{"id":"https://openalex.org/W7162095020","doi":"https://doi.org/10.48550/arxiv.2605.22074","title":"From Reasoning Chains to Verifiable Subproblems: Curriculum Reinforcement Learning Enables Credit Assignment for LLM Reasoning","display_name":"From Reasoning Chains to Verifiable Subproblems: Curriculum Reinforcement Learning Enables Credit Assignment for LLM Reasoning","publication_year":2026,"publication_date":"2026-05-21","ids":{"openalex":"https://openalex.org/W7162095020","doi":"https://doi.org/10.48550/arxiv.2605.22074"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.22074","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.22074","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":null,"license_id":null,"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.2605.22074","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5125206336","display_name":"Xitai Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Xitai","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136739409","display_name":"Zihan Tang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tang, Zihan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5123326411","display_name":"Wenze Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Wenze","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136801775","display_name":"Yang Yue","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yue, Yang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136737375","display_name":"Shenzhi Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Shenzhi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136799790","display_name":"Gao Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Gao","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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.3221000134944916,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.3221000134944916,"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":0.2320999950170517,"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/T10028","display_name":"Topic Modeling","score":0.13199999928474426,"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/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.8511999845504761},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.6509000062942505},{"id":"https://openalex.org/keywords/curriculum","display_name":"Curriculum","score":0.45829999446868896},{"id":"https://openalex.org/keywords/rubric","display_name":"Rubric","score":0.44429999589920044},{"id":"https://openalex.org/keywords/position","display_name":"Position (finance)","score":0.3953000009059906},{"id":"https://openalex.org/keywords/point","display_name":"Point (geometry)","score":0.38690000772476196}],"concepts":[{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.8511999845504761},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6589999794960022},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.6509000062942505},{"id":"https://openalex.org/C47177190","wikidata":"https://www.wikidata.org/wiki/Q207137","display_name":"Curriculum","level":2,"score":0.45829999446868896},{"id":"https://openalex.org/C111640148","wikidata":"https://www.wikidata.org/wiki/Q847349","display_name":"Rubric","level":2,"score":0.44429999589920044},{"id":"https://openalex.org/C198082294","wikidata":"https://www.wikidata.org/wiki/Q3399648","display_name":"Position (finance)","level":2,"score":0.3953000009059906},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.387800008058548},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.38690000772476196},{"id":"https://openalex.org/C139002025","wikidata":"https://www.wikidata.org/wiki/Q3001212","display_name":"Lift (data mining)","level":2,"score":0.3513999879360199},{"id":"https://openalex.org/C78780964","wikidata":"https://www.wikidata.org/wiki/Q7233193","display_name":"Position paper","level":2,"score":0.31949999928474426},{"id":"https://openalex.org/C77967617","wikidata":"https://www.wikidata.org/wiki/Q4677561","display_name":"Active learning (machine learning)","level":2,"score":0.29750001430511475},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.29249998927116394},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.28369998931884766},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2833000123500824},{"id":"https://openalex.org/C206729178","wikidata":"https://www.wikidata.org/wiki/Q2271896","display_name":"Scheduling (production processes)","level":2,"score":0.26739999651908875},{"id":"https://openalex.org/C127705205","wikidata":"https://www.wikidata.org/wiki/Q5748245","display_name":"Heuristics","level":2,"score":0.2583000063896179}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.22074","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.22074","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.22074","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.22074","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},"sustainable_development_goals":[{"display_name":"Quality Education","score":0.804205596446991,"id":"https://metadata.un.org/sdg/4"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Reinforcement":[0,43],"learning":[1,75],"from":[2,53],"verifiable":[3,51,74],"rewards":[4,84],"(RLVR)":[5],"has":[6],"shown":[7],"strong":[8,141],"promise":[9],"for":[10],"LLM":[11],"reasoning,":[12],"but":[13],"outcome-based":[14],"RLVR":[15],"remains":[16],"inefficient":[17],"on":[18,70,152,157,176,181],"hard":[19,71,117,182],"problems":[20,72,118],"because":[21],"correct":[22],"final-answer":[23],"rollouts":[24],"are":[25],"rare":[26],"and":[27,57,90,154,162,171],"sample-level":[28],"credit":[29,102],"assignment":[30,103],"cannot":[31],"use":[32],"partial":[33,68],"progress":[34,69],"in":[35],"failed":[36],"attempts.":[37],"We":[38],"introduce":[39],"SCRL":[40,78,139,164],"(Subproblem":[41],"Curriculum":[42],"Learning),":[44],"a":[45],"curriculum":[46],"RL":[47],"framework":[48],"that":[49,113],"derives":[50],"subproblems":[52],"reference":[54],"reasoning":[55,137,183],"chains":[56],"fixes":[58],"the":[59,63,92,96,129],"final":[60],"subproblem":[61,88,114],"as":[62,128],"original":[64,130],"problem.":[65],"This":[66],"turns":[67],"into":[73],"signals.":[76],"Algorithmically,":[77],"uses":[79],"subproblem-level":[80],"normalization,":[81],"which":[82],"normalizes":[83],"independently":[85],"at":[86],"each":[87],"position":[89],"assigns":[91],"resulting":[93],"advantages":[94],"to":[95],"corresponding":[97],"answer":[98],"spans,":[99],"enabling":[100],"finer-grained":[101],"without":[104],"external":[105],"rubrics":[106],"or":[107],"reward":[108],"models.":[109],"Our":[110],"analysis":[111],"shows":[112],"curricula":[115],"lift":[116],"out":[119],"of":[120],"gradient":[121],"dead":[122],"zones,":[123],"with":[124],"larger":[125],"relative":[126],"gains":[127],"problem":[131],"becomes":[132],"harder.":[133],"Across":[134],"seven":[135],"mathematical":[136],"benchmarks,":[138],"outperforms":[140],"curriculum-learning":[142],"baselines,":[143],"improving":[144],"average":[145],"accuracy":[146],"over":[147],"GRPO":[148],"by":[149,168,173],"+4.1":[150],"points":[151,156,170,175],"Qwen3-4B-Base":[153],"+1.9":[155],"Qwen3-14B-Base.":[158],"On":[159],"AIME24,":[160],"AIME25,":[161],"IMO-Bench,":[163],"further":[165],"improves":[166],"pass@1":[167],"+3.7":[169],"pass@64":[172],"+4.6":[174],"Qwen3-4B-Base,":[177],"indicating":[178],"better":[179],"exploration":[180],"problems.":[184]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-23T00:00:00"}
