{"id":"https://openalex.org/W4281994620","doi":"https://doi.org/10.48550/arxiv.2205.14318","title":"Learning Math Reasoning from Self-Sampled Correct and Partially-Correct Solutions","display_name":"Learning Math Reasoning from Self-Sampled Correct and Partially-Correct Solutions","publication_year":2022,"publication_date":"2022-05-28","ids":{"openalex":"https://openalex.org/W4281994620","doi":"https://doi.org/10.48550/arxiv.2205.14318"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2205.14318","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2205.14318","pdf_url":"https://arxiv.org/pdf/2205.14318","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":"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/2205.14318","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087977697","display_name":"Ansong Ni","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Ni, Ansong","raw_affiliation_strings":["Yale University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yale University ,","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5020203532","display_name":"Jeevana Priya Inala","orcid":"https://orcid.org/0000-0003-1843-589X","observed_orcids":["https://orcid.org/0000-0003-1843-589X"]},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Inala, Jeevana Priya","raw_affiliation_strings":["Microsoft Research , 3 Google ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research , 3 Google ,","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5100367825","display_name":"Chenglong Wang","orcid":"https://orcid.org/0000-0003-2391-0923","observed_orcids":["https://orcid.org/0000-0003-2391-0923","https://orcid.org/0009-0008-8617-4453"]},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Wang, Chenglong","raw_affiliation_strings":["Microsoft Research , 3 Google ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research , 3 Google ,","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I1291425158"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5066539391","display_name":"Oleksandr Polozov","orcid":"https://orcid.org/0000-0003-3669-4262","observed_orcids":["https://orcid.org/0000-0003-3669-4262"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Polozov, Oleksandr","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5010587765","display_name":"Christopher Meek","orcid":"https://orcid.org/0000-0002-6744-0591","observed_orcids":["https://orcid.org/0000-0002-6744-0591"]},"institutions":[{"id":"https://openalex.org/I201448701","display_name":"University of Washington","ror":"https://ror.org/00cvxb145","country_code":"US","type":"education","lineage":["https://openalex.org/I201448701"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Meek, Christopher","raw_affiliation_strings":["University of Washington"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Washington","institution_ids":["https://openalex.org/I201448701"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5081787254","display_name":"Dragomir Radev","orcid":"https://orcid.org/0000-0001-7830-6489","observed_orcids":["https://orcid.org/0000-0001-7830-6489"]},"institutions":[{"id":"https://openalex.org/I32971472","display_name":"Yale University","ror":"https://ror.org/03v76x132","country_code":"US","type":"education","lineage":["https://openalex.org/I32971472"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Radev, Dragomir","raw_affiliation_strings":["Yale University ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Yale University ,","institution_ids":["https://openalex.org/I32971472"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5114910293","display_name":"Jianfeng Gao","orcid":"https://orcid.org/0000-0002-5702-6143","observed_orcids":["https://orcid.org/0000-0002-5702-6143"]},"institutions":[{"id":"https://openalex.org/I1290206253","display_name":"Microsoft (United States)","ror":"https://ror.org/00d0nc645","country_code":"US","type":"company","lineage":["https://openalex.org/I1290206253"]},{"id":"https://openalex.org/I1291425158","display_name":"Google (United States)","ror":"https://ror.org/00njsd438","country_code":"US","type":"company","lineage":["https://openalex.org/I1291425158","https://openalex.org/I4210128969"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gao, Jianfeng","raw_affiliation_strings":["Microsoft Research , 3 Google ,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Microsoft Research , 3 Google ,","institution_ids":["https://openalex.org/I1290206253","https://openalex.org/I1291425158"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":4,"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/T10028","display_name":"Topic Modeling","score":0.6996999979019165,"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/T10028","display_name":"Topic Modeling","score":0.6996999979019165,"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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.05640000104904175,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.04280000180006027,"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/mathematical-reasoning","display_name":"mathematical reasoning","score":0.8769999742507935},{"id":"https://openalex.org/keywords/multi-step-reasoning","display_name":"multi-step reasoning","score":0.656000018119812},{"id":"https://openalex.org/keywords/self-sampling","display_name":"self-sampling","score":0.578000009059906},{"id":"https://openalex.org/keywords/alternative-solutions","display_name":"alternative solutions","score":0.640999972820282},{"id":"https://openalex.org/keywords/training-objectives","display_name":"training objectives","score":0.41499999165534973},{"id":"https://openalex.org/keywords/solution-space-exploration","display_name":"solution space exploration","score":0.6209999918937683},{"id":"https://openalex.org/keywords/pre-trained-language-models","display_name":"pre-trained language models","score":0.5910000205039978},{"id":"https://openalex.org/keywords/fine-tuning","display_name":"fine-tuning","score":0.6809999942779541},{"id":"https://openalex.org/keywords/gsm8k","display_name":"GSM8K","score":0.7689999938011169}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7581273317337036},{"id":"https://openalex.org/C177148314","wikidata":"https://www.wikidata.org/wiki/Q170084","display_name":"Generalization","level":2,"score":0.6947031021118164},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.6209807991981506},{"id":"https://openalex.org/C2776760102","wikidata":"https://www.wikidata.org/wiki/Q5139990","display_name":"Code (set theory)","level":3,"score":0.5191959142684937},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5159878730773926},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5105713605880737},{"id":"https://openalex.org/C2778572836","wikidata":"https://www.wikidata.org/wiki/Q380933","display_name":"Space (punctuation)","level":2,"score":0.4965861439704895},{"id":"https://openalex.org/C48103436","wikidata":"https://www.wikidata.org/wiki/Q599031","display_name":"State (computer science)","level":2,"score":0.46245336532592773},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.4045320451259613},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3643622398376465},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.23572206497192383},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.21514597535133362},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.17810967564582825},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.13836488127708435},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","level":1,"score":0.0},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2205.14318","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2205.14318","pdf_url":"https://arxiv.org/pdf/2205.14318","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"doi:10.48550/arxiv.2205.14318","doi":"https://doi.org/10.48550/arxiv.2205.14318","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2205.14318","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":"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2205.14318","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2205.14318","pdf_url":"https://arxiv.org/pdf/2205.14318","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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.6164000034332275,"display_name":"Quality education"}],"study_designs":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320308943","display_name":"Microsoft Research","ror":"https://ror.org/00d0nc645"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4410357133","https://openalex.org/W4412664026","https://openalex.org/W4404782353","https://openalex.org/W4403443836","https://openalex.org/W4385571387","https://openalex.org/W4414360457","https://openalex.org/W7131877086","https://openalex.org/W7128097308","https://openalex.org/W4403345331","https://openalex.org/W7116869808"],"abstract_inverted_index":{"Pretrained":[0],"language":[1,10],"models":[2,73],"have":[3],"shown":[4],"superior":[5],"performance":[6],"on":[7,182],"many":[8,41],"natural":[9],"processing":[11],"tasks,":[12],"yet":[13],"they":[14,176],"still":[15],"struggle":[16],"at":[17,233],"multi-step":[18],"formal":[19],"reasoning":[20,37,63,185],"tasks":[21],"like":[22],"grade":[23],"school":[24],"math":[25,36,184],"problems.":[26],"One":[27],"key":[28],"challenge":[29],"of":[30,126,136,156,190],"finetuning":[31],"them":[32],"to":[33,65,85,94,152,166,194,209,215],"solve":[34],"such":[35],"problems":[38],"is":[39,231],"that":[40,55,133],"existing":[42],"datasets":[43,186],"only":[44],"contain":[45],"one":[46],"reference":[47,79,199],"solution":[48,158,200],"for":[49,211,218],"each":[50],"problem,":[51],"despite":[52],"the":[53,66,71,77,96,111,148,157,179,188],"fact":[54],"there":[56],"are":[57,74,222],"often":[58],"alternative":[59],"solutions":[60,141,171],"resembling":[61],"different":[62,226],"paths":[64],"final":[67],"answer.":[68],"This":[69],"way,":[70],"finetuned":[72],"biased":[75],"towards":[76],"limited":[78],"solutions,":[80,108,118],"which":[81,109],"limits":[82],"their":[83],"generalization":[84],"unseen":[86],"examples.":[87],"To":[88],"mitigate":[89],"this":[90],"issue,":[91],"we":[92,161,204],"propose":[93],"let":[95],"model":[97,227],"perform":[98],"sampling":[99,149],"during":[100],"training":[101,164],"and":[102,116,139,145,174,213],"learn":[103],"from":[104,169,196,207],"both":[105],"self-sampled":[106,137],"fully-correct":[107],"yield":[110],"correct":[112,129,138],"answer":[113],"upon":[114],"execution,":[115],"partially-correct":[117,140],"whose":[119],"intermediate":[120,124],"state":[121,125],"matches":[122],"an":[123],"a":[127,197],"known":[128],"solution.":[130],"We":[131],"show":[132,187],"our":[134,191],"use":[135],"can":[142],"benefit":[143],"learning":[144,168,195],"help":[146],"guide":[147],"process,":[150],"leading":[151],"more":[153],"efficient":[154],"exploration":[155],"space.":[159],"Additionally,":[160],"explore":[162],"various":[163],"objectives":[165],"support":[167],"multiple":[170],"per":[172],"example":[173],"find":[175],"greatly":[177],"affect":[178],"performance.":[180],"Experiments":[181],"two":[183],"effectiveness":[189],"method":[192],"compared":[193],"single":[198],"with":[201],"MLE,":[202],"where":[203],"improve":[205],"PASS@100":[206],"35.5%":[208],"44.5%":[210],"GSM8K,":[212],"27.6%":[214],"36.2%":[216],"PASS@80":[217],"MathQA.":[219],"Such":[220],"improvements":[221],"also":[223],"consistent":[224],"across":[225],"sizes.":[228],"Our":[229],"code":[230],"available":[232],"https://github.com/microsoft/TraceCodegen.":[234]},"counts_by_year":[{"year":2024,"cited_by_count":3},{"year":2023,"cited_by_count":1}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2022-06-13T00:00:00"}
