"Fast Learning Rate Transfer in Shallow Linear Networks at Growing Training Horizons","publication_year":2026,"publication_date":"2026-09-28","ids":{"openalex":"https://openalex.org/W7214768121","doi":"https://doi.org/10.48550/arxiv.2609.35029"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.35029","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35029","pdf_url":"https://arxiv.org/pdf/2609.35029","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"},"volume":null,"type":"preprint","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.35029","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5041609700","display_name":"Mana Sakai","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210126580","display_name":"RIKEN Center for Advanced Intelligence Project","ror":"https://ror.org/03ckxwf91","country_code":"JP","type":"facility","lineage":["https://openalex.org/I4210110652","https://openalex.org/I4210126580"]},{"id":"https://openalex.org/I74801974","display_name":"The University of Tokyo","ror":"https://ror.org/057zh3y96","country_code":"JP","type":"education","lineage":["https://openalex.org/I74801974"]}],"countries":["JP"],"is_corresponding":false,"raw_author_name":"Sakai, Mana","raw_affiliation_strings":["RIKEN Center for Advanced Intelligence Project","The University of Tokyo"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"RIKEN Center for Advanced Intelligence Project","institution_ids":["https://openalex.org/I4210126580"]},{"raw_affiliation_string":"The University of Tokyo","institution_ids":["https://openalex.org/I74801974"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5066308746","display_name":"Masaaki Imaizumi","orcid":"https://orcid.org/0000-0001-6186-613X","observed_orcids":["https://orcid.org/0000-0001-6186-613X"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Imaizumi, Masaaki","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9937000274658203,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9937000274658203,"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/T10320","display_name":"Neural Networks and Applications","score":0.0024999999441206455,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.0010999999940395355,"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/hyperparameter-transfer","display_name":"hyperparameter transfer","score":0.9580000042915344},{"id":"https://openalex.org/keywords/extreme-eigenvalues","display_name":"extreme eigenvalues","score":0.8259999752044678},{"id":"https://openalex.org/keywords/asymptotic-distribution","display_name":"asymptotic distribution","score":0.7409999966621399},{"id":"https://openalex.org/keywords/optimal-learning-rate","display_name":"optimal learning rate","score":0.6380000114440918}],"concepts":[{"id":"https://openalex.org/C8642999","wikidata":"https://www.wikidata.org/wiki/Q4171168","display_name":"Hyperparameter","level":2,"score":0.8359000086784363},{"id":"https://openalex.org/C81299745","wikidata":"https://www.wikidata.org/wiki/Q334269","display_name":"Transfer function","level":2,"score":0.6881999969482422},{"id":"https://openalex.org/C2776175482","wikidata":"https://www.wikidata.org/wiki/Q1195816","display_name":"Transfer (computing)","level":2,"score":0.6151000261306763},{"id":"https://openalex.org/C150899416","wikidata":"https://www.wikidata.org/wiki/Q1820378","display_name":"Transfer of learning","level":2,"score":0.608299970626831},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5521000027656555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5266000032424927},{"id":"https://openalex.org/C177918212","wikidata":"https://www.wikidata.org/wiki/Q803623","display_name":"Perturbation (astronomy)","level":2,"score":0.439300000667572},{"id":"https://openalex.org/C188198153","wikidata":"https://www.wikidata.org/wiki/Q1613840","display_name":"Limiting","level":2,"score":0.3921999931335449},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3837999999523163},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.38100001215934753},{"id":"https://openalex.org/C158693339","wikidata":"https://www.wikidata.org/wiki/Q190524","display_name":"Eigenvalues and eigenvectors","level":2,"score":0.37290000915527344},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3456000089645386},{"id":"https://openalex.org/C2992143177","wikidata":"https://www.wikidata.org/wiki/Q7973862","display_name":"Water transfer","level":2,"score":0.34139999747276306},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.3402000069618225},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.33559998869895935},{"id":"https://openalex.org/C557945733","wikidata":"https://www.wikidata.org/wiki/Q389772","display_name":"Data transmission","level":2,"score":0.3303999900817871},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.328900009393692},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.32760000228881836},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C2779066501","wikidata":"https://www.wikidata.org/wiki/Q1761267","display_name":"Transfer problem","level":2,"score":0.27790001034736633},{"id":"https://openalex.org/C47446073","wikidata":"https://www.wikidata.org/wiki/Q5165890","display_name":"Control theory (sociology)","level":3,"score":0.2630000114440918},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2605000138282776},{"id":"https://openalex.org/C21200559","wikidata":"https://www.wikidata.org/wiki/Q7451068","display_name":"Sensitivity (control systems)","level":2,"score":0.25920000672340393},{"id":"https://openalex.org/C6802819","wikidata":"https://www.wikidata.org/wiki/Q1072174","display_name":"Linear system","level":2,"score":0.25119999051094055}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.35029","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35029","pdf_url":"https://arxiv.org/pdf/2609.35029","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.2609.35029","doi":"https://doi.org/10.48550/arxiv.2609.35029","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.35029","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.35029","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.35029","pdf_url":"https://arxiv.org/pdf/2609.35029","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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4653877330","display_name":null,"funder_award_id":"JPMJCR21D2","funder_id":"https://openalex.org/F4320338075","funder_display_name":"Core Research for Evolutional Science and Technology"},{"id":"https://openalex.org/G596873297","display_name":"Theoretical development of non-sparse high-dimensional statistics for statistical understanding and utilization of large-degree-of-freedom models","funder_award_id":"24K02904","funder_id":"https://openalex.org/F4320334764","funder_display_name":"Japan Society for the Promotion of Science"}],"funders":[{"id":"https://openalex.org/F4320334764","display_name":"Japan Society for the Promotion of Science","ror":"https://ror.org/00hhkn466"},{"id":"https://openalex.org/F4320335125","display_name":"RIKEN","ror":"https://ror.org/01sjwvz98"},{"id":"https://openalex.org/F4320338075","display_name":"Core Research for Evolutional Science and Technology","ror":"https://ror.org/00097mb19"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214768121.pdf","grobid_xml":"https://content.openalex.org/works/W7214768121.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W4394673581","https://openalex.org/W4415333373","https://openalex.org/W7127923911","https://openalex.org/W7159581508","https://openalex.org/W7160834952"],"related_works":["https://openalex.org/W4407186888","https://openalex.org/W4416438542","https://openalex.org/W4415795894","https://openalex.org/W7221809970","https://openalex.org/W7117698012","https://openalex.org/W7128488623","https://openalex.org/W7162036416","https://openalex.org/W7222681622","https://openalex.org/W7167934154","https://openalex.org/W7139099463"],"abstract_inverted_index":{"Hyperparameter":[0],"transfer":[1,36,44,53,62,93,102,165],"across":[2],"model":[3],"width":[4,24],"can":[5],"substantially":[6],"reduce":[7],"the":[8,19,31,55,101,105,109,113,123,133,145,149],"cost":[9],"of":[10,33,112,148],"tuning":[11],"large":[12],"neural":[13],"networks,":[14],"but":[15],"its":[16,116],"behavior":[17],"when":[18,43],"training":[20],"horizon":[21],"grows":[22],"with":[23,68,144],"is":[25,45],"not":[26],"fully":[27],"understood.":[28],"Building":[29],"on":[30],"framework":[32],"fast":[34,52,91],"hyperparameter":[35],"(Ghosh":[37],"et":[38],"al.,":[39],"2026),":[40],"which":[41],"formalizes":[42],"effective,":[46],"we":[47,59],"investigate":[48],"conditions":[49],"that":[50],"ensure":[51],"in":[54,63],"growing-horizon":[56],"regime.":[57],"Specifically,":[58],"study":[60],"learning-rate":[61,92,117,164],"a":[64,69],"shallow":[65],"linear":[66],"network":[67],"single":[70],"trainable":[71],"hidden":[72],"matrix,":[73],"trained":[74],"by":[75,141],"full-batch":[76],"gradient":[77],"descent.":[78],"Under":[79],"additional":[80],"spectral":[81,157],"assumptions,":[82],"our":[83],"main":[84],"results":[85,154],"are":[86],"threefold.":[87],"(i)":[88],"We":[89,99,128],"prove":[90],"as":[94],"$n,T\\to\\infty$":[95],"whenever":[96],"$T=o(\\sqrt{n})$.":[97],"(ii)":[98],"characterize":[100],"rates":[103],"through":[104],"finite-width":[106,120],"perturbation":[107],"scale,":[108],"first-order":[110],"sensitivities":[111,162],"loss":[114,125,161],"and":[115,122,137,159],"derivative":[118],"to":[119],"perturbations,":[121],"local":[124,160],"curvature.":[126],"(iii)":[127],"derive":[129],"limiting":[130],"distributions":[131],"for":[132],"optimal":[134],"learning":[135],"rate":[136],"optimized":[138],"loss,":[139],"governed":[140],"fluctuations":[142],"associated":[143],"extreme":[146],"eigenvalues":[147],"data":[150],"Gram":[151],"matrix.":[152],"These":[153],"clarify":[155],"how":[156],"structure":[158],"govern":[163],"at":[166],"growing":[167],"horizons.":[168]},"counts_by_year":[],"updated_date":"2026-11-07T11:25:07.637180","created_date":"2026-09-30T00:00:00"}