{"id":"https://openalex.org/W7166568563","doi":"https://doi.org/10.48550/arxiv.2606.27739","title":"The Weakest Link Tells It All: Outcome-Supervised Process Reward Modeling via Learnable Credit Assignment","display_name":"The Weakest Link Tells It All: Outcome-Supervised Process Reward Modeling via Learnable Credit Assignment","publication_year":2026,"publication_date":"2026-06-26","ids":{"openalex":"https://openalex.org/W7166568563","doi":"https://doi.org/10.48550/arxiv.2606.27739"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.27739","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27739","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.2606.27739","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5139545564","display_name":"Tianyu Jia","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jia, Tianyu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5103512462","display_name":"Y D Fang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fang, Yue","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139544250","display_name":"Hongxin Ding","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ding, Hongxin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5111325732","display_name":"Rihong Qiu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiu, Rihong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139557688","display_name":"Zhibang Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Zhibang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139556413","display_name":"Zhijing Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Zhijing","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056733554","display_name":"Xi Chu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chu, Xu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5139566264","display_name":"Junfeng Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Junfeng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5139612316","display_name":"Yasha Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Yasha","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":0.18729999661445618,"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":0.18729999661445618,"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/T13702","display_name":"Machine Learning in Healthcare","score":0.12800000607967377,"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":0.12470000237226486,"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/correctness","display_name":"Correctness","score":0.8037999868392944},{"id":"https://openalex.org/keywords/consistency","display_name":"Consistency (knowledge bases)","score":0.6003000140190125},{"id":"https://openalex.org/keywords/pooling","display_name":"Pooling","score":0.5990999937057495},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.5626999735832214},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.541100025177002}],"concepts":[{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.8037999868392944},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7846999764442444},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.6003000140190125},{"id":"https://openalex.org/C70437156","wikidata":"https://www.wikidata.org/wiki/Q7228652","display_name":"Pooling","level":2,"score":0.5990999937057495},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.5626999735832214},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5533000230789185},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.541100025177002},{"id":"https://openalex.org/C48044578","wikidata":"https://www.wikidata.org/wiki/Q727490","display_name":"Scalability","level":2,"score":0.46939998865127563},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4562999904155731},{"id":"https://openalex.org/C2778753846","wikidata":"https://www.wikidata.org/wiki/Q6554239","display_name":"Link (geometry)","level":2,"score":0.43149998784065247},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32109999656677246},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2815999984741211}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.27739","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27739","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.2606.27739","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.27739","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":[{"id":"https://metadata.un.org/sdg/4","display_name":"Quality Education","score":0.544432520866394}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Process":[0,83],"reward":[1,101,128],"models":[2,11],"(PRMs)":[3],"enhance":[4],"the":[5,104],"reasoning":[6,50,111,157],"capabilities":[7],"of":[8,62,106,163],"large":[9],"language":[10],"(LLMs)":[12],"by":[13,31],"providing":[14],"fine-grained":[15],"feedback,":[16],"yet":[17],"training":[18],"PRMs":[19,26,178],"typically":[20],"requires":[21],"expensive":[22],"stepwise":[23],"annotations.":[24],"Outcome-supervised":[25],"offer":[27],"a":[28,40,110,135],"scalable":[29],"alternative":[30],"learning":[32],"from":[33],"final-answer":[34],"correctness":[35,70],"alone,":[36],"but":[37],"this":[38,78],"introduces":[39],"fundamental":[41],"*credit":[42],"assignment*":[43],"challenge,":[44],"i.e.,":[45],"attributing":[46],"outcomes":[47],"to":[48,65],"responsible":[49],"steps.":[51],"Existing":[52],"approaches":[53],"rely":[54],"on":[55],"either":[56],"uniform":[57],"or":[58],"causal":[59],"assignment,":[60],"both":[61],"which":[63],"fail":[64],"anchor":[66],"credit":[67,98,125],"in":[68],"step":[69],"and":[71,100,127,141,154,182],"thus":[72],"hinder":[73],"process":[74],"error":[75],"identification.":[76],"In":[77],"work,":[79],"we":[80,130],"propose":[81],"Outcome-Supervised":[82],"Reward":[84],"Modeling":[85],"via":[86],"**L**earnable":[87],"**C**redit":[88],"**A**ssignment":[89],"(**LCA**),":[90],"an":[91,146],"outcome-supervised":[92,132,177],"PRM":[93,133],"framework":[94],"that":[95,172],"jointly":[96],"learns":[97],"assignment":[99,126],"modeling":[102],"under":[103,166],"principle":[105],"*Weakest":[107],"Link":[108],"Assignment:":[109],"chain":[112],"is":[113,185],"as":[114,116,134],"strong":[115,152],"its":[117],"weakest":[118],"link*.":[119],"To":[120],"address":[121],"mutual":[122],"dependence":[123,153],"between":[124],"modeling,":[129],"formalize":[131],"Multiple":[136],"Instance":[137],"Learning":[138],"(MIL)":[139],"problem":[140],"introduce":[142],"Softmax-Weighted-Sum":[143],"(SWS)":[144],"pooling,":[145],"MIL":[147],"pooling":[148],"technique":[149],"tailored":[150],"for":[151],"redundancy":[155],"among":[156],"states.":[158],"We":[159],"prove":[160],"Bayes":[161],"consistency":[162],"our":[164],"algorithm":[165],"mild":[167],"assumptions.":[168],"Extensive":[169],"experiments":[170],"demonstrate":[171],"**LCA**":[173],"consistently":[174],"outperforms":[175],"state-of-the-art":[176],"across":[179],"multiple":[180],"tasks":[181],"backbones.":[183],"Code":[184],"available":[186],"at":[187],"https://anonymous.4open.science/r/LCA.":[188]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-30T00:00:00"}