{"id":"https://openalex.org/W7164911842","doi":"https://doi.org/10.48550/arxiv.2606.15576","title":"Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoning","display_name":"Localizing Credit at the Divergence: Path-Conditioned Self-Distillation for LLM Reasoning","publication_year":2026,"publication_date":"2026-06-14","ids":{"openalex":"https://openalex.org/W7164911842","doi":"https://doi.org/10.48550/arxiv.2606.15576"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.15576","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.15576","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.2606.15576","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138744922","display_name":"Yu Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Yu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138696144","display_name":"Shu Hong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hong, Shu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138698005","display_name":"Tian Lan","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lan, Tian","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/T10028","display_name":"Topic Modeling","score":0.4410000145435333,"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":0.4410000145435333,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.13619999587535858,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.09359999746084213,"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/hindsight-bias","display_name":"Hindsight bias","score":0.8162999749183655},{"id":"https://openalex.org/keywords/continuation","display_name":"Continuation","score":0.7785000205039978},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.5882999897003174},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.5033000111579895},{"id":"https://openalex.org/keywords/sample","display_name":"Sample (material)","score":0.4970000088214874},{"id":"https://openalex.org/keywords/reset","display_name":"Reset (finance)","score":0.4821000099182129},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.444599986076355},{"id":"https://openalex.org/keywords/fidelity","display_name":"Fidelity","score":0.4189000129699707}],"concepts":[{"id":"https://openalex.org/C10347200","wikidata":"https://www.wikidata.org/wiki/Q1960297","display_name":"Hindsight bias","level":2,"score":0.8162999749183655},{"id":"https://openalex.org/C88626702","wikidata":"https://www.wikidata.org/wiki/Q1128903","display_name":"Continuation","level":2,"score":0.7785000205039978},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.5882999897003174},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5716999769210815},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.5033000111579895},{"id":"https://openalex.org/C198531522","wikidata":"https://www.wikidata.org/wiki/Q485146","display_name":"Sample (material)","level":2,"score":0.4970000088214874},{"id":"https://openalex.org/C2779795794","wikidata":"https://www.wikidata.org/wiki/Q7315343","display_name":"Reset (finance)","level":2,"score":0.4821000099182129},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.444599986076355},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.4189000129699707},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.41679999232292175},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3538999855518341},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.3409999907016754},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.32850000262260437},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.32710000872612},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3160000145435333},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.30959999561309814},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3041999936103821},{"id":"https://openalex.org/C134448949","wikidata":"https://www.wikidata.org/wiki/Q1384274","display_name":"Expediting","level":2,"score":0.3025999963283539},{"id":"https://openalex.org/C2778445095","wikidata":"https://www.wikidata.org/wiki/Q18354077","display_name":"Sample complexity","level":2,"score":0.28999999165534973},{"id":"https://openalex.org/C162118730","wikidata":"https://www.wikidata.org/wiki/Q1128453","display_name":"Actuarial science","level":1,"score":0.28040000796318054},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.27480000257492065},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.2712000012397766},{"id":"https://openalex.org/C2780922921","wikidata":"https://www.wikidata.org/wiki/Q255189","display_name":"Paraphrase","level":2,"score":0.2689000070095062},{"id":"https://openalex.org/C2779458634","wikidata":"https://www.wikidata.org/wiki/Q24963715","display_name":"Debiasing","level":2,"score":0.26089999079704285},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2506999969482422}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.15576","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.15576","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.2606.15576","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.15576","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":[{"score":0.41993919014930725,"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Reinforcement":[0],"learning":[1],"from":[2,87,99],"verifiable":[3],"rewards":[4],"assigns":[5],"a":[6,32,39,48,82,93,110,130,134],"single":[7],"scalar":[8],"to":[9],"each":[10],"rollout,":[11],"leaving":[12],"token-level":[13],"credit":[14,122],"assignment":[15],"underspecified":[16],"in":[17],"long":[18],"reasoning":[19],"traces.":[20],"On-policy":[21],"self-distillation":[22],"addresses":[23],"this":[24],"by":[25],"letting":[26],"the":[27,44,59,64,79,88,100,117,120,126,148,159],"same":[28],"model":[29],"act":[30],"as":[31,166],"teacher":[33,60,80],"conditioned":[34],"on":[35,56,81,141,162],"privileged":[36],"information,":[37],"producing":[38],"dense":[40],"per-token":[41],"signal.":[42],"But":[43],"common":[45],"choice":[46],"of":[47],"ground-truth":[49],"answer":[50],"is":[51,95],"only":[52,116],"an":[53,96],"endpoint":[54],"cue:":[55],"terse-answer":[57,163],"tasks,":[58],"falls":[61],"silent":[62],"at":[63,125],"intermediate":[65],"positions":[66],"where":[67],"path-level":[68],"guidance":[69],"matters":[70],"most.":[71],"We":[72],"propose":[73],"Hindsight":[74],"Self-Distillation":[75],"(HSD),":[76],"which":[77],"conditions":[78],"successful":[83,112,135],"peer":[84,94],"rollout":[85,132],"drawn":[86],"current":[89],"training":[90],"group.":[91],"Such":[92],"exact":[97],"sample":[98],"success-conditioned":[101],"policy,":[102],"requiring":[103],"no":[104],"additional":[105],"sampled":[106],"rollouts.":[107],"By":[108],"providing":[109],"full":[111],"continuation":[113],"rather":[114],"than":[115],"final":[118],"answer,":[119],"resulting":[121],"signal":[123],"concentrates":[124],"divergence":[127],"position":[128],"between":[129],"failed":[131],"and":[133,139,143,154],"peer.":[136],"Across":[137],"Qwen3-8B":[138],"Qwen3-32B":[140],"math":[142],"code":[144],"benchmarks,":[145],"HSD":[146],"obtains":[147],"best":[149],"result":[150],"against":[151],"GRPO":[152],"variants":[153],"on-policy":[155],"distillation":[156],"baselines,":[157],"with":[158],"largest":[160],"gains":[161],"tasks":[164],"such":[165],"AIME.":[167]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-17T00:00:00"}
