{"id":"https://openalex.org/W7202213136","doi":"https://doi.org/10.48550/arxiv.2608.08176","title":"Matching Supervision to the Student's Learning Capacity: A Unified Framework for On-Policy Self-Distillation","display_name":"Matching Supervision to the Student's Learning Capacity: A Unified Framework for On-Policy Self-Distillation","publication_year":2026,"publication_date":"2026-08-08","ids":{"openalex":"https://openalex.org/W7202213136","doi":"https://doi.org/10.48550/arxiv.2608.08176"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2608.08176","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.08176","pdf_url":"https://arxiv.org/pdf/2608.08176","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","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2608.08176","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5146466671","display_name":"Yongkang Yang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yang, Yongkang","raw_affiliation_strings":["Tencent , Workbuddy Team"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tencent , Workbuddy Team","institution_ids":["https://openalex.org/I2250653659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5058931839","display_name":"Zhezheng Hao","orcid":"https://orcid.org/0000-0001-9900-894X","observed_orcids":["https://orcid.org/0000-0001-9900-894X"]},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Hao, Zhezheng","raw_affiliation_strings":["Zhejiang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5146520486","display_name":"Hong Zhang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Hong","raw_affiliation_strings":["Independent Researcher"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Researcher","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5146437452","display_name":"Yi Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Yi","raw_affiliation_strings":["Tencent , Workbuddy Team"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tencent , Workbuddy Team","institution_ids":["https://openalex.org/I2250653659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137377098","display_name":"Xiankun Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin, Xiankun","raw_affiliation_strings":["Tencent , Workbuddy Team"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tencent , Workbuddy Team","institution_ids":["https://openalex.org/I2250653659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137359149","display_name":"Wence Ji","orcid":"https://orcid.org/0009-0007-3858-3298","observed_orcids":["https://orcid.org/0009-0007-3858-3298"]},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ji, Wence","raw_affiliation_strings":["Tencent , Workbuddy Team"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tencent , Workbuddy Team","institution_ids":["https://openalex.org/I2250653659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128184125","display_name":"Fanjunduo Wei","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wei, Fanjunduo","raw_affiliation_strings":["Zhejiang University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Zhejiang University","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133057291","display_name":"Jiarui Yu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu, Jiarui","raw_affiliation_strings":["Tencent , Workbuddy Team"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tencent , Workbuddy Team","institution_ids":["https://openalex.org/I2250653659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134183962","display_name":"Qiang Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Lin, Qiang","raw_affiliation_strings":["Tencent , Workbuddy Team"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tencent , Workbuddy Team","institution_ids":["https://openalex.org/I2250653659"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136733322","display_name":"Xiaoyun Liang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liang, Xiaoyun","raw_affiliation_strings":["Tencent , Workbuddy Team"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tencent , Workbuddy Team","institution_ids":["https://openalex.org/I2250653659"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5007017628","display_name":"Hande Dong","orcid":"https://orcid.org/0000-0003-0074-2664","observed_orcids":["https://orcid.org/0000-0003-0074-2664"]},"institutions":[{"id":"https://openalex.org/I2250653659","display_name":"Tencent (China)","ror":"https://ror.org/00hhjss72","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250653659"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Dong, Hande","raw_affiliation_strings":["Tencent , Workbuddy Team"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tencent , Workbuddy Team","institution_ids":["https://openalex.org/I2250653659"]}]}],"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/T10028","display_name":"Topic Modeling","score":0.6420999765396118,"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/T10028","display_name":"Topic Modeling","score":0.6420999765396118,"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":0.14329999685287476,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.06289999932050705,"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/on-policy-self-distillation","display_name":"on-policy self-distillation","score":0.996999979019165},{"id":"https://openalex.org/keywords/privileged-information","display_name":"privileged information","score":0.6240000128746033},{"id":"https://openalex.org/keywords/token-selection","display_name":"token selection","score":0.5839999914169312},{"id":"https://openalex.org/keywords/learning-ability","display_name":"learning ability","score":0.6610000133514404},{"id":"https://openalex.org/keywords/lagrangian-optimization","display_name":"Lagrangian optimization","score":0.890999972820282},{"id":"https://openalex.org/keywords/unified-optimization-framework","display_name":"unified optimization framework","score":0.6790000200271606},{"id":"https://openalex.org/keywords/large-language-model-reasoning","display_name":"large language model reasoning","score":0.7509999871253967},{"id":"https://openalex.org/keywords/online-learning-algorithms","display_name":"online learning algorithms","score":0.4580000042915344}],"concepts":[{"id":"https://openalex.org/C4679612","wikidata":"https://www.wikidata.org/wiki/Q866298","display_name":"Aggregate (composite)","level":2,"score":0.6891999840736389},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6694999933242798},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.6498000025749207},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6470999717712402},{"id":"https://openalex.org/C183115368","wikidata":"https://www.wikidata.org/wiki/Q856577","display_name":"Weighting","level":2,"score":0.6080999970436096},{"id":"https://openalex.org/C182365436","wikidata":"https://www.wikidata.org/wiki/Q50701","display_name":"Variable (mathematics)","level":2,"score":0.5985999703407288},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.48579999804496765},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.4828999936580658},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.44769999384880066},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4291999936103821},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3919999897480011},{"id":"https://openalex.org/C198352243","wikidata":"https://www.wikidata.org/wiki/Q37105","display_name":"Line (geometry)","level":2,"score":0.3765999972820282},{"id":"https://openalex.org/C27574286","wikidata":"https://www.wikidata.org/wiki/Q320723","display_name":"Variables","level":2,"score":0.35519999265670776},{"id":"https://openalex.org/C45493050","wikidata":"https://www.wikidata.org/wiki/Q7884934","display_name":"Unified Model","level":2,"score":0.3433000147342682},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.34220001101493835},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.33079999685287476},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.3248000144958496},{"id":"https://openalex.org/C2780339515","wikidata":"https://www.wikidata.org/wiki/Q3074698","display_name":"Arrow","level":2,"score":0.32339999079704285},{"id":"https://openalex.org/C2777855551","wikidata":"https://www.wikidata.org/wiki/Q12310021","display_name":"Subject (documents)","level":2,"score":0.30570000410079956},{"id":"https://openalex.org/C171752962","wikidata":"https://www.wikidata.org/wiki/Q255166","display_name":"Kullback\u2013Leibler divergence","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C2780980858","wikidata":"https://www.wikidata.org/wiki/Q110022","display_name":"Dual (grammatical number)","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.28299999237060547},{"id":"https://openalex.org/C5274069","wikidata":"https://www.wikidata.org/wiki/Q2285707","display_name":"Categorical variable","level":2,"score":0.2750999927520752},{"id":"https://openalex.org/C8505890","wikidata":"https://www.wikidata.org/wiki/Q605095","display_name":"Budget constraint","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C77967617","wikidata":"https://www.wikidata.org/wiki/Q4677561","display_name":"Active learning (machine learning)","level":2,"score":0.27160000801086426},{"id":"https://openalex.org/C86037889","wikidata":"https://www.wikidata.org/wiki/Q4330127","display_name":"Learning to rank","level":3,"score":0.26179999113082886},{"id":"https://openalex.org/C25343380","wikidata":"https://www.wikidata.org/wiki/Q277521","display_name":"Relation (database)","level":2,"score":0.2506999969482422}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2608.08176","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.08176","pdf_url":"https://arxiv.org/pdf/2608.08176","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.2608.08176","doi":"https://doi.org/10.48550/arxiv.2608.08176","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2608.08176","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:2608.08176","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2608.08176","pdf_url":"https://arxiv.org/pdf/2608.08176","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":[{"id":"https://metadata.un.org/sdg/4","score":0.6164000034332275,"display_name":"Quality education"}],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320316083","display_name":"Tencent","ror":"https://ror.org/00hhjss72"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7202213136.pdf","grobid_xml":"https://content.openalex.org/works/W7202213136.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7167239848","https://openalex.org/W7204470223","https://openalex.org/W7204449334","https://openalex.org/W7222997000","https://openalex.org/W7162137784","https://openalex.org/W7125861034","https://openalex.org/W7161147084","https://openalex.org/W7204908525","https://openalex.org/W7214887446","https://openalex.org/W7203880136"],"abstract_inverted_index":{"On-policy":[0],"self-distillation":[1],"(OPSD)":[2],"improves":[3],"the":[4,39,54,66,72,76,80,83,93,99,111,120,124,143,164,168,177],"reasoning":[5,202],"abilities":[6],"of":[7,91,102,170],"LLMs":[8],"by":[9,25,33],"internalizing":[10],"privileged":[11,37,77],"context":[12],"into":[13,104],"model":[14,198],"parameters":[15],"through":[16,71],"self-distillation.":[17],"Two":[18],"recent":[19],"research":[20],"lines":[21,101],"promote":[22],"vanilla":[23],"OPSD":[24,190],"choosing":[26],"which":[27,57,90,109],"tokens":[28],"to":[29,59,116,141,176],"learn":[30],"from":[31],"and":[32,167,191,193],"controlling":[34],"how":[35],"much":[36],"information":[38,78],"teacher":[40,84],"receives,":[41],"respectively.":[42],"However,":[43],"we":[44,131],"show":[45],"that":[46,65,147],"each":[47],"line":[48],"optimizes":[49],"one":[50,156],"variable":[51,151],"while":[52,86],"holding":[53],"other":[55],"fixed,":[56],"leads":[58],"a":[60,105,117,137,148],"suboptimal":[61],"solution.":[62],"We":[63,97],"argue":[64],"two":[67,100],"variables":[68],"are":[69],"coupled":[70],"student's":[73,178],"learning":[74,122,159],"capacity:":[75],"sets":[79,163],"per-token":[81],"divergence":[82],"prescribes,":[85],"token":[87],"weighting":[88],"selects":[89],"these":[92],"student":[94,125],"must":[95],"absorb.":[96,127],"formalize":[98],"work":[103],"unified":[106],"optimization":[107],"framework,":[108],"maximizes":[110],"aggregate":[112,121],"teacher--student":[113],"divergence,":[114],"subject":[115],"budget":[118],"on":[119,200],"difficulty":[123],"can":[126],"Under":[128],"this":[129],"modelling,":[130],"propose":[132],"Unified":[133],"On-Policy":[134],"Self-Distillation":[135],"(USD),":[136],"lightweight":[138],"online":[139],"algorithm":[140],"solve":[142],"Lagrangian.":[144],"USD":[145,184],"reveals":[146],"single":[149],"dual":[150],"governs":[152],"both":[153],"decisions:":[154],"at":[155,207],"price":[157],"for":[158],"difficulty,":[160],"it":[161],"simultaneously":[162],"token-selection":[165],"threshold":[166],"direction":[169],"privileged-information":[171],"adjustment,":[172],"keeping":[173],"supervision":[174],"matched":[175],"evolving":[179],"capacity.":[180],"Through":[181],"extensive":[182],"experiments,":[183],"consistently":[185],"demonstrates":[186],"superior":[187],"performance":[188],"over":[189],"token-":[192],"PI-side":[194],"baselines":[195],"across":[196],"various":[197,201],"scales":[199],"benchmarks.":[203],"Code":[204],"is":[205],"available":[206],"https://github.com/lauvlalala/USD.":[208]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-08-12T00:00:00"}