{"id":"https://openalex.org/W7164014171","doi":"https://doi.org/10.48550/arxiv.2606.09076","title":"Beyond Scalar Rewards by Internalizing Reasoning into Score Distributions","display_name":"Beyond Scalar Rewards by Internalizing Reasoning into Score Distributions","publication_year":2026,"publication_date":"2026-06-08","ids":{"openalex":"https://openalex.org/W7164014171","doi":"https://doi.org/10.48550/arxiv.2606.09076"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.09076","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.09076","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.2606.09076","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5138247911","display_name":"Xin Jin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin, Xin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5002997835","display_name":"Huanqia Cai","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cai, Huanqia","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138251865","display_name":"Zhen Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Zhen","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5134068969","display_name":"Zechao Zhan","orcid":"https://orcid.org/0009-0003-8752-9360"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhan, Zechao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138283684","display_name":"Dengyang Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Dengyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5110806029","display_name":"Aiming Hao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hao, Aiming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138208031","display_name":"Yuming Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiang, Yuming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120725893","display_name":"Chunle Guo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Guo, Chunle","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138247691","display_name":"Peng Gao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gao, Peng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5138204606","display_name":"Ming-Ming Cheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng, Ming-Ming","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5138262575","display_name":"Steven C. H. Hoi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Hoi, Steven C. H.","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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.7078999876976013,"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"}},"topics":[{"id":"https://openalex.org/T11714","display_name":"Multimodal Machine Learning Applications","score":0.7078999876976013,"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"}},{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.07859999686479568,"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"}},{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.039500001817941666,"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/pairwise-comparison","display_name":"Pairwise comparison","score":0.5989000201225281},{"id":"https://openalex.org/keywords/pointwise","display_name":"Pointwise","score":0.5787000060081482},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5404999852180481},{"id":"https://openalex.org/keywords/rubric","display_name":"Rubric","score":0.5371999740600586},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.492900013923645},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.4903999865055084},{"id":"https://openalex.org/keywords/probability-distribution","display_name":"Probability distribution","score":0.4569999873638153},{"id":"https://openalex.org/keywords/score","display_name":"Score","score":0.4465000033378601},{"id":"https://openalex.org/keywords/generative-model","display_name":"Generative model","score":0.4189999997615814}],"concepts":[{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.5989000201225281},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.5787000060081482},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5428000092506409},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5404999852180481},{"id":"https://openalex.org/C111640148","wikidata":"https://www.wikidata.org/wiki/Q847349","display_name":"Rubric","level":2,"score":0.5371999740600586},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.5347999930381775},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.492900013923645},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.4903999865055084},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.486299991607666},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.4569999873638153},{"id":"https://openalex.org/C65660741","wikidata":"https://www.wikidata.org/wiki/Q3952743","display_name":"Score","level":2,"score":0.4465000033378601},{"id":"https://openalex.org/C167966045","wikidata":"https://www.wikidata.org/wiki/Q5532625","display_name":"Generative model","level":3,"score":0.4189999997615814},{"id":"https://openalex.org/C12725497","wikidata":"https://www.wikidata.org/wiki/Q810247","display_name":"Baseline (sea)","level":2,"score":0.39430001378059387},{"id":"https://openalex.org/C177769412","wikidata":"https://www.wikidata.org/wiki/Q278090","display_name":"Prior probability","level":3,"score":0.38029998540878296},{"id":"https://openalex.org/C17923572","wikidata":"https://www.wikidata.org/wiki/Q7250160","display_name":"Propensity score matching","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C181204326","wikidata":"https://www.wikidata.org/wiki/Q7239820","display_name":"Preference learning","level":3,"score":0.37310001254081726},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3393999934196472},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.3249000012874603},{"id":"https://openalex.org/C193221554","wikidata":"https://www.wikidata.org/wiki/Q5153664","display_name":"Commonsense reasoning","level":2,"score":0.3222000002861023},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.32179999351501465},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3147999942302704},{"id":"https://openalex.org/C148524875","wikidata":"https://www.wikidata.org/wiki/Q6975395","display_name":"F1 score","level":2,"score":0.3133000135421753},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.3093999922275543},{"id":"https://openalex.org/C2777508537","wikidata":"https://www.wikidata.org/wiki/Q7936620","display_name":"Visual reasoning","level":2,"score":0.3070000112056732},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.30550000071525574},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.30390000343322754},{"id":"https://openalex.org/C15744967","wikidata":"https://www.wikidata.org/wiki/Q9418","display_name":"Psychology","level":0,"score":0.28679999709129333},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.2851000130176544},{"id":"https://openalex.org/C180747234","wikidata":"https://www.wikidata.org/wiki/Q23373","display_name":"Cognitive psychology","level":1,"score":0.27149999141693115},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.2669000029563904}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.09076","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.09076","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.2606.09076","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.09076","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","id":"https://metadata.un.org/sdg/4","score":0.6876470446586609}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Reward":[0],"models":[1,32],"are":[2,47],"central":[3],"to":[4,49,53,84],"text-to-image":[5,195],"post-training,":[6],"but":[7,46],"visual":[8],"preference":[9,158],"is":[10,77,90,119],"subjective":[11],"and":[12,29,35,51,89,108,114,163,176],"better":[13],"represented":[14],"as":[15,22,55,189],"a":[16,23,62,78,134,190,198],"distribution":[17,103,132],"over":[18,203],"rubric":[19],"scores":[20],"than":[21],"deterministic":[24],"scalar.":[25],"Existing":[26],"scalar,":[27],"score-token,":[28],"pairwise":[30,109],"reward":[31,64,73,192],"over-compress":[33],"uncertainty":[34],"fine-grained":[36],"score":[37,87,112,115,131],"differences,":[38],"while":[39,165],"reasoning-based":[40],"generative":[41],"rewards":[42,101],"provide":[43],"stronger":[44],"judgments":[45],"costly":[48],"deploy":[50],"difficult":[52],"use":[54],"direct":[56,106],"optimization":[57],"signals.":[58],"We":[59,182],"propose":[60],"Z-Reward,":[61],"teacher-student":[63],"modeling":[65],"framework":[66],"that":[67,81,185],"decouples":[68],"reasoning-heavy":[69],"judgment":[70],"from":[71,102],"efficient":[72],"deployment.":[74],"The":[75,117],"teacher":[76,154],"large":[79],"VLM":[80,136],"uses":[82],"reasoning":[83,140],"infer":[85],"rubric-aligned":[86],"distributions,":[88],"trained":[91,120],"with":[92,105,121],"Group-wise":[93],"Direct":[94],"Score":[95,123],"Optimization":[96],"(GDSO),":[97],"which":[98,126],"combines":[99],"policy-gradient":[100],"expectations":[104],"pointwise":[107],"supervision":[110],"on":[111],"distributions":[113],"gaps.":[116],"student":[118,169],"Reasoning-Internalized":[122],"Distillation":[124],"(RISD),":[125],"transfers":[127],"the":[128,151,166,173,179,204],"teacher's":[129],"reasoning-conditioned":[130],"into":[133],"compact":[135],"without":[137],"requiring":[138],"explicit":[139],"chains":[141],"at":[142],"inference":[143],"time.":[144],"On":[145],"our":[146],"internally":[147],"annotated":[148],"evaluation":[149],"set,":[150],"27B":[152],"GDSO":[153],"reaches":[155,170],"89.6%":[156],"human":[157],"accuracy,":[159],"outperforming":[160,172],"SFT,":[161],"RewardDance,":[162],"GRPO,":[164],"9B":[167],"RISD":[168],"88.6%,":[171],"OPD":[174],"baseline":[175],"closely":[177],"matching":[178],"larger":[180],"teacher.":[181],"further":[183],"show":[184],"Z-Reward":[186],"can":[187],"serve":[188],"differentiable":[191],"signal":[193],"for":[194],"optimization,":[196],"yielding":[197],"41.3%":[199],"net":[200],"human-preference":[201],"improvement":[202],"SFT":[205],"baseline.":[206]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-10T00:00:00"}
