{"id":"https://openalex.org/W7161942339","doi":"https://doi.org/10.48550/arxiv.2605.21467","title":"DelTA: Discriminative Token Credit Assignment for Reinforcement Learning from Verifiable Rewards","display_name":"DelTA: Discriminative Token Credit Assignment for Reinforcement Learning from Verifiable Rewards","publication_year":2026,"publication_date":"2026-05-20","ids":{"openalex":"https://openalex.org/W7161942339","doi":"https://doi.org/10.48550/arxiv.2605.21467"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.21467","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21467","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,"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.2605.21467","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136681814","display_name":"Kaiyi Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Kaiyi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136682156","display_name":"Wu, Wei, 1963-","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wu, Wei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5136665435","display_name":"Yankai Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Yankai","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":0.3774000108242035,"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":0.3774000108242035,"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":0.12870000302791595,"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":0.051600001752376556,"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/discriminative-model","display_name":"Discriminative model","score":0.8133999705314636},{"id":"https://openalex.org/keywords/discriminator","display_name":"Discriminator","score":0.7853000164031982},{"id":"https://openalex.org/keywords/centroid","display_name":"Centroid","score":0.6891999840736389},{"id":"https://openalex.org/keywords/security-token","display_name":"Security token","score":0.6759999990463257},{"id":"https://openalex.org/keywords/generalization","display_name":"Generalization","score":0.6527000069618225},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.49970000982284546},{"id":"https://openalex.org/keywords/reinforcement","display_name":"Reinforcement","score":0.4311999976634979}],"concepts":[{"id":"https://openalex.org/C97931131","wikidata":"https://www.wikidata.org/wiki/Q5282087","display_name":"Discriminative model","level":2,"score":0.8133999705314636},{"id":"https://openalex.org/C2779803651","wikidata":"https://www.wikidata.org/wiki/Q5282088","display_name":"Discriminator","level":3,"score":0.7853000164031982},{"id":"https://openalex.org/C146599234","wikidata":"https://www.wikidata.org/wiki/Q511093","display_name":"Centroid","level":2,"score":0.6891999840736389},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.6759999990463257},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.657800018787384},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6527000069618225},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5236999988555908},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.49970000982284546},{"id":"https://openalex.org/C67203356","wikidata":"https://www.wikidata.org/wiki/Q1321905","display_name":"Reinforcement","level":2,"score":0.4311999976634979},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4117000102996826},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.39590001106262207},{"id":"https://openalex.org/C118505674","wikidata":"https://www.wikidata.org/wiki/Q42586063","display_name":"Encoder","level":2,"score":0.357699990272522},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.3357999920845032},{"id":"https://openalex.org/C46900642","wikidata":"https://www.wikidata.org/wiki/Q2647","display_name":"Huffman coding","level":3,"score":0.31369999051094055},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.3041999936103821},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.29589998722076416},{"id":"https://openalex.org/C112313634","wikidata":"https://www.wikidata.org/wiki/Q7886648","display_name":"Complement (music)","level":5,"score":0.29280000925064087}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.21467","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21467","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,"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.2605.21467","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21467","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,"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":[{"id":"https://metadata.un.org/sdg/10","display_name":"Reduced inequalities","score":0.8004850745201111}],"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":[2,78,115],"verifiable":[3],"rewards":[4,26],"(RLVR)":[5],"has":[6],"emerged":[7],"as":[8,51,102],"a":[9,37,52,125,150,194],"central":[10],"technique":[11],"for":[12],"improving":[13],"the":[14,45,155,164,174,202],"reasoning":[15],"capabilities":[16],"of":[17,40,87,205],"large":[18],"language":[19],"models.":[20],"Despite":[21],"its":[22],"effectiveness,":[23],"how":[24],"response-level":[25],"translate":[27],"into":[28],"token-level":[29],"probability":[30],"changes":[31],"remains":[32],"poorly":[33],"understood.":[34],"We":[35],"introduce":[36],"discriminator":[38,54,75],"view":[39],"RLVR":[41,152,165],"updates,":[42],"showing":[43],"that":[44,110,131],"policy-gradient":[46],"update":[47,166],"direction":[48],"implicitly":[49],"acts":[50],"linear":[53],"over":[55],"token-gradient":[56,88,138],"vectors":[57],"and":[58,80,140,161,180,186,197],"thereby":[59,162],"determines":[60],"which":[61],"token":[62,127,133],"probabilities":[63],"are":[64],"increased":[65],"or":[66,143],"decreased":[67],"during":[68],"learning.":[69],"Under":[70],"standard":[71],"sequence-level":[72],"RLVR,":[73],"this":[74,120],"is":[76],"constructed":[77],"positive-":[79],"negative-side":[81],"centroids":[82,158],"formed":[83],"by":[84,97,178],"advantage-weighted":[85],"averaging":[86],"vectors.":[89],"However,":[90],"such":[91,101],"centroid":[92],"construction":[93],"can":[94],"be":[95],"dominated":[96],"shared":[98,142],"high-frequency":[99],"patterns,":[100],"formatting":[103],"tokens,":[104],"diluting":[105],"sparse":[106],"yet":[107],"discriminative":[108,126,145],"directions":[109,139],"better":[111],"distinguish":[112],"high-reward":[113],"responses":[114],"low-reward":[116],"ones.":[117,146],"To":[118],"address":[119],"limitation,":[121],"we":[122],"propose":[123],"$\\textbf{DelTA}$,":[124],"credit":[128],"assignment":[129],"method":[130],"estimates":[132],"coefficients":[134,148],"to":[135],"amplify":[136],"side-specific":[137],"downweight":[141],"weakly":[144],"These":[147],"reweight":[149],"self-normalized":[151],"surrogate,":[153],"making":[154],"effective":[156],"side-wise":[157],"more":[159],"contrastive":[160],"reshaping":[163],"direction.":[167],"On":[168],"seven":[169],"mathematical":[170],"benchmarks,":[171],"DelTA":[172],"outperforms":[173],"strongest":[175],"same-scale":[176],"baselines":[177],"3.26":[179],"2.62":[181],"average":[182],"points":[183],"on":[184,191],"Qwen3-8B-Base":[185],"Qwen3-14B-Base,":[187],"respectively.":[188],"Additional":[189],"results":[190],"code":[192],"generation,":[193],"different":[195],"backbone,":[196],"out-of-domain":[198],"evaluations":[199],"further":[200],"demonstrate":[201],"generalization":[203],"ability":[204],"DelTA.":[206]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-05-22T00:00:00"}