{"id":"https://openalex.org/W7160959773","doi":"https://doi.org/10.48550/arxiv.2605.10325","title":"Verifiable Process Rewards for Agentic Reasoning","display_name":"Verifiable Process Rewards for Agentic Reasoning","publication_year":2026,"publication_date":"2026-05-11","ids":{"openalex":"https://openalex.org/W7160959773","doi":"https://doi.org/10.48550/arxiv.2605.10325"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2605.10325","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.10325","pdf_url":"https://arxiv.org/pdf/2605.10325","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2605.10325","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135941419","display_name":"Huining Yuan","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":"Yuan, Huining","raw_affiliation_strings":["Tsinghua University Project Page Code Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University Project Page Code Models","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Xu, Zelai","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":"Xu, Zelai","raw_affiliation_strings":["Tsinghua University Project Page Code Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University Project Page Code Models","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125685131","display_name":"Huaijie 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, Huaijie","raw_affiliation_strings":["Tsinghua University Project Page Code Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University Project Page Code Models","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126025025","display_name":"Xiangmin Yi","orcid":"https://orcid.org/0009-0009-0078-4945","observed_orcids":["https://orcid.org/0009-0009-0078-4945"]},"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":"Yi, Xiangmin","raw_affiliation_strings":["Tsinghua University Project Page Code Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University Project Page Code Models","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135987849","display_name":"Jiaxuan 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, Jiaxuan","raw_affiliation_strings":["Tsinghua University Project Page Code Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University Project Page Code Models","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133542893","display_name":"Xiao-Ping 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, Xiao-Ping","raw_affiliation_strings":["Tsinghua University Project Page Code Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University Project Page Code Models","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135983239","display_name":"Yu Wang","orcid":"https://orcid.org/0000-0002-8683-6196","observed_orcids":["https://orcid.org/0000-0002-8683-6196"]},"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, Yu","raw_affiliation_strings":["Tsinghua University Project Page Code Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University Project Page Code Models","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125637105","display_name":"Chao Yu","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":"Yu, Chao","raw_affiliation_strings":["Tsinghua University Project Page Code Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University Project Page Code Models","institution_ids":["https://openalex.org/I99065089"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5135990283","display_name":"Yi Wu","orcid":"https://orcid.org/0000-0002-5243-7488","observed_orcids":["https://orcid.org/0000-0002-5243-7488"]},"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":"Wu, Yi","raw_affiliation_strings":["Tsinghua University Project Page Code Models"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Tsinghua University Project Page Code Models","institution_ids":["https://openalex.org/I99065089"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I99065089"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":13,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9570000171661377,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.9570000171661377,"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/T10906","display_name":"AI-based Problem Solving and Planning","score":0.007199999876320362,"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/T11574","display_name":"Artificial Intelligence in Games","score":0.007000000216066837,"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/reinforcement-learning-from-verifiable-rewards","display_name":"reinforcement learning from verifiable rewards","score":0.902999997138977},{"id":"https://openalex.org/keywords/agentic-reasoning","display_name":"agentic reasoning","score":0.9700000286102295},{"id":"https://openalex.org/keywords/credit-assignment","display_name":"credit assignment","score":0.7599999904632568},{"id":"https://openalex.org/keywords/sokoban","display_name":"Sokoban","score":0.8859999775886536},{"id":"https://openalex.org/keywords/sudoku","display_name":"Sudoku","score":0.9879999756813049},{"id":"https://openalex.org/keywords/minesweeper","display_name":"Minesweeper","score":0.9990000128746033},{"id":"https://openalex.org/keywords/qwen3","display_name":"Qwen3","score":0.5099999904632568},{"id":"https://openalex.org/keywords/group-relative-policy-optimization","display_name":"Group Relative Policy Optimization","score":0.5709999799728394},{"id":"https://openalex.org/keywords/mathematical-reasoning","display_name":"mathematical reasoning","score":0.5},{"id":"https://openalex.org/keywords/tool-use","display_name":"tool use","score":0.6380000114440918}],"concepts":[{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.886900007724762},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7386000156402588},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.6520000100135803},{"id":"https://openalex.org/C55166926","wikidata":"https://www.wikidata.org/wiki/Q2892946","display_name":"Oracle","level":2,"score":0.5989999771118164},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.5684000253677368},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5522000193595886},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5253999829292297},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.43140000104904175},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.4214000105857849},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4004000127315521},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.3677999973297119},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.3278000056743622},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2957000136375427},{"id":"https://openalex.org/C2779110517","wikidata":"https://www.wikidata.org/wiki/Q1240788","display_name":"Supervisor","level":2,"score":0.2624000012874603},{"id":"https://openalex.org/C43971567","wikidata":"https://www.wikidata.org/wiki/Q3142865","display_name":"Logical reasoning","level":2,"score":0.26109999418258667},{"id":"https://openalex.org/C2777530160","wikidata":"https://www.wikidata.org/wiki/Q41796","display_name":"Sentence","level":2,"score":0.2533000111579895},{"id":"https://openalex.org/C193221554","wikidata":"https://www.wikidata.org/wiki/Q5153664","display_name":"Commonsense reasoning","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2605.10325","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.10325","pdf_url":"https://arxiv.org/pdf/2605.10325","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"},{"id":"doi:10.48550/arxiv.2605.10325","doi":"https://doi.org/10.48550/arxiv.2605.10325","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.10325","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":"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2605.10325","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2605.10325","pdf_url":"https://arxiv.org/pdf/2605.10325","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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7160959773.pdf","grobid_xml":"https://content.openalex.org/works/W7160959773.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W2964121744","https://openalex.org/W2973727699","https://openalex.org/W3126325318","https://openalex.org/W4310290453","https://openalex.org/W4386185625","https://openalex.org/W4387560542","https://openalex.org/W4391631327","https://openalex.org/W4405766390","https://openalex.org/W4414281281","https://openalex.org/W4414810229","https://openalex.org/W4414939355","https://openalex.org/W4417093501","https://openalex.org/W4417097658"],"related_works":["https://openalex.org/W7084035026","https://openalex.org/W7166862171","https://openalex.org/W7168302452","https://openalex.org/W7154948584","https://openalex.org/W7166806848","https://openalex.org/W7155413322","https://openalex.org/W7214088552","https://openalex.org/W4403365357","https://openalex.org/W4417029006","https://openalex.org/W7139932157"],"abstract_inverted_index":{"Reinforcement":[0],"learning":[1],"from":[2],"verifiable":[3],"rewards":[4,70],"(RLVR)":[5],"has":[6],"improved":[7,185],"the":[8,143,153,216,224],"reasoning":[9,41],"capabilities":[10],"of":[11,220,226],"large":[12],"language":[13],"models":[14],"(LLMs),":[15],"yet":[16],"existing":[17],"approaches":[18],"predominantly":[19],"rely":[20],"on":[21,133,190,215],"sparse":[22],"outcome-level":[23],"feedback,":[24],"posing":[25],"a":[26,56,86,91,97,180,199],"substantial":[27],"credit-assignment":[28],"challenge":[29,225],"in":[30,82],"long-horizon":[31],"agentic":[32,40,150,165,209],"tasks.":[33,192],"In":[34],"this":[35],"work,":[36],"we":[37,108,168],"study":[38],"structured":[39],"problems":[42],"that":[43,59],"admit":[44],"symbolic":[45],"or":[46],"algorithmic":[47],"task-solving":[48],"oracles.":[49],"We":[50,79],"propose":[51],"Verifiable":[52],"Process":[53],"Rewards":[54],"(VPR),":[55],"training":[57,128,155],"framework":[58],"repurposes":[60],"such":[61],"task":[62,205,221],"oracles":[63,206,222],"as":[64,179,198],"action-level":[65,171],"process":[66],"verifiers,":[67],"providing":[68],"dense":[69],"for":[71,89,94,100,202],"intermediate":[72,228],"actions":[73],"and":[74,96,113,123,136,148,183,218,223],"enabling":[75],"fine-grained":[76],"credit":[77],"assignment.":[78],"instantiate":[80],"VPR":[81,141,197],"three":[83,127,138],"distinct":[84],"settings:":[85],"search-based":[87],"oracle":[88,93,99],"Sokoban,":[90],"constraint-based":[92],"Sudoku,":[95],"posterior-based":[98],"Minesweeper.":[101],"To":[102,157],"optimize":[103],"policies":[104],"with":[105],"these":[106,194],"rewards,":[107],"introduce":[109],"oracle-guided":[110],"state-group":[111],"rollout":[112],"locally":[114],"normalized":[115],"optimization.":[116],"Empirically,":[117],"VPR-trained":[118],"Qwen3-4B":[119],"outperforms":[120],"outcome-reward":[121,188],"GRPO":[122,189],"VinePPO":[124],"across":[125],"all":[126,137],"environments.":[129,234],"When":[130],"jointly":[131],"trained":[132],"math":[134],"data":[135],"game":[139],"environments,":[140],"achieves":[142],"highest":[144],"average":[145],"general-reasoning":[146],"performance":[147,186],"strongest":[149],"results":[151,195],"among":[152],"compared":[154],"configurations.":[156],"further":[158],"assess":[159],"its":[160,213],"applicability":[161],"to":[162,173,207,230],"more":[163],"general":[164],"tool-use":[166],"settings,":[167],"apply":[169],"VPR-style":[170],"supervision":[172],"$\u03c4^2$-bench":[174],"using":[175],"an":[176],"expert":[177],"LLM":[178],"reference":[181],"policy":[182],"observe":[184],"over":[187],"held-out":[191],"Together,":[193],"position":[196],"promising":[200],"approach":[201],"leveraging":[203],"reliable":[204],"improve":[208],"reasoning,":[210],"while":[211],"highlighting":[212],"dependence":[214],"availability":[217],"reliability":[219],"extending":[227],"verification":[229],"less":[231],"structured,":[232],"open-ended":[233]},"counts_by_year":[{"year":2026,"cited_by_count":13}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2026-05-13T00:00:00"}