{"id":"https://openalex.org/W7214200768","doi":"https://doi.org/10.48550/arxiv.2609.27156","title":"Giving Credit Where It's Due: Redundancy-Aware Learning for Efficient Reasoning","display_name":"Giving Credit Where It's Due: Redundancy-Aware Learning for Efficient Reasoning","publication_year":2026,"publication_date":"2026-09-22","ids":{"openalex":"https://openalex.org/W7214200768","doi":"https://doi.org/10.48550/arxiv.2609.27156"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2609.27156","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27156","pdf_url":"https://arxiv.org/pdf/2609.27156","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2609.27156","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5100951608","display_name":"Yuqing Zhou","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhou, Yuqing","raw_affiliation_strings":["George Mason University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"George Mason University ,","institution_ids":["https://openalex.org/I162714631"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152650469","display_name":"Hong Wang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1311688040","display_name":"Amazon (United States)","ror":"https://ror.org/04mv4n011","country_code":"US","type":"company","lineage":["https://openalex.org/I1311688040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wang, Hong","raw_affiliation_strings":["Amazon , Inc"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amazon , Inc","institution_ids":["https://openalex.org/I1311688040"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109673732","display_name":"M Mao","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1311688040","display_name":"Amazon (United States)","ror":"https://ror.org/04mv4n011","country_code":"US","type":"company","lineage":["https://openalex.org/I1311688040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mao, Manqing","raw_affiliation_strings":["Amazon , Inc"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amazon , Inc","institution_ids":["https://openalex.org/I1311688040"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043118539","display_name":"Zhuoer Wang","orcid":"https://orcid.org/0009-0007-6134-0630","observed_orcids":["https://orcid.org/0009-0007-6134-0630"]},"institutions":[{"id":"https://openalex.org/I1311688040","display_name":"Amazon (United States)","ror":"https://ror.org/04mv4n011","country_code":"US","type":"company","lineage":["https://openalex.org/I1311688040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wang, Zhuoer","raw_affiliation_strings":["Amazon , Inc"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amazon , Inc","institution_ids":["https://openalex.org/I1311688040"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5144869067","display_name":"Samson Koelle","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1311688040","display_name":"Amazon (United States)","ror":"https://ror.org/04mv4n011","country_code":"US","type":"company","lineage":["https://openalex.org/I1311688040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Koelle, Samson","raw_affiliation_strings":["Amazon , Inc"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amazon , Inc","institution_ids":["https://openalex.org/I1311688040"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152718877","display_name":"Jie Yuan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1311688040","display_name":"Amazon (United States)","ror":"https://ror.org/04mv4n011","country_code":"US","type":"company","lineage":["https://openalex.org/I1311688040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Yuan, Jie","raw_affiliation_strings":["Amazon , Inc"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amazon , Inc","institution_ids":["https://openalex.org/I1311688040"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152719526","display_name":"Yanjun Lin","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1311688040","display_name":"Amazon (United States)","ror":"https://ror.org/04mv4n011","country_code":"US","type":"company","lineage":["https://openalex.org/I1311688040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lin, Yanjun","raw_affiliation_strings":["Amazon , Inc"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amazon , Inc","institution_ids":["https://openalex.org/I1311688040"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152602697","display_name":"James Feng","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1311688040","display_name":"Amazon (United States)","ror":"https://ror.org/04mv4n011","country_code":"US","type":"company","lineage":["https://openalex.org/I1311688040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Feng, James","raw_affiliation_strings":["Amazon , Inc"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amazon , Inc","institution_ids":["https://openalex.org/I1311688040"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5030020226","display_name":"Nikki Lijing Kuang","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I1311688040","display_name":"Amazon (United States)","ror":"https://ror.org/04mv4n011","country_code":"US","type":"company","lineage":["https://openalex.org/I1311688040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kuang, Nikki Lijing","raw_affiliation_strings":["Amazon , Inc"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amazon , Inc","institution_ids":["https://openalex.org/I1311688040"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5152725622","display_name":"Ziwei Zhu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I162714631","display_name":"George Mason University","ror":"https://ror.org/02jqj7156","country_code":"US","type":"education","lineage":["https://openalex.org/I162714631"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Zhu, Ziwei","raw_affiliation_strings":["George Mason University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"George Mason University ,","institution_ids":["https://openalex.org/I162714631"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5083080675","display_name":"Wei Niu","orcid":"https://orcid.org/0000-0002-1169-2116","observed_orcids":["https://orcid.org/0000-0002-1169-2116"]},"institutions":[{"id":"https://openalex.org/I1311688040","display_name":"Amazon (United States)","ror":"https://ror.org/04mv4n011","country_code":"US","type":"company","lineage":["https://openalex.org/I1311688040"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Niu, Wei","raw_affiliation_strings":["Amazon , Inc"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Amazon , Inc","institution_ids":["https://openalex.org/I1311688040"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"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":0.43549999594688416,"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":0.43549999594688416,"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":0.06880000233650208,"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":0.06840000301599503,"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/reasoning-efficiency","display_name":"reasoning efficiency","score":0.6800000071525574},{"id":"https://openalex.org/keywords/credit-assignment","display_name":"credit assignment","score":0.949999988079071},{"id":"https://openalex.org/keywords/structural-responsibility","display_name":"structural responsibility","score":0.7889999747276306},{"id":"https://openalex.org/keywords/group-relative-policy-optimization","display_name":"Group Relative Policy Optimization","score":0.5180000066757202},{"id":"https://openalex.org/keywords/large-language-models","display_name":"large language models","score":0.5830000042915344},{"id":"https://openalex.org/keywords/mathematical-reasoning","display_name":"mathematical reasoning","score":0.9559999704360962},{"id":"https://openalex.org/keywords/token-reduction","display_name":"token reduction","score":0.44200000166893005},{"id":"https://openalex.org/keywords/accuracy-efficiency-trade-off","display_name":"accuracy-efficiency trade-off","score":0.8220000267028809},{"id":"https://openalex.org/keywords/recap","display_name":"RECAP","score":0.5360000133514404}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6757000088691711},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.6080999970436096},{"id":"https://openalex.org/C89288958","wikidata":"https://www.wikidata.org/wiki/Q7301504","display_name":"Reasoning system","level":2,"score":0.5892999768257141},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5220999717712402},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.5212000012397766},{"id":"https://openalex.org/C103057564","wikidata":"https://www.wikidata.org/wiki/Q4751139","display_name":"Analytic reasoning","level":3,"score":0.5210999846458435},{"id":"https://openalex.org/C159032336","wikidata":"https://www.wikidata.org/wiki/Q2488768","display_name":"Non-monotonic logic","level":2,"score":0.4885999858379364},{"id":"https://openalex.org/C86827895","wikidata":"https://www.wikidata.org/wiki/Q7098582","display_name":"Opportunistic reasoning","level":4,"score":0.486299991607666},{"id":"https://openalex.org/C2780009758","wikidata":"https://www.wikidata.org/wiki/Q6804172","display_name":"Measure (data warehouse)","level":2,"score":0.4853000044822693},{"id":"https://openalex.org/C83725634","wikidata":"https://www.wikidata.org/wiki/Q7268699","display_name":"Qualitative reasoning","level":2,"score":0.4595000147819519},{"id":"https://openalex.org/C2776207758","wikidata":"https://www.wikidata.org/wiki/Q5303302","display_name":"Downstream (manufacturing)","level":2,"score":0.4528999924659729},{"id":"https://openalex.org/C107848011","wikidata":"https://www.wikidata.org/wiki/Q4680756","display_name":"Adaptive reasoning","level":4,"score":0.444599986076355},{"id":"https://openalex.org/C97364631","wikidata":"https://www.wikidata.org/wiki/Q484284","display_name":"Deductive reasoning","level":2,"score":0.40290001034736633},{"id":"https://openalex.org/C20162079","wikidata":"https://www.wikidata.org/wiki/Q1151406","display_name":"Case-based reasoning","level":2,"score":0.3928000032901764},{"id":"https://openalex.org/C37335422","wikidata":"https://www.wikidata.org/wiki/Q6888134","display_name":"Model-based reasoning","level":3,"score":0.39259999990463257},{"id":"https://openalex.org/C19768560","wikidata":"https://www.wikidata.org/wiki/Q320727","display_name":"Dependency (UML)","level":2,"score":0.384799987077713},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.29750001430511475},{"id":"https://openalex.org/C62611344","wikidata":"https://www.wikidata.org/wiki/Q1062658","display_name":"Node (physics)","level":2,"score":0.2816999852657318},{"id":"https://openalex.org/C193221554","wikidata":"https://www.wikidata.org/wiki/Q5153664","display_name":"Commonsense reasoning","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C2777508537","wikidata":"https://www.wikidata.org/wiki/Q7936620","display_name":"Visual reasoning","level":2,"score":0.267300009727478},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.26589998602867126},{"id":"https://openalex.org/C43971567","wikidata":"https://www.wikidata.org/wiki/Q3142865","display_name":"Logical reasoning","level":2,"score":0.2639999985694885}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2609.27156","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27156","pdf_url":"https://arxiv.org/pdf/2609.27156","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2609.27156","doi":"https://doi.org/10.48550/arxiv.2609.27156","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2609.27156","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:2609.27156","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2609.27156","pdf_url":"https://arxiv.org/pdf/2609.27156","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":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7214200768.pdf","grobid_xml":"https://content.openalex.org/works/W7214200768.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7222999870","https://openalex.org/W7137986045","https://openalex.org/W7162422627","https://openalex.org/W4417127468","https://openalex.org/W7128788626","https://openalex.org/W6948109617","https://openalex.org/W7166827583","https://openalex.org/W7128616912","https://openalex.org/W7123648576","https://openalex.org/W7214726484"],"abstract_inverted_index":{"Large":[0],"reasoning":[1,9,14,50,82,107,137,192,210,227],"models":[2,188],"can":[3,129],"produce":[4],"correct":[5,141],"yet":[6,134],"unnecessarily":[7],"long":[8],"traces.":[10],"Existing":[11],"methods":[12],"improve":[13],"efficiency":[15],"with":[16],"trajectory-level":[17],"objectives":[18],"or":[19],"local":[20],"token-":[21],"and":[22,84,189,229],"step-level":[23],"signals,":[24],"but":[25],"rarely":[26],"model":[27,180],"inter-step":[28],"semantic":[29,123],"dependencies.":[30],"This":[31],"limits":[32],"their":[33],"ability":[34],"to":[35,48,87,96,148,215],"distinguish":[36],"redundant":[37],"steps":[38],"from":[39,115,139],"those":[40],"that":[41],"support":[42],"later":[43,106],"deductions,":[44],"making":[45],"it":[46,70,201],"harder":[47],"shorten":[49],"without":[51],"sacrificing":[52],"accuracy.":[53],"We":[54,92],"introduce":[55],"RECAP":[56,143,172,194],"(REdundancy-aware":[57],"Credit":[58],"Assignment":[59],"via":[60],"Propagation),":[61],"which":[62],"addresses":[63],"this":[64],"limitation":[65],"by":[66,102,204,212],"assigning":[67],"credit":[68,112],"where":[69],"is":[71,160],"due":[72],"based":[73],"on":[74,109],"both":[75],"a":[76,127,175],"step's":[77,99],"downstream":[78,100],"role":[79,101],"in":[80,154],"the":[81,89,98,116,136,140,196],"structure":[83],"its":[85],"contribution":[86],"solving":[88],"problem":[90],"correctly.":[91],"define":[93],"structural":[94,132],"responsibility":[95,133],"capture":[97],"measuring":[103],"how":[104],"strongly":[105],"depends":[108],"it,":[110],"using":[111],"propagated":[113],"backward":[114],"final-answer":[117],"node":[118],"through":[119,152],"an":[120],"outcome-independent,":[121],"LLM-annotated":[122],"dependency":[124],"graph.":[125],"However,":[126],"step":[128,146,159],"have":[130],"high":[131],"steer":[135],"away":[138],"solution.":[142],"therefore":[144],"introduces":[145],"efficacy":[147],"measure":[149],"answer-directed":[150],"progress":[151],"changes":[153],"gold-answer":[155],"log-likelihood":[156],"as":[157],"each":[158],"added.":[161],"Together,":[162],"these":[163,223],"signals":[164],"reshape":[165],"rollout-level":[166],"GRPO":[167,216],"advantages":[168],"into":[169],"step-specific":[170],"updates.":[171],"requires":[173],"neither":[174],"separately":[176],"trained":[177],"process":[178],"reward":[179],"nor":[181],"preconstructed":[182],"concise":[183],"trajectories.":[184],"Across":[185],"two":[186],"7B":[187],"four":[190,219],"mathematical":[191],"benchmarks,":[193],"improves":[195,202],"accuracy-efficiency":[197],"trade-off.":[198],"On":[199],"Qwen2.5-Math-7B,":[200],"pass@1":[203],"2.0-3.7":[205],"percentage":[206],"points":[207],"while":[208],"reducing":[209],"tokens":[211],"8%-31%":[213],"relative":[214],"across":[217],"all":[218],"benchmarks.":[220],"Analysis":[221],"suggests":[222],"savings":[224],"reflect":[225],"fewer":[226],"operations":[228],"less":[230],"dead-end":[231],"reasoning,":[232],"rather":[233],"than":[234],"more":[235],"compact":[236],"expression.":[237]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-09-25T00:00:00"}