{"id":"https://openalex.org/W4407123339","doi":"https://doi.org/10.48550/arxiv.2502.00212","title":"STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving","display_name":"STP: Self-play LLM Theorem Provers with Iterative Conjecturing and Proving","publication_year":2025,"publication_date":"2025-01-31","ids":{"openalex":"https://openalex.org/W4407123339","doi":"https://doi.org/10.48550/arxiv.2502.00212"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2502.00212","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.00212","pdf_url":"https://arxiv.org/pdf/2502.00212","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","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/2502.00212","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5047803614","display_name":"Kefan Dong","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Dong, Kefan","raw_affiliation_strings":["Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5101821970","display_name":"Tengyu Ma","orcid":"https://orcid.org/0000-0002-1072-8738","observed_orcids":["https://orcid.org/0000-0002-1072-8738"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ma, Tengyu","raw_affiliation_strings":["Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":[],"corresponding_institution_ids":["https://openalex.org/I97018004"],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":1,"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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.3122999966144562,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.3122999966144562,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/T10126","display_name":"Logic, programming, and type systems","score":0.305400013923645,"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/T13904","display_name":"Artificial Intelligence Applications","score":0.10050000250339508,"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/conjecture-generation","display_name":"conjecture generation","score":0.8849999904632568},{"id":"https://openalex.org/keywords/formal-verification","display_name":"formal verification","score":0.6320000290870667},{"id":"https://openalex.org/keywords/lean-manufacturing","display_name":"lean manufacturing","score":0.460999995470047},{"id":"https://openalex.org/keywords/isabelle-proof-assistant","display_name":"Isabelle","score":0.984000027179718},{"id":"https://openalex.org/keywords/limited-training-data","display_name":"limited training data","score":0.6600000262260437},{"id":"https://openalex.org/keywords/sparse-rewards","display_name":"sparse rewards","score":0.41499999165534973}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4476696848869324},{"id":"https://openalex.org/C159694833","wikidata":"https://www.wikidata.org/wiki/Q2321565","display_name":"Iterative method","level":2,"score":0.41458195447921753},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34889620542526245},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.3382837772369385},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3244640529155731},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2693781554698944},{"id":"https://openalex.org/C202444582","wikidata":"https://www.wikidata.org/wiki/Q837863","display_name":"Pure mathematics","level":1,"score":0.20032140612602234},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0},{"id":"https://openalex.org/C199343813","wikidata":"https://www.wikidata.org/wiki/Q12128","display_name":"Dentistry","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2502.00212","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.00212","pdf_url":"https://arxiv.org/pdf/2502.00212","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2502.00212","doi":"https://doi.org/10.48550/arxiv.2502.00212","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2502.00212","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2502.00212","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2502.00212","pdf_url":"https://arxiv.org/pdf/2502.00212","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G1138995730","display_name":"Collaborative Research: RI:Medium:MoDL:Mathematical and Conceptual Understanding of Large Language Models","funder_award_id":"2211780","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5973348372","display_name":"Collaborative Research: CIF: Medium: MoDL:Toward a Mathematical Foundation of Deep Reinforcement Learning","funder_award_id":"2212263","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4407123339.pdf","grobid_xml":"https://content.openalex.org/works/W4407123339.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4404088889","https://openalex.org/W4416361225","https://openalex.org/W4404352990","https://openalex.org/W7133195287","https://openalex.org/W4398796786","https://openalex.org/W4404783189","https://openalex.org/W4407425807","https://openalex.org/W4417268860","https://openalex.org/W4407571385","https://openalex.org/W4416256036"],"abstract_inverted_index":{"A":[0],"fundamental":[1],"challenge":[2],"in":[3,167,175,218],"formal":[4,157],"theorem":[5],"proving":[6],"by":[7,26,70,124],"LLMs":[8],"is":[9,113],"the":[10,44,54,90,109,125,143,165,173,176,180],"lack":[11],"of":[12,46,80,172,184],"high-quality":[13],"training":[14,106,166],"data.":[15],"Although":[16],"reinforcement":[17],"learning":[18],"or":[19,74],"expert":[20,147,188],"iteration":[21],"partially":[22],"mitigates":[23],"this":[24,219],"issue":[25],"alternating":[27],"between":[28],"LLM":[29],"generating":[30],"proofs":[31,48],"and":[32,83,102,155,207,216],"finetuning":[33],"them":[34],"on":[35,98,116,200],"correctly":[36],"generated":[37,118,163],"ones,":[38],"performance":[39,195],"quickly":[40],"plateaus":[41],"due":[42],"to":[43,85,108,131,141],"scarcity":[45],"correct":[47],"(sparse":[49],"rewards).":[50],"To":[51],"keep":[52],"improving":[53],"models":[55],"with":[56,145,152],"limited":[57],"data,":[58],"we":[59],"draw":[60],"inspiration":[61],"from":[62],"mathematicians,":[63],"who":[64],"continuously":[65],"develop":[66],"new":[67],"results,":[68],"partly":[69],"proposing":[71],"novel":[72],"conjectures":[73,119,135,144],"exercises":[75],"(which":[76],"are":[77,121],"often":[78],"variants":[79],"known":[81],"results)":[82],"attempting":[84],"solve":[86],"them.":[87],"We":[88,149,211],"design":[89],"Self-play":[91],"Theorem":[92],"Prover":[93],"(STP)":[94],"that":[95,120],"simultaneously":[96],"takes":[97],"two":[99],"roles,":[100],"conjecturer":[101,112],"prover,":[103,127],"each":[104],"providing":[105],"signals":[107],"other.":[110],"The":[111,138,190],"trained":[114],"iteratively":[115],"previously":[117],"barely":[122],"provable":[123],"current":[126],"which":[128],"incentivizes":[129],"it":[130],"generate":[132],"increasingly":[133],"challenging":[134],"over":[136],"time.":[137],"prover":[139],"attempts":[140],"prove":[142],"standard":[146],"iteration.":[148,189],"evaluate":[150],"STP":[151,169],"both":[153],"Lean":[154],"Isabelle":[156],"versifiers.":[158],"With":[159],"51.3":[160],"billion":[161],"tokens":[162],"during":[164],"Lean,":[168],"proves":[170],"28.5%":[171],"statements":[174],"LeanWorkbook":[177],"dataset,":[178],"doubling":[179],"previous":[181],"best":[182],"result":[183],"13.2%":[185],"achieved":[186],"through":[187],"final":[191],"model":[192],"achieves":[193],"state-of-the-art":[194],"among":[196],"whole-proof":[197],"generation":[198],"methods":[199],"miniF2F-test":[201],"(65.0%,":[202],"pass@3200),":[203],"Proofnet-test":[204],"(23.9%,":[205],"pass@3200)":[206],"PutnamBench":[208],"(8/644,":[209],"pass@3200).":[210],"release":[212],"our":[213],"code,":[214],"model,":[215],"dataset":[217],"URL:":[220],"https://github.com/kfdong/STP.":[221]},"counts_by_year":[{"year":2025,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-02-05T00:00:00"}
