{"id":"https://openalex.org/W7146986302","doi":"https://doi.org/10.48550/arxiv.2603.28204","title":"ERPO: Token-Level Entropy-Regulated Policy Optimization for Large Reasoning Models","display_name":"ERPO: Token-Level Entropy-Regulated Policy Optimization for Large Reasoning Models","publication_year":2026,"publication_date":"2026-03-30","ids":{"openalex":"https://openalex.org/W7146986302","doi":"https://doi.org/10.48550/arxiv.2603.28204"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.28204","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28204","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.28204","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132603411","display_name":"Song Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Song","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132600718","display_name":"Li Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Li","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Zhao, Wenwen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhao, Wenwen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Yang, Zhisheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yang, Zhisheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"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":0.37619999051094055,"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":0.37619999051094055,"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":0.12729999423027039,"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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.11249999701976776,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/debiasing","display_name":"Debiasing","score":0.49540001153945923},{"id":"https://openalex.org/keywords/security-token","display_name":"Security token","score":0.4909999966621399},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.4885999858379364},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.4383000135421753},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.4320000112056732},{"id":"https://openalex.org/keywords/leverage","display_name":"Leverage (statistics)","score":0.4205000102519989},{"id":"https://openalex.org/keywords/trajectory","display_name":"Trajectory","score":0.3564999997615814}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6818000078201294},{"id":"https://openalex.org/C2779458634","wikidata":"https://www.wikidata.org/wiki/Q24963715","display_name":"Debiasing","level":2,"score":0.49540001153945923},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.4909999966621399},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.4885999858379364},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4507000148296356},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.4383000135421753},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.4320000112056732},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.4205000102519989},{"id":"https://openalex.org/C13662910","wikidata":"https://www.wikidata.org/wiki/Q193139","display_name":"Trajectory","level":2,"score":0.3564999997615814},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.3303000032901764},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.3179999887943268},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.2985999882221222},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.2985000014305115},{"id":"https://openalex.org/C2777735758","wikidata":"https://www.wikidata.org/wiki/Q817765","display_name":"Path (computing)","level":2,"score":0.29420000314712524},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.2913999855518341},{"id":"https://openalex.org/C83725634","wikidata":"https://www.wikidata.org/wiki/Q7268699","display_name":"Qualitative reasoning","level":2,"score":0.289900004863739},{"id":"https://openalex.org/C166052673","wikidata":"https://www.wikidata.org/wiki/Q83021","display_name":"Empirical evidence","level":2,"score":0.2768000066280365},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.27469998598098755},{"id":"https://openalex.org/C137822555","wikidata":"https://www.wikidata.org/wiki/Q2587068","display_name":"Information sensitivity","level":2,"score":0.26649999618530273},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.25099998712539673}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.28204","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28204","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.28204","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28204","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":"article"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/16","score":0.6334353089332581,"display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Reinforcement":[0],"learning":[1],"from":[2,120],"verifiable":[3],"rewards":[4],"has":[5],"significantly":[6,180,193],"advanced":[7],"the":[8,32,53,75,86,89,117],"reasoning":[9,37,59,188],"capabilities":[10],"of":[11,209],"large":[12,205],"language":[13],"models.":[14],"However,":[15],"Group":[16],"Relative":[17],"Policy":[18,112],"Optimization":[19,113],"(GRPO)":[20],"typically":[21],"assigns":[22],"a":[23],"uniform,":[24],"sequence-level":[25],"advantage":[26,103],"to":[27,47,55,81,123,141,204],"all":[28],"tokens,":[29],"thereby":[30],"overlooking":[31],"intrinsic":[33],"information":[34],"heterogeneity":[35],"along":[36],"chains.":[38],"We":[39],"show":[40],"that":[41,178],"this":[42],"coarse-grained":[43],"credit":[44],"assignment":[45],"leads":[46],"premature":[48],"entropy":[49],"collapse":[50],"and":[51,159,196],"encourages":[52],"model":[54],"generate":[56],"redundant,":[57],"low-quality":[58],"paths.":[60],"Through":[61],"systematic":[62],"empirical":[63],"analysis,":[64],"we":[65,109],"identify":[66],"Critical":[67],"Decision":[68],"Pivots":[69],"(CDPs):":[70],"transient":[71],"high-entropy":[72],"states":[73],"where":[74,91],"policy's":[76],"trajectory":[77],"is":[78,95],"most":[79,96],"sensitive":[80],"perturbations.":[82],"These":[83],"pivots":[84],"represent":[85],"\"forks":[87],"in":[88],"road\"":[90],"effective":[92],"multi-path":[93],"exploration":[94,138],"crucial":[97],"yet":[98],"often":[99],"suppressed":[100],"by":[101,154],"uniform":[102],"signals.":[104],"Building":[105],"on":[106,173],"these":[107],"insights,":[108],"propose":[110],"Entropy-Regulated":[111],"(ERPO),":[114],"which":[115,135,150,164],"transitions":[116],"optimization":[118],"focus":[119],"coarse":[121],"sequences":[122],"fine-grained":[124],"token":[125,156],"dynamics.":[126],"ERPO":[127,179,184],"introduces":[128],"three":[129],"synergistic":[130],"components:":[131],"(i)":[132],"Entropy-aware":[133],"Gating,":[134],"adaptively":[136],"amplifies":[137],"at":[139],"CDPs":[140],"facilitate":[142],"diverse":[143],"path":[144],"discovery;":[145],"(ii)":[146],"Bucket-based":[147],"Implicit":[148],"Normalization,":[149],"mitigates":[151],"difficulty":[152],"bias":[153],"aligning":[155],"progress":[157],"windows;":[158],"(iii)":[160],"Result-anchored":[161],"Advantage":[162],"Synthesis,":[163],"re-weights":[165],"token-level":[166],"signals":[167],"via":[168],"outcome-driven":[169],"anchors.":[170],"Extensive":[171],"experiments":[172],"competitive":[174],"mathematical":[175],"benchmarks":[176],"demonstrate":[177],"outperforms":[181],"GRPO.":[182],"Notably,":[183],"not":[185],"only":[186],"boosts":[187],"accuracy":[189],"but":[190],"also":[191],"yields":[192],"more":[194,211],"concise":[195],"robust":[197],"derivation":[198],"paths,":[199],"while":[200],"achieving":[201],"performance":[202],"comparable":[203],"models":[206],"with":[207],"orders":[208],"magnitude":[210],"parameters.":[212]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-04-02T00:00:00"}