{"id":"https://openalex.org/W7133308448","doi":"https://doi.org/10.48550/arxiv.2603.00296","title":"Stepwise Penalization for Length-Efficient Chain-of-Thought Reasoning","display_name":"Stepwise Penalization for Length-Efficient Chain-of-Thought Reasoning","publication_year":2026,"publication_date":"2026-02-27","ids":{"openalex":"https://openalex.org/W7133308448","doi":"https://doi.org/10.48550/arxiv.2603.00296"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.00296","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00296","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.2603.00296","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5127995589","display_name":"Xintong Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Li, Xintong","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5128017973","display_name":"Sha Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Sha","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127875582","display_name":"Rongmei Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Rongmei","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5063597595","display_name":"Hongye Jin","orcid":"https://orcid.org/0009-0009-7920-632X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jin, Hongye","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127893913","display_name":"Linwei Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Linwei","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5033157677","display_name":"Hejie Cui","orcid":"https://orcid.org/0000-0001-6388-2619"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cui, Hejie","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127942560","display_name":"Sarah Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Sarah","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127913682","display_name":"Chia-Yuan Chang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chang, Chia-Yuan","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5086810302","display_name":"Kewei Cheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng, Kewei","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001039604","display_name":"Besnik Fetahu","orcid":"https://orcid.org/0000-0002-3343-7992"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Fetahu, Besnik","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127944974","display_name":"Priyanka Nigam","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nigam, Priyanka","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5127874076","display_name":"Jingbo Shang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shang, Jingbo","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5127985300","display_name":"Bing Yin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yin, Bing","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":13,"corresponding_author_ids":["https://openalex.org/A5127995589"],"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.1777999997138977,"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/T10462","display_name":"Reinforcement Learning in Robotics","score":0.1777999997138977,"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":0.149399995803833,"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/T10028","display_name":"Topic Modeling","score":0.13850000500679016,"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/swap","display_name":"Swap (finance)","score":0.5296000242233276},{"id":"https://openalex.org/keywords/reduction","display_name":"Reduction (mathematics)","score":0.44429999589920044},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.41429999470710754},{"id":"https://openalex.org/keywords/outcome","display_name":"Outcome (game theory)","score":0.40880000591278076},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.34380000829696655},{"id":"https://openalex.org/keywords/case-based-reasoning","display_name":"Case-based reasoning","score":0.328000009059906}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5824999809265137},{"id":"https://openalex.org/C99821215","wikidata":"https://www.wikidata.org/wiki/Q1136583","display_name":"Swap (finance)","level":2,"score":0.5296000242233276},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4537000060081482},{"id":"https://openalex.org/C111335779","wikidata":"https://www.wikidata.org/wiki/Q3454686","display_name":"Reduction (mathematics)","level":2,"score":0.44429999589920044},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.41429999470710754},{"id":"https://openalex.org/C148220186","wikidata":"https://www.wikidata.org/wiki/Q7111912","display_name":"Outcome (game theory)","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3763999938964844},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.34380000829696655},{"id":"https://openalex.org/C20162079","wikidata":"https://www.wikidata.org/wiki/Q1151406","display_name":"Case-based reasoning","level":2,"score":0.328000009059906},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.32589998841285706},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.29809999465942383},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C134121241","wikidata":"https://www.wikidata.org/wiki/Q899301","display_name":"Yield (engineering)","level":2,"score":0.2874000072479248},{"id":"https://openalex.org/C86827895","wikidata":"https://www.wikidata.org/wiki/Q7098582","display_name":"Opportunistic reasoning","level":4,"score":0.2822999954223633},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2621999979019165}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.00296","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00296","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.2603.00296","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.00296","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":[{"score":0.6641771793365479,"id":"https://metadata.un.org/sdg/16","display_name":"Peace, Justice and strong institutions"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Large":[0],"reasoning":[1,42,66,148],"models":[2],"improve":[3],"with":[4,32,133],"more":[5,125],"test-time":[6],"computation,":[7],"but":[8],"often":[9],"overthink,":[10],"producing":[11],"unnecessarily":[12],"long":[13],"chains-of-thought":[14],"that":[15,88,145],"raise":[16],"cost":[17],"without":[18],"improving":[19,155],"accuracy.":[20],"Prior":[21],"reinforcement":[22],"learning":[23],"approaches":[24],"typically":[25],"rely":[26],"on":[27,95,152],"a":[28,85,117,134],"single":[29],"outcome":[30],"reward":[31],"trajectory-level":[33],"length":[34,67,90,115,149],"penalties,":[35],"which":[36],"cannot":[37],"distinguish":[38],"essential":[39],"from":[40,102],"redundant":[41],"steps":[43,93,124],"and":[44],"therefore":[45],"yield":[46],"blunt":[47],"compression.":[48],"Although":[49],"recent":[50],"work":[51],"incorporates":[52],"step-level":[53,74],"signals,":[54],"such":[55],"as":[56,71,116],"offline":[57],"pruning,":[58],"supervised":[59],"data":[60],"construction,":[61],"or":[62],"verifier-based":[63],"intermediate":[64],"rewards,":[65],"is":[68],"rarely":[69],"treated":[70],"an":[72],"explicit":[73],"optimization":[75],"objective":[76],"during":[77],"RL.":[78],"We":[79,98,131],"propose":[80],"Step-wise":[81],"Adaptive":[82],"Penalization":[83],"(SWAP),":[84],"fine-grained":[86],"framework":[87],"allocates":[89],"reduction":[91],"across":[92],"based":[94],"intrinsic":[96],"contribution.":[97],"estimate":[99],"step":[100],"importance":[101],"the":[103,109,161],"model's":[104],"on-policy":[105],"log-probability":[106],"improvement":[107],"toward":[108],"correct":[110],"answer,":[111],"then":[112],"treat":[113],"excess":[114],"penalty":[118],"mass":[119],"redistributed":[120],"to":[121,160],"penalize":[122],"low-importance":[123],"heavily":[126],"while":[127,154],"preserving":[128],"high-importance":[129],"reasoning.":[130],"optimize":[132],"unified":[135],"outcome-process":[136],"advantage":[137],"within":[138],"group-relative":[139],"policy":[140],"optimization.":[141],"Extensive":[142],"experiments":[143],"demonstrate":[144],"SWAP":[146],"reduces":[147],"by":[150,157],"64.3%":[151],"average":[153],"accuracy":[156],"5.7%":[158],"relative":[159],"base":[162],"model.":[163]},"counts_by_year":[],"updated_date":"2026-03-04T07:09:34.246503","created_date":"2026-03-04T00:00:00"}