{"id":"https://openalex.org/W7208838824","doi":null,"title":"Rethinking On-Policy Distillation of Large Language Models II: One Training Example","display_name":"Rethinking On-Policy Distillation of Large Language Models II: One Training Example","publication_year":2026,"publication_date":"2026-09-03","ids":{"openalex":"https://openalex.org/W7208838824"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.04172","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04172","pdf_url":"https://arxiv.org/pdf/2609.04172","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"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.04172","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125070971","display_name":"Zixuan Fu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Fu, Zixuan","raw_affiliation_strings":["Equal Contribution","Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equal Contribution","institution_ids":[]},{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140869968","display_name":"Bingxiang He","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"He, Bingxiang","raw_affiliation_strings":["Equal Contribution","Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equal Contribution","institution_ids":[]},{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5113051745","display_name":"Yuxin Zuo","orcid":"https://orcid.org/0009-0005-2771-7997","observed_orcids":["https://orcid.org/0009-0005-2771-7997"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zuo, Yuxin","raw_affiliation_strings":["Equal Contribution"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Equal Contribution","institution_ids":[]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130817390","display_name":"Haohuan Huang","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Haohuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125960392","display_name":"Jinqian Zhang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Zhang, Jinqian","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5150286891","display_name":"Ruhang Xiao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I12912129","display_name":"Northeastern University","ror":"https://ror.org/04t5xt781","country_code":"US","type":"education","lineage":["https://openalex.org/I12912129"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xiao, Ruhang","raw_affiliation_strings":["Northeastern University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Northeastern University","institution_ids":["https://openalex.org/I12912129"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139764426","display_name":"Cheng Qian","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I157725225","display_name":"University of Illinois Urbana-Champaign","ror":"https://ror.org/047426m28","country_code":"US","type":"education","lineage":["https://openalex.org/I157725225"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qian, Cheng","raw_affiliation_strings":["University of Illinois Urbana-Champaign"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Illinois Urbana-Champaign","institution_ids":["https://openalex.org/I157725225"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5140907301","display_name":"Qinyu Luo","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I145311948","display_name":"Johns Hopkins University","ror":"https://ror.org/00za53h95","country_code":"US","type":"education","lineage":["https://openalex.org/I145311948"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Luo, Qinyu","raw_affiliation_strings":["Johns Hopkins University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Johns Hopkins University","institution_ids":["https://openalex.org/I145311948"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128644194","display_name":"Huan-ang Gao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Gao, Huan-ang","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125087101","display_name":"Yudong Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Wang, Yudong","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5150203812","display_name":"Zhiyuan Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Zhiyuan","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133894415","display_name":"Ning Ding","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Ding, Ning","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5014699953","display_name":"Chaojun Xiao","orcid":"https://orcid.org/0000-0001-6039-0942","observed_orcids":["https://orcid.org/0000-0001-6039-0942","https://orcid.org/0009-0003-4475-0946"]},"institutions":[{"id":"https://openalex.org/I99065089","display_name":"Tsinghua University","ror":"https://ror.org/03cve4549","country_code":"CN","type":"education","lineage":["https://openalex.org/I99065089"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiao, Chaojun","raw_affiliation_strings":["Tsinghua University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"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":0.4065000116825104,"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":0.4065000116825104,"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":0.34470000863075256,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.09229999780654907,"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-distillation","display_name":"on-policy distillation","score":0.9990000128746033},{"id":"https://openalex.org/keywords/large-language-models","display_name":"large language models","score":0.890999972820282},{"id":"https://openalex.org/keywords/state-coverage","display_name":"state coverage","score":0.7170000076293945},{"id":"https://openalex.org/keywords/teacher-student-alignment","display_name":"teacher-student alignment","score":0.8169999718666077},{"id":"https://openalex.org/keywords/multi-teacher-knowledge-distillation","display_name":"multi-teacher distillation","score":0.7929999828338623},{"id":"https://openalex.org/keywords/training-data-efficiency","display_name":"training data efficiency","score":0.5120000243186951},{"id":"https://openalex.org/keywords/post-training","display_name":"post-training","score":0.40400001406669617},{"id":"https://openalex.org/keywords/rollout","display_name":"rollout","score":0.5429999828338623}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.8295000195503235},{"id":"https://openalex.org/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"score":0.6858999729156494},{"id":"https://openalex.org/C2777526511","wikidata":"https://www.wikidata.org/wiki/Q691543","display_name":"Pace","level":2,"score":0.6478000283241272},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.5895000100135803},{"id":"https://openalex.org/C149629883","wikidata":"https://www.wikidata.org/wiki/Q660926","display_name":"Fraction (chemistry)","level":2,"score":0.5378999710083008},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.5031999945640564},{"id":"https://openalex.org/C190839683","wikidata":"https://www.wikidata.org/wiki/Q2448197","display_name":"Train","level":2,"score":0.4984000027179718},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.48080000281333923},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.4733999967575073},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C99016210","wikidata":"https://www.wikidata.org/wiki/Q5488129","display_name":"Query expansion","level":2,"score":0.39250001311302185},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3912999927997589},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.3589000105857849},{"id":"https://openalex.org/C189430467","wikidata":"https://www.wikidata.org/wiki/Q7293293","display_name":"Ranking (information retrieval)","level":2,"score":0.3481000065803528},{"id":"https://openalex.org/C204030448","wikidata":"https://www.wikidata.org/wiki/Q101017","display_name":"Distillation","level":2,"score":0.34599998593330383},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3357999920845032},{"id":"https://openalex.org/C192028432","wikidata":"https://www.wikidata.org/wiki/Q845739","display_name":"Query language","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C9652623","wikidata":"https://www.wikidata.org/wiki/Q190109","display_name":"Field (mathematics)","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.2989000082015991},{"id":"https://openalex.org/C12725497","wikidata":"https://www.wikidata.org/wiki/Q810247","display_name":"Baseline (sea)","level":2,"score":0.29600000381469727},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C136197465","wikidata":"https://www.wikidata.org/wiki/Q1729295","display_name":"Variety (cybernetics)","level":2,"score":0.2915000021457672},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28540000319480896},{"id":"https://openalex.org/C157692150","wikidata":"https://www.wikidata.org/wiki/Q2919848","display_name":"Query optimization","level":2,"score":0.28360000252723694},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.28060001134872437},{"id":"https://openalex.org/C23123220","wikidata":"https://www.wikidata.org/wiki/Q816826","display_name":"Information retrieval","level":1,"score":0.2734000086784363},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.26989999413490295},{"id":"https://openalex.org/C175154964","wikidata":"https://www.wikidata.org/wiki/Q380077","display_name":"Task analysis","level":3,"score":0.2694999873638153}],"mesh":[],"locations_count":1,"locations":[{"id":"pmh:oai:arXiv.org:2609.04172","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04172","pdf_url":"https://arxiv.org/pdf/2609.04172","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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2609.04172","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.04172","pdf_url":"https://arxiv.org/pdf/2609.04172","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":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality education","score":0.5}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7208838824.pdf","grobid_xml":"https://content.openalex.org/works/W7208838824.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7211899717","https://openalex.org/W7221072085","https://openalex.org/W7154505894","https://openalex.org/W7213256728","https://openalex.org/W7148454362","https://openalex.org/W7141388625","https://openalex.org/W7160438937","https://openalex.org/W7168964786","https://openalex.org/W7221829010","https://openalex.org/W7161054869"],"abstract_inverted_index":{"On-policy":[0],"distillation":[1],"(OPD)":[2],"combines":[3],"student-generated":[4],"rollouts":[5,100,172],"with":[6,81],"dense":[7],"token-level":[8],"supervision":[9,182],"from":[10],"a":[11,39,97,139,154,203,243],"teacher.":[12,83],"Existing":[13],"work":[14,234],"has":[15],"mainly":[16],"studied":[17],"its":[18,252],"algorithmic":[19],"behavior,":[20],"leaving":[21],"the":[22,33,68,74,78,82,88,91,112,149,178,215,236,246,249],"role":[23,31],"of":[24,48,53,90,109,157,161,239,245],"training":[25,37,72],"data":[26,247],"unclear.":[27],"We":[28,63,84,228],"examine":[29],"this":[30,65],"at":[32,76,138],"data-minimal":[34],"limit":[35],"by":[36],"on":[38,145],"single":[40,103],"query.":[41],"One-shot":[42],"OPD":[43,94,143,165],"keeps":[44],"improving":[45],"for":[46],"hundreds":[47,160],"steps":[49,162],"and":[50,60,73,122,131,152,209,220,241,248],"recovers":[51],"most":[52,108],"full-data":[54,93,133,200],"OPD's":[55],"gain":[56],"across":[57],"task":[58],"domains":[59],"model":[61],"families.":[62],"explain":[64],"result":[66,187],"through":[67],"states":[69,92,158],"visited":[70],"during":[71],"rate":[75],"which":[77],"student":[79,179],"aligns":[80],"measure":[85],"\\emph{state":[86],"coverage},":[87],"fraction":[89],"visits":[95],"that":[96,181],"query":[98,104,147],"set's":[99],"reach.":[101],"A":[102],"already":[105],"reaches":[106],"\\(71.5\\%\\),":[107],"it":[110],"within":[111],"first":[113],"100":[114],"steps.":[115],"Adding":[116],"semantically":[117,194],"distinct":[118],"queries":[119,128,196,212],"raises":[120],"coverage":[121,223],"validation":[123],"accuracy":[124],"together,":[125],"until":[126],"16":[127,193],"reach":[129],"\\(98.9\\%\\)":[130],"match":[132,199],"training.":[134],"Yet":[135],"alignment":[136],"slows":[137],"similar":[140],"pace":[141],"whether":[142],"trains":[144],"one":[146],"or":[148],"whole":[150],"dataset,":[151],"even":[153],"fixed":[155],"set":[156],"takes":[159],"to":[163,189],"absorb.":[164],"is":[166],"therefore":[167,225],"data-overfed":[168],"but":[169],"algorithm-starved.":[170],"Its":[171],"quickly":[173],"expose":[174],"broad":[175],"supervision,":[176],"while":[177],"absorbs":[180],"increasingly":[183],"slowly.":[184],"The":[185],"state-coverage":[186],"extends":[188],"multi-teacher":[190],"OPD,":[191,240],"where":[192],"diverse":[195],"per":[197],"domain":[198],"MOPD.":[201],"As":[202],"further":[204],"stress":[205],"test,":[206],"content-light":[207],"templates":[208],"off-domain":[210],"WildChat":[211],"also":[213],"approach":[214],"real-query":[216],"baseline.":[217],"Task":[218],"content":[219],"induced":[221],"state":[222],"can":[224],"come":[226],"apart.":[227],"hope":[229],"these":[230],"findings":[231],"direct":[232],"future":[233],"toward":[235],"step":[237],"efficiency":[238],"prompt":[242],"re-examination":[244],"mechanisms":[250],"behind":[251],"recent":[253],"successes":[254],"in":[255],"frontier":[256],"post-training.":[257]},"counts_by_year":[],"updated_date":"2026-10-29T09:56:32.521200","created_date":"2026-09-06T00:00:00"}