{"id":"https://openalex.org/W7162017189","doi":"https://doi.org/10.48550/arxiv.2605.21260","title":"On the Cost and Benefit of Chain of Thought: A Learning-Theoretic Perspective","display_name":"On the Cost and Benefit of Chain of Thought: A Learning-Theoretic Perspective","publication_year":2026,"publication_date":"2026-05-20","ids":{"openalex":"https://openalex.org/W7162017189","doi":"https://doi.org/10.48550/arxiv.2605.21260"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.21260","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21260","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.2605.21260","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5136632395","display_name":"Yue Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Yue","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5136646798","display_name":"Zhiyi Dong","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dong, Zhiyi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135593654","display_name":"Tommaso Cesari","orcid":"https://orcid.org/0000-0001-5010-1094"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cesari, Tommaso","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5004793184","display_name":"Yongyi Mao","orcid":"https://orcid.org/0000-0001-5298-5778"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mao, Yongyi","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/T10656","display_name":"Child and Animal Learning Development","score":0.18459999561309814,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},"topics":[{"id":"https://openalex.org/T10656","display_name":"Child and Animal Learning Development","score":0.18459999561309814,"subfield":{"id":"https://openalex.org/subfields/3204","display_name":"Developmental and Educational Psychology"},"field":{"id":"https://openalex.org/fields/32","display_name":"Psychology"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}},{"id":"https://openalex.org/T10028","display_name":"Topic Modeling","score":0.09570000320672989,"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/T11010","display_name":"Logic, Reasoning, and Knowledge","score":0.08470000326633453,"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/perspective","display_name":"Perspective (graphical)","score":0.6696000099182129},{"id":"https://openalex.org/keywords/chain","display_name":"Chain (unit)","score":0.521399974822998},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.4406000077724457},{"id":"https://openalex.org/keywords/upper-and-lower-bounds","display_name":"Upper and lower bounds","score":0.4020000100135803},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.3723999857902527},{"id":"https://openalex.org/keywords/decomposition","display_name":"Decomposition","score":0.34470000863075256}],"concepts":[{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.6696000099182129},{"id":"https://openalex.org/C199185054","wikidata":"https://www.wikidata.org/wiki/Q552299","display_name":"Chain (unit)","level":2,"score":0.521399974822998},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49880000948905945},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.4578000009059906},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.4406000077724457},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.4020000100135803},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C124681953","wikidata":"https://www.wikidata.org/wiki/Q339062","display_name":"Decomposition","level":2,"score":0.34470000863075256},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.33559998869895935},{"id":"https://openalex.org/C2780813799","wikidata":"https://www.wikidata.org/wiki/Q3274237","display_name":"Zero (linguistics)","level":2,"score":0.32739999890327454},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.3125999867916107},{"id":"https://openalex.org/C113336015","wikidata":"https://www.wikidata.org/wiki/Q574010","display_name":"Complete information","level":2,"score":0.30489999055862427},{"id":"https://openalex.org/C139807058","wikidata":"https://www.wikidata.org/wiki/Q352374","display_name":"Adaptation (eye)","level":2,"score":0.2955999970436096},{"id":"https://openalex.org/C112930515","wikidata":"https://www.wikidata.org/wiki/Q4389547","display_name":"Risk analysis (engineering)","level":1,"score":0.288100004196167},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.28209999203681946}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.21260","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21260","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.2605.21260","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.21260","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":{"We":[0,11,97],"develop":[1],"a":[2,22,36,45,71,75,80,150,175],"learning-theoretic":[3],"framework":[4],"for":[5],"understanding":[6],"Chain":[7],"of":[8,35,49,66,88,110,178],"Thought":[9],"(CoT).":[10],"model":[12],"CoT":[13,67,89,180],"as":[14],"the":[15,32,64,86,111,113,118,123,131,136,142,155,188,191],"interaction":[16],"between":[17,190],"an":[18,58,159],"answer":[19,115],"map":[20],"and":[21,30,68,79,135,167,185],"chain":[23,119],"rule":[24,120],"that":[25,100,163],"generates":[26],"intermediate":[27],"questions":[28],"autoregressively,":[29],"define":[31],"reasoning":[33,95],"risk":[34,51,60,73,82],"hypothesis":[37,114,137],"under":[38,146],"this":[39,50,101],"interaction.":[40],"Our":[41],"first":[42],"result":[43],"is":[44,103,133,138],"tight":[46,151],"canonical":[47],"decomposition":[48],"into":[52],"two":[53],"terms":[54],"with":[55],"opposing":[56],"roles:":[57],"oracle-trajectory":[59],"(OTR),":[61],"which":[62,84],"captures":[63,85],"benefit":[65],"reduces":[69],"to":[70,141],"target-domain":[72],"in":[74],"domain":[76],"adaptation":[77],"problem,":[78],"trajectory-mismatch":[81],"(TMR),":[83],"cost":[87,102],"through":[90],"error":[91],"accumulation":[92],"along":[93],"mismatched":[94],"trajectories.":[96],"then":[98],"show":[99],"unavoidable":[104],"without":[105],"structure:":[106],"if":[107],"any":[108],"one":[109],"loss,":[112],"map,":[116],"or":[117],"lacks":[121],"stability,":[122,147],"TMR":[124,156],"can":[125],"be":[126],"arbitrarily":[127],"large":[128],"even":[129],"when":[130,179,182],"OTR":[132],"zero":[134],"uniformly":[139],"close":[140],"ground":[143],"truth.":[144],"Conversely,":[145],"we":[148],"prove":[149],"upper":[152],"bound":[153],"on":[154],"governed":[157],"by":[158],"exact":[160],"amplification":[161],"factor":[162],"identifies":[164],"bounded,":[165],"linear,":[166],"exponential":[168],"error-growth":[169],"regimes.":[170],"Together,":[171],"these":[172],"results":[173],"give":[174],"precise":[176],"theory":[177],"helps,":[181],"it":[183],"hurts,":[184],"what":[186],"controls":[187],"transition":[189],"two.":[192]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-22T00:00:00"}