{"id":"https://openalex.org/W7139922378","doi":"https://doi.org/10.48550/arxiv.2603.18325","title":"Learning to Reason with Curriculum I: Provable Benefits of Autocurriculum","display_name":"Learning to Reason with Curriculum I: Provable Benefits of Autocurriculum","publication_year":2026,"publication_date":"2026-03-18","ids":{"openalex":"https://openalex.org/W7139922378","doi":"https://doi.org/10.48550/arxiv.2603.18325"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.18325","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18325","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":"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.2603.18325","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5064641699","display_name":"Nived Rajaraman","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rajaraman, Nived","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130237001","display_name":"Audrey Huang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Huang, Audrey","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5130252298","display_name":"Miro Dudik","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dudik, Miro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5084108666","display_name":"Robert E. Schapire","orcid":"https://orcid.org/0000-0001-8616-1611"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Schapire, Robert","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5075069827","display_name":"Dylan J. Foster","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Foster, Dylan J.","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5130252809","display_name":"Akshay Krishnamurthy","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Krishnamurthy, Akshay","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/T11714","display_name":"Multimodal Machine Learning Applications","score":0.2671999931335449,"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"}},"topics":[{"id":"https://openalex.org/T11714","display_name":"Multimodal Machine Learning Applications","score":0.2671999931335449,"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":0.1145000010728836,"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":0.09449999779462814,"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/boosting","display_name":"Boosting (machine learning)","score":0.6955000162124634},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.6438000202178955},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.4296000003814697},{"id":"https://openalex.org/keywords/focus","display_name":"Focus (optics)","score":0.41780000925064087},{"id":"https://openalex.org/keywords/quality","display_name":"Quality (philosophy)","score":0.38929998874664307},{"id":"https://openalex.org/keywords/curriculum","display_name":"Curriculum","score":0.38510000705718994}],"concepts":[{"id":"https://openalex.org/C46686674","wikidata":"https://www.wikidata.org/wiki/Q466303","display_name":"Boosting (machine learning)","level":2,"score":0.6955000162124634},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6736000180244446},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.6438000202178955},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5723000168800354},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.4296000003814697},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.41780000925064087},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4140999913215637},{"id":"https://openalex.org/C2779530757","wikidata":"https://www.wikidata.org/wiki/Q1207505","display_name":"Quality (philosophy)","level":2,"score":0.38929998874664307},{"id":"https://openalex.org/C47177190","wikidata":"https://www.wikidata.org/wiki/Q207137","display_name":"Curriculum","level":2,"score":0.38510000705718994},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.2903999984264374},{"id":"https://openalex.org/C51632099","wikidata":"https://www.wikidata.org/wiki/Q3985153","display_name":"Training set","level":2,"score":0.28870001435279846},{"id":"https://openalex.org/C132758656","wikidata":"https://www.wikidata.org/wiki/Q5307365","display_name":"Dreyfus model of skill acquisition","level":2,"score":0.26829999685287476}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.18325","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18325","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":"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.2603.18325","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.18325","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":"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":[{"id":"https://metadata.un.org/sdg/4","score":0.6865882277488708,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Chain-of-thought":[0],"reasoning,":[1],"where":[2,77,127],"language":[3],"models":[4,27],"expend":[5],"additional":[6],"computation":[7],"by":[8,121],"producing":[9],"thinking":[10],"tokens":[11],"prior":[12],"to":[13,84,88,150],"final":[14],"responses,":[15],"has":[16],"driven":[17],"significant":[18],"advances":[19],"in":[20,31],"model":[21,56,79,130],"capabilities.":[22],"However,":[23],"training":[24,90,96],"these":[25,61],"reasoning":[26,45,116],"is":[28,155],"extremely":[29],"costly":[30],"terms":[32],"of":[33,44,143,158,189],"both":[34,99],"data":[35,168],"and":[36,52,103,176,180],"compute,":[37],"as":[38],"it":[39],"involves":[40],"collecting":[41],"long":[42],"traces":[43],"behavior":[46],"from":[47,140,166,174,178],"humans":[48],"or":[49,64,187],"synthetic":[50],"generators":[51],"further":[53],"post-training":[54],"the":[55,78,128,137,141,144,148,159,185],"via":[57],"reinforcement":[58,104],"learning.":[59],"Are":[60],"costs":[62],"fundamental,":[63],"can":[65],"they":[66],"be":[67],"reduced":[68],"through":[69],"better":[70],"algorithmic":[71],"design?":[72],"We":[73],"show":[74,110],"that":[75,111,154],"autocurriculum,":[76],"uses":[80],"its":[81],"own":[82],"performance":[83],"decide":[85],"which":[86],"problems":[87],"focus":[89],"on,":[91],"provably":[92],"improves":[93],"upon":[94],"standard":[95],"recipes":[97],"for":[98],"supervised":[100],"fine-tuning":[101],"(SFT)":[102],"learning":[105,177],"(RL).":[106],"For":[107,132],"SFT,":[108],"we":[109],"autocurriculum":[112,135],"requires":[113],"exponentially":[114],"fewer":[115],"demonstrations":[117],"than":[118],"non-adaptive":[119],"fine-tuning,":[120,134],"focusing":[122],"teacher":[123],"supervision":[124],"on":[125,171,184],"prompts":[126],"current":[129],"struggles.":[131],"RL":[133],"decouples":[136],"computational":[138],"cost":[139,153],"quality":[142],"reference":[145],"model,":[146],"reducing":[147],"latter":[149],"a":[151],"burn-in":[152],"nearly":[156],"independent":[157],"target":[160],"accuracy.":[161],"These":[162],"improvements":[163],"arise":[164],"purely":[165],"adaptive":[167],"selection,":[169],"drawing":[170],"classical":[172],"techniques":[173],"boosting":[175],"counterexamples,":[179],"requiring":[181],"no":[182],"assumption":[183],"distribution":[186],"difficulty":[188],"prompts.":[190]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-03-21T00:00:00"}