{"id":"https://openalex.org/W7160453045","doi":"https://doi.org/10.48550/arxiv.2605.03373","title":"Learning Dynamics of Zeroth-Order Optimization: A Kernel Perspective","display_name":"Learning Dynamics of Zeroth-Order Optimization: A Kernel Perspective","publication_year":2026,"publication_date":"2026-05-05","ids":{"openalex":"https://openalex.org/W7160453045","doi":"https://doi.org/10.48550/arxiv.2605.03373"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.03373","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03373","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":"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"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.03373","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135420379","display_name":"Zhe Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Zhe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5005538082","display_name":"Bicheng Ying","orcid":"https://orcid.org/0000-0002-5246-2982"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ying, Bicheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101438462","display_name":"Zidong Liu","orcid":"https://orcid.org/0000-0002-9375-2409"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Zidong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135531897","display_name":"Haibo Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Haibo","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":null,"has_fulltext":false,"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":0.3736000061035156,"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":0.3736000061035156,"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":0.1534000039100647,"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":0.06449999660253525,"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/kernel","display_name":"Kernel (algebra)","score":0.5228999853134155},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.4909999966621399},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.4595000147819519},{"id":"https://openalex.org/keywords/convergence","display_name":"Convergence (economics)","score":0.43950000405311584},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4178999960422516},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.41029998660087585},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.40790000557899475},{"id":"https://openalex.org/keywords/tangent","display_name":"Tangent","score":0.40049999952316284},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.39959999918937683}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5623000264167786},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.5228999853134155},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.4909999966621399},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.46369999647140503},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4595000147819519},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.43950000405311584},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4178999960422516},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.41029998660087585},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.40790000557899475},{"id":"https://openalex.org/C138187205","wikidata":"https://www.wikidata.org/wiki/Q131251","display_name":"Tangent","level":2,"score":0.40049999952316284},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.39959999918937683},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.38269999623298645},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3750999867916107},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.36800000071525574},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36070001125335693},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.353300005197525},{"id":"https://openalex.org/C122280245","wikidata":"https://www.wikidata.org/wiki/Q620622","display_name":"Kernel method","level":3,"score":0.34310001134872437},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.33480000495910645},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.32910001277923584},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3260999917984009},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.3138999938964844},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.3066999912261963},{"id":"https://openalex.org/C157157409","wikidata":"https://www.wikidata.org/wiki/Q909601","display_name":"Tangent space","level":2,"score":0.30480000376701355},{"id":"https://openalex.org/C120936955","wikidata":"https://www.wikidata.org/wiki/Q2155640","display_name":"Empirical research","level":2,"score":0.27559998631477356},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.26899999380111694},{"id":"https://openalex.org/C59404180","wikidata":"https://www.wikidata.org/wiki/Q17013334","display_name":"Feature learning","level":2,"score":0.2687000036239624},{"id":"https://openalex.org/C61797465","wikidata":"https://www.wikidata.org/wiki/Q1188986","display_name":"Term (time)","level":2,"score":0.2685000002384186},{"id":"https://openalex.org/C145912823","wikidata":"https://www.wikidata.org/wiki/Q113558","display_name":"Dynamics (music)","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.26260000467300415},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.2513999938964844}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.03373","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03373","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.03373","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.03373","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":"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"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Classical":[0],"optimization":[1],"theory":[2],"establishes":[3],"that":[4,95,122,172],"zeroth-order":[5],"(ZO)":[6],"algorithms":[7],"suffer":[8],"from":[9],"a":[10,33,109,157,177],"dimension-dependent":[11],"slowdown,":[12],"with":[13,18,52],"convergence":[14],"rates":[15],"typically":[16],"scaling":[17],"the":[19,40,62,70,79,83,88,100,116,123,126,133,138,143,149,161,185],"model":[20,144],"dimension":[21],"compared":[22],"to":[23,29,46,99,166],"first-order":[24],"methods.":[25],"However,":[26],"in":[27],"contrast":[28],"these":[30],"theoretical":[31,158],"expectations,":[32],"growing":[34],"body":[35],"of":[36,43,54,66,87,103,125,135,163,187],"recent":[37],"work":[38],"demonstrates":[39],"successful":[41],"application":[42],"ZO":[44,67,92,127,164,182],"methods":[45,165,183],"fine-tuning":[47],"Large":[48],"Language":[49],"Models":[50],"(LLMs)":[51],"billions":[53],"parameters.":[55],"To":[56],"explain":[57],"this":[58,173],"paradox,":[59],"we":[60],"derive":[61],"one-step":[63],"learning":[64,84,188],"dynamics":[65],"SGD,":[68],"where":[69],"empirical":[71],"Neural":[72],"Tangent":[73],"Kernel":[74],"(eNTK)":[75],"naturally":[76],"emerges":[77],"as":[78],"key":[80],"term":[81],"governing":[82],"behavior.":[85],"Inspection":[86],"eNTK":[89,128],"produced":[90],"by":[91,114,132],"SGD":[93],"reveals":[94],"each":[96],"element":[97],"corresponds":[98],"inner":[101],"product":[102],"neural":[104],"tangent":[105],"vectors":[106],"projected":[107],"onto":[108],"random":[110],"low-dimensional":[111],"subspace.":[112],"Thus,":[113],"invoking":[115],"Johnson-Lindenstrauss":[117],"Lemma,":[118],"our":[119],"analysis":[120],"shows":[121],"fidelity":[124],"is":[129],"governed":[130],"primarily":[131],"number":[134],"perturbations.":[136],"Crucially,":[137],"approximation":[139],"error":[140],"depends":[141],"on":[142],"output":[145],"size":[146],"rather":[147],"than":[148],"massive":[150],"parameter":[151],"dimension.":[152],"This":[153],"dimension-free":[154],"property":[155],"provides":[156],"justification":[159],"for":[160,180],"scalability":[162],"LLMs":[167],"finetuning":[168],"tasks.":[169],"We":[170],"believe":[171],"kernel-based":[174],"framework":[175],"offers":[176],"novel":[178],"perspective":[179],"understanding":[181],"within":[184],"context":[186],"dynamics.":[189]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-07T00:00:00"}