{"id":"https://openalex.org/W7207756367","doi":"https://doi.org/10.48550/arxiv.2609.01952","title":"Convergence Theory of Knowledge Distillation in Asynchronous P2P Gossip Learning Network","display_name":"Convergence Theory of Knowledge Distillation in Asynchronous P2P Gossip Learning Network","publication_year":2026,"publication_date":"2026-09-01","ids":{"openalex":"https://openalex.org/W7207756367","doi":"https://doi.org/10.48550/arxiv.2609.01952"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.01952","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01952","pdf_url":"https://arxiv.org/pdf/2609.01952","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.01952","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5147161535","display_name":"Lucas Qingyang Fang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Fang, Lucas Qingyang","raw_affiliation_strings":["University of California , Santa Cruz , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California , Santa Cruz , USA","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033342570","display_name":"Tiyao Liu","orcid":"https://orcid.org/0009-0004-9140-3653","observed_orcids":["https://orcid.org/0009-0004-9140-3653"]},"institutions":[{"id":"https://openalex.org/I204553293","display_name":"China University of Petroleum, Beijing","ror":"https://ror.org/041qf4r12","country_code":"CN","type":"education","lineage":["https://openalex.org/I204553293"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Tiyao","raw_affiliation_strings":["China University of Petroleum , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"China University of Petroleum , China","institution_ids":["https://openalex.org/I204553293"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127394635","display_name":"Jinhao Jing","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I4210116924","display_name":"Chinese University of Hong Kong, Shenzhen","ror":"https://ror.org/02d5ks197","country_code":"CN","type":"education","lineage":["https://openalex.org/I177725633","https://openalex.org/I180726961","https://openalex.org/I4210116924"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Jing, Jinhao","raw_affiliation_strings":["The Chinese University of Hong Kong , Shenzhen , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The Chinese University of Hong Kong , Shenzhen , China","institution_ids":["https://openalex.org/I4210116924"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5149521263","display_name":"Zeji Li","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Li, Zeji","raw_affiliation_strings":["City University of Hong Kong , Hong Kong SAR , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"City University of Hong Kong , Hong Kong SAR , China","institution_ids":["https://openalex.org/I168719708"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5149509308","display_name":"Kaijie Chen","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I51556381","display_name":"University of Virginia","ror":"https://ror.org/0153tk833","country_code":"US","type":"education","lineage":["https://openalex.org/I51556381"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chen, Kaijie","raw_affiliation_strings":["University of Virginia , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Virginia , USA","institution_ids":["https://openalex.org/I51556381"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5064796621","display_name":"Harikrishna Kuttivelil","orcid":"https://orcid.org/0000-0002-3186-6590","observed_orcids":["https://orcid.org/0000-0002-3186-6590"]},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kuttivelil, Harikrishna","raw_affiliation_strings":["University of California , Santa Cruz , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California , Santa Cruz , USA","institution_ids":["https://openalex.org/I185103710"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5067832138","display_name":"Katia Obraczka","orcid":"https://orcid.org/0000-0001-9720-1690","observed_orcids":["https://orcid.org/0000-0001-9720-1690"]},"institutions":[{"id":"https://openalex.org/I185103710","display_name":"University of California, Santa Cruz","ror":"https://ror.org/03s65by71","country_code":"US","type":"education","lineage":["https://openalex.org/I185103710"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Obraczka, Katia","raw_affiliation_strings":["University of California , Santa Cruz , USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of California , Santa Cruz , USA","institution_ids":["https://openalex.org/I185103710"]}]}],"institutions":[],"countries_distinct_count":3,"institutions_distinct_count":5,"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":0.5160999894142151,"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":0.5160999894142151,"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/T10764","display_name":"Privacy-Preserving Technologies in Data","score":0.24279999732971191,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.09269999712705612,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/knowledge-distillation","display_name":"knowledge distillation","score":1.0},{"id":"https://openalex.org/keywords/decentralized-learning","display_name":"decentralized learning","score":0.7289999723434448},{"id":"https://openalex.org/keywords/convergence-analysis","display_name":"convergence analysis","score":0.7850000262260437},{"id":"https://openalex.org/keywords/predictive-distribution","display_name":"predictive distribution","score":0.44999998807907104},{"id":"https://openalex.org/keywords/task-heterogeneity","display_name":"task heterogeneity","score":0.5830000042915344},{"id":"https://openalex.org/keywords/step-size-selection","display_name":"step size selection","score":0.3659999966621399}],"concepts":[{"id":"https://openalex.org/C151319957","wikidata":"https://www.wikidata.org/wiki/Q752739","display_name":"Asynchronous communication","level":2,"score":0.5845000147819519},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5113999843597412},{"id":"https://openalex.org/C174348530","wikidata":"https://www.wikidata.org/wiki/Q188635","display_name":"Bridging (networking)","level":2,"score":0.4456999897956848},{"id":"https://openalex.org/C2776378722","wikidata":"https://www.wikidata.org/wiki/Q3454417","display_name":"Realizability","level":2,"score":0.4327999949455261},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.42989999055862427},{"id":"https://openalex.org/C62799726","wikidata":"https://www.wikidata.org/wiki/Q190056","display_name":"Hilbert space","level":2,"score":0.42160001397132874},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.37139999866485596},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.3610000014305115},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.35040000081062317},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.34529998898506165},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.3395000100135803},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.3393999934196472},{"id":"https://openalex.org/C2780704645","wikidata":"https://www.wikidata.org/wiki/Q9251458","display_name":"Observer (physics)","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.321399986743927},{"id":"https://openalex.org/C23130292","wikidata":"https://www.wikidata.org/wiki/Q5275358","display_name":"Differential privacy","level":2,"score":0.3098999857902527},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.29429998993873596},{"id":"https://openalex.org/C57869625","wikidata":"https://www.wikidata.org/wiki/Q1783502","display_name":"Rate of convergence","level":3,"score":0.2897000014781952},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.28859999775886536},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.2800999879837036},{"id":"https://openalex.org/C62989814","wikidata":"https://www.wikidata.org/wiki/Q854648","display_name":"Gossip","level":2,"score":0.27730000019073486},{"id":"https://openalex.org/C73586568","wikidata":"https://www.wikidata.org/wiki/Q2600211","display_name":"Parameter space","level":2,"score":0.2694999873638153},{"id":"https://openalex.org/C142730499","wikidata":"https://www.wikidata.org/wiki/Q934367","display_name":"Function space","level":2,"score":0.2605000138282776},{"id":"https://openalex.org/C91873725","wikidata":"https://www.wikidata.org/wiki/Q3445816","display_name":"Function approximation","level":3,"score":0.25529998540878296}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.01952","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01952","pdf_url":"https://arxiv.org/pdf/2609.01952","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.01952","doi":"https://doi.org/10.48550/arxiv.2609.01952","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.01952","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:2609.01952","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.01952","pdf_url":"https://arxiv.org/pdf/2609.01952","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7207756367.pdf","grobid_xml":"https://content.openalex.org/works/W7207756367.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7199276252","https://openalex.org/W4414706271","https://openalex.org/W3013255770","https://openalex.org/W7133221871","https://openalex.org/W7222924403","https://openalex.org/W4287888549","https://openalex.org/W4403716440","https://openalex.org/W7118260457","https://openalex.org/W4368353259","https://openalex.org/W7171521515"],"abstract_inverted_index":{"Decentralized,":[0],"serverless":[1],"learning":[2],"increasingly":[3],"connects":[4],"devices":[5],"running":[6],"different":[7,20],"architectures,":[8],"where":[9],"the":[10,75,83,105,114,132,135,139,156,179,184,189],"standard":[11,93],"tool,":[12],"decentralized":[13],"SGD,":[14],"is":[15,49,66,131],"undefined":[16],"as":[17],"models":[18],"with":[19],"parameter":[21,57,102],"counts":[22],"cannot":[23],"be":[24],"averaged.":[25],"Knowledge":[26],"distillation":[27],"(KD)":[28],"exchanges":[29],"soft":[30],"predictions":[31,87],"rather":[32],"than":[33],"weights":[34],"and":[35,96,108,118,143,152,183],"sidesteps":[36],"this":[37],"obstacle,":[38],"yet":[39],"convergence":[40],"theory":[41],"for":[42],"fully":[43],"decentralized,":[44],"asynchronous":[45],"peer-to-peer":[46],"(P2P)":[47],"KD":[48,64,158],"lacking.":[50],"We":[51],"provide":[52],"one,":[53],"relocating":[54],"consensus":[55],"from":[56,134],"space":[58,73,85],"to":[59,104,125,138],"function":[60,160],"(output)":[61],"space:":[62],"a":[63,67,89],"event":[65],"geometric":[68],"contraction":[69],"operator":[70],"in":[71,82],"logit":[72],"on":[74,88,178],"peers'":[76,140],"predictive":[77],"distributions,":[78],"which":[79],"we":[80],"analyse":[81],"Hilbert":[84],"of":[86,155],"reference":[90],"measure.":[91],"Under":[92],"smoothness/variance":[94],"assumptions":[95],"two":[97],"realizability":[98],"assumptions,":[99],"one":[100,109],"bridging":[101],"SGD":[103],"functional":[106,116],"step":[107],"controlling":[110],"restricted":[111],"task/KD":[112],"alignment,":[113],"time-averaged":[115],"stationarity":[117,171],"function-space":[119],"disagreement":[120,161],"converge":[121],"at":[122],"rate":[123],"$O(1/(\u03b7T))$":[124],"an":[126],"$O(\u03b7)+O(B_f^2)+O(\u03b6_f^2)$":[127],"neighbourhood.":[128],"Here":[129],"$B_f$":[130],"distance":[133],"task":[136],"optimum":[137],"reachable":[141],"classes":[142],"$\u03b6_f$":[144],"measures":[145],"persistent":[146],"local-task":[147],"heterogeneity.":[148],"Across":[149],"homogeneous,":[150],"width-heterogeneous,":[151],"mixed-family":[153],"networks":[154],"experiments,":[157],"contracts":[159],"by":[162],"$40-61\\times$,":[163],"while":[164],"isolated":[165],"training":[166],"does":[167],"not.":[168],"The":[169],"sampled":[170],"diagnostic":[172],"has":[173],"late":[174],"transient":[175],"exponents":[176],"$0.99-1.90$":[177],"shared-skeleton":[180],"main":[181],"runs,":[182],"four-point":[185],"step-size":[186],"sweep":[187],"exhibits":[188],"predicted":[190],"transient:":[191],"neighbourhood":[192],"tradeoff.":[193]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-04T00:00:00"}