{"id":"https://openalex.org/W7160526886","doi":"https://doi.org/10.48550/arxiv.2605.04077","title":"Balanced Aggregation: Understanding and Fixing Aggregation Bias in GRPO","display_name":"Balanced Aggregation: Understanding and Fixing Aggregation Bias in GRPO","publication_year":2026,"publication_date":"2026-04-14","ids":{"openalex":"https://openalex.org/W7160526886","doi":"https://doi.org/10.48550/arxiv.2605.04077"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.04077","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04077","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.2605.04077","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5135575790","display_name":"Zhiyuan Zeng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zeng, Zhiyuan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129654782","display_name":"Jiameng Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Jiameng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135622378","display_name":"Zhangyue Yin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yin, Zhangyue","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135582263","display_name":"Jiashuo Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Jiashuo","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135609619","display_name":"Ziniu Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Ziniu","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101653513","display_name":"Bingrui Li","orcid":"https://orcid.org/0000-0002-4807-1452"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Bingrui","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135548279","display_name":"Yuhao Wu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Yuhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135601985","display_name":"Yining Zheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Yining","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135543979","display_name":"Ge Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Ge","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135587860","display_name":"Wenhao Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Wenhao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135554480","display_name":"Xipeng Qiu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Qiu, Xipeng","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":0.19050000607967377,"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":0.19050000607967377,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.16459999978542328,"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":0.13259999454021454,"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/security-token","display_name":"Security token","score":0.8490999937057495},{"id":"https://openalex.org/keywords/sequence","display_name":"Sequence (biology)","score":0.6419000029563904},{"id":"https://openalex.org/keywords/coding","display_name":"Coding (social sciences)","score":0.5419999957084656},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.4731000065803528},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.4690999984741211},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.4032999873161316},{"id":"https://openalex.org/keywords/code","display_name":"Code (set theory)","score":0.3912999927997589},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.3716999888420105}],"concepts":[{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.8490999937057495},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.6419000029563904},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6281999945640564},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.5419999957084656},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.4731000065803528},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.4690999984741211},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.4032999873161316},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3912999927997589},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.3716999888420105},{"id":"https://openalex.org/C82578977","wikidata":"https://www.wikidata.org/wiki/Q16773055","display_name":"Data aggregator","level":3,"score":0.361299991607666},{"id":"https://openalex.org/C40506919","wikidata":"https://www.wikidata.org/wiki/Q7452469","display_name":"Sequence learning","level":2,"score":0.35690000653266907},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.34790000319480896},{"id":"https://openalex.org/C2776372474","wikidata":"https://www.wikidata.org/wiki/Q508291","display_name":"Simplicity","level":2,"score":0.3476000130176544},{"id":"https://openalex.org/C2778207910","wikidata":"https://www.wikidata.org/wiki/Q397610","display_name":"Agr\u00e9gation","level":3,"score":0.328900009393692},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32670000195503235},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.31869998574256897},{"id":"https://openalex.org/C2778334786","wikidata":"https://www.wikidata.org/wiki/Q1586270","display_name":"Variation (astronomy)","level":2,"score":0.311599999666214},{"id":"https://openalex.org/C32172795","wikidata":"https://www.wikidata.org/wiki/Q4692266","display_name":"Aggregation problem","level":2,"score":0.28929999470710754},{"id":"https://openalex.org/C2986046992","wikidata":"https://www.wikidata.org/wiki/Q16773055","display_name":"Information aggregation","level":2,"score":0.28690001368522644},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.2741999924182892},{"id":"https://openalex.org/C77618280","wikidata":"https://www.wikidata.org/wiki/Q1155772","display_name":"Scheme (mathematics)","level":2,"score":0.2531999945640564}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.04077","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04077","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.2605.04077","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.04077","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":[],"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],"with":[2,120,124],"verifiable":[3],"rewards":[4],"(RLVR)":[5],"has":[6,58],"become":[7],"a":[8,63,101,182],"central":[9],"paradigm":[10],"for":[11,27],"improving":[12],"reasoning":[13,135],"and":[14,21,30,113,116,126,130,136,146,152,165,174],"code":[15],"generation":[16],"in":[17,186],"large":[18],"language":[19],"models,":[20],"GRPO-style":[22,187],"training":[23,144],"is":[24,168],"widely":[25],"adopted":[26],"its":[28],"simplicity":[29],"effectiveness.":[31],"However,":[32],"an":[33],"important":[34],"design":[35,184],"choice":[36],"remains":[37],"underexplored:":[38],"how":[39],"token-level":[40,107],"policy":[41],"gradient":[42],"terms":[43],"are":[44],"aggregated":[45],"within":[46,110],"each":[47],"sampled":[48],"group.":[49],"Standard":[50],"GRPO":[51],"uses":[52],"sequence":[53,82,153,166],"aggregation,":[54],"while":[55,81],"recent":[56],"work":[57],"advocated":[59],"token":[60,76,151,164],"aggregation":[61,77,83,167,180],"as":[62,181],"better":[64],"alternative.":[65],"We":[66],"show":[67,139],"that":[68,105,140,159],"these":[69],"two":[70],"rules":[71],"induce":[72],"different":[73],"optimization":[74],"biases:":[75],"introduces":[78],"sign-length":[79],"coupling,":[80],"implicitly":[84],"downweights":[85],"longer":[86],"responses":[87],"through":[88],"sequence-level":[89],"equal":[90],"weighting.":[91],"To":[92],"address":[93],"this":[94],"tension,":[95],"we":[96],"propose":[97],"\\textbf{Balanced":[98],"Aggregation":[99],"(BA)},":[100],"simple":[102],"drop-in":[103],"replacement":[104],"computes":[106],"means":[108],"separately":[109],"the":[111,160,175],"positive":[112],"negative":[114],"subsets":[115],"then":[117],"combines":[118],"them":[119],"sequence-count-based":[121],"weights.":[122],"Experiments":[123],"Qwen2.5-Math-7B":[125],"Qwen3-1.7B":[127],"on":[128,133],"DAPO-17k":[129],"Polaris,":[131],"evaluated":[132],"six":[134],"coding":[137],"benchmarks,":[138],"BA":[141],"consistently":[142],"improves":[143],"stability":[145],"final":[147],"performance":[148],"over":[149],"standard":[150],"aggregation.":[154],"Our":[155],"analysis":[156],"further":[157],"shows":[158],"relative":[161],"effectiveness":[162],"of":[163],"largely":[169],"governed":[170],"by":[171],"response-length":[172],"variation":[173],"positive-negative":[176],"length":[177],"gap,":[178],"highlighting":[179],"critical":[183],"dimension":[185],"RLVR.":[188]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-08T00:00:00"}
