{"id":"https://openalex.org/W7163418146","doi":"https://doi.org/10.48550/arxiv.2606.03503","title":"ThoughtFold: Folding Reasoning Chains via Introspective Preference Learning","display_name":"ThoughtFold: Folding Reasoning Chains via Introspective Preference Learning","publication_year":2026,"publication_date":"2026-06-02","ids":{"openalex":"https://openalex.org/W7163418146","doi":"https://doi.org/10.48550/arxiv.2606.03503"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.03503","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03503","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.2606.03503","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137730320","display_name":"Ziyan Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Ziyan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085951200","display_name":"Xueda Shen","orcid":"https://orcid.org/0000-0003-1218-5068"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shen, Xueda","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137750944","display_name":"Yuzhe Gu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gu, Yuzhe","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137783813","display_name":"Songyang Gao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Gao, Songyang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050684712","display_name":"Kuikun Liu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Liu, Kuikun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137748962","display_name":"Guangran Cheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Cheng, Guangran","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067731176","display_name":"Chengqi Lyu","orcid":"https://orcid.org/0000-0002-4438-1314"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lyu, Chengqi","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137779106","display_name":"Dahua Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Dahua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137726624","display_name":"Wenwei Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Wenwei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137802549","display_name":"Kai Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Kai","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/T13702","display_name":"Machine Learning in Healthcare","score":0.15399999916553497,"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/T13702","display_name":"Machine Learning in Healthcare","score":0.15399999916553497,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.14339999854564667,"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":0.11919999867677689,"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/redundancy","display_name":"Redundancy (engineering)","score":0.5557000041007996},{"id":"https://openalex.org/keywords/preference","display_name":"Preference","score":0.4742000102996826},{"id":"https://openalex.org/keywords/memorization","display_name":"Memorization","score":0.46700000762939453},{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.4560000002384186},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.40880000591278076},{"id":"https://openalex.org/keywords/introspection","display_name":"Introspection","score":0.3939000070095062},{"id":"https://openalex.org/keywords/folding","display_name":"Folding (DSP implementation)","score":0.3788999915122986},{"id":"https://openalex.org/keywords/chaining","display_name":"Chaining","score":0.33820000290870667}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7175999879837036},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.6065000295639038},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.5557000041007996},{"id":"https://openalex.org/C2781249084","wikidata":"https://www.wikidata.org/wiki/Q908656","display_name":"Preference","level":2,"score":0.4742000102996826},{"id":"https://openalex.org/C30038468","wikidata":"https://www.wikidata.org/wiki/Q4354775","display_name":"Memorization","level":2,"score":0.46700000762939453},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.4560000002384186},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.43070000410079956},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.40880000591278076},{"id":"https://openalex.org/C129671850","wikidata":"https://www.wikidata.org/wiki/Q210501","display_name":"Introspection","level":2,"score":0.3939000070095062},{"id":"https://openalex.org/C2776545253","wikidata":"https://www.wikidata.org/wiki/Q5464292","display_name":"Folding (DSP implementation)","level":2,"score":0.3788999915122986},{"id":"https://openalex.org/C49020025","wikidata":"https://www.wikidata.org/wiki/Q1059099","display_name":"Chaining","level":2,"score":0.33820000290870667},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.32170000672340393},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.3151000142097473},{"id":"https://openalex.org/C100776233","wikidata":"https://www.wikidata.org/wiki/Q2532492","display_name":"Bridge (graph theory)","level":2,"score":0.31200000643730164},{"id":"https://openalex.org/C2779808786","wikidata":"https://www.wikidata.org/wiki/Q6664603","display_name":"Locality","level":2,"score":0.305400013923645},{"id":"https://openalex.org/C48145219","wikidata":"https://www.wikidata.org/wiki/Q1335365","display_name":"Security token","level":2,"score":0.2930999994277954},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2757999897003174},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.2718999981880188},{"id":"https://openalex.org/C2778833722","wikidata":"https://www.wikidata.org/wiki/Q28457372","display_name":"Tact","level":2,"score":0.26899999380111694},{"id":"https://openalex.org/C148324565","wikidata":"https://www.wikidata.org/wiki/Q784221","display_name":"Rote learning","level":4,"score":0.2687000036239624},{"id":"https://openalex.org/C193221554","wikidata":"https://www.wikidata.org/wiki/Q5153664","display_name":"Commonsense reasoning","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.03503","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03503","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.2606.03503","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03503","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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Large":[0],"Reasoning":[1],"Models":[2],"(LRMs)":[3],"have":[4],"achieved":[5],"remarkable":[6],"progress":[7],"thanks":[8],"to":[9,57,65,97,109,142],"Reinforcement":[10],"Learning":[11],"with":[12],"Verifiable":[13],"Rewards":[14],"(RLVR)":[15],"on":[16],"Chain-of-Thoughts":[17],"(CoTs).":[18],"However,":[19],"since":[20],"long":[21,42,84],"CoTs":[22,43],"naturally":[23],"contain":[24],"trial":[25],"and":[26,28,75,138],"errors":[27],"mainstream":[29],"RLVR":[30],"approaches":[31],"choose":[32],"outcome-correct":[33],"CoT":[34],"trajectories":[35],"for":[36,101],"memorization,":[37],"the":[38,50,78,140,168],"redundant":[39,81,99,136],"explorations":[40,82,100,137],"in":[41,49,83],"are":[44,72],"inevitably":[45],"reinforced,":[46],"which":[47,116],"results":[48],"over-thinking":[51],"issues":[52],"of":[53,80,120,171],"LRMs.":[54],"Previous":[55],"attempts":[56],"resolve":[58],"this":[59,124],"issue":[60],"mainly":[61],"give":[62],"more":[63,155],"advantage":[64],"shorter":[66],"trajectories,":[67],"yet":[68],"their":[69],"learning":[70,96],"signals":[71],"still":[73],"outcome-based":[74],"cannot":[76],"reduce":[77],"memorization":[79],"CoTs.":[85],"Therefore,":[86],"we":[87,126],"propose":[88],"ThoughtFold,":[89],"a":[90,118,128,154],"framework":[91],"that":[92,133,161],"leverages":[93],"fine-grained":[94],"preference":[95,130],"mitigate":[98],"efficient":[102],"reasoning.":[103],"ThoughtFold":[104,162],"employs":[105],"an":[106],"introspective":[107],"strategy":[108],"identify":[110],"redundancy":[111],"within":[112],"each":[113],"correct":[114],"trajectory,":[115],"yields":[117],"spectrum":[119],"candidate":[121],"sub-trajectories.":[122],"Leveraging":[123],"spectrum,":[125],"introduce":[127],"masked":[129],"optimization":[131],"objective":[132],"explicitly":[134],"penalizes":[135],"encourages":[139],"model":[141],"directly":[143],"bridge":[144],"essential":[145],"reasoning":[146,151],"segments,":[147],"effectively":[148],"folding":[149],"its":[150],"chains":[152],"into":[153],"concise":[156],"path.":[157],"Extensive":[158],"experiments":[159],"show":[160],"significantly":[163],"enhances":[164],"efficiency.":[165],"It":[166],"reduces":[167],"token":[169],"usage":[170],"DeepSeek-R1-Distill-Qwen-7B":[172],"by":[173],"approximately":[174],"56%":[175],"while":[176],"maintaining":[177],"state-of-the-art":[178],"accuracy.":[179]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-04T00:00:00"}
