{"id":"https://openalex.org/W7140132769","doi":"https://doi.org/10.18653/v1/2026.findings-eacl.93","title":"RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library","display_name":"RV-Syn: Rational and Verifiable Mathematical Reasoning Data Synthesis based on Structured Function Library","publication_year":2026,"publication_date":"2026-01-01","ids":{"openalex":"https://openalex.org/W7140132769","doi":"https://doi.org/10.18653/v1/2026.findings-eacl.93"},"language":null,"primary_location":{"id":"doi:10.18653/v1/2026.findings-eacl.93","is_oa":true,"landing_page_url":"https://doi.org/10.18653/v1/2026.findings-eacl.93","pdf_url":"https://aclanthology.org/2026.findings-eacl.93.pdf","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Findings of the Association for Computational Linguistics: EACL 2026","raw_type":"proceedings-article"},"type":"conference-paper","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://aclanthology.org/2026.findings-eacl.93.pdf","any_repository_has_fulltext":null},"authorships":[{"author_position":"first","author":{"id":null,"display_name":"Jiapeng Wang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jiapeng Wang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Jinhao Jiang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jinhao Jiang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Zhiqiang Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhiqiang Zhang","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":null,"display_name":"Jun Zhou","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jun Zhou","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":null,"display_name":"Xin Zhao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Xin Zhao","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":true,"cited_by_count":0,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"1812","last_page":"1827"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.3605000078678131,"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":0.3605000078678131,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.06159999966621399,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.05979999899864197,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/verifiable-secret-sharing","display_name":"Verifiable secret sharing","score":0.6194999814033508},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.48570001125335693},{"id":"https://openalex.org/keywords/structured-prediction","display_name":"Structured prediction","score":0.3050000071525574},{"id":"https://openalex.org/keywords/algebra-over-a-field","display_name":"Algebra over a field","score":0.3005000054836273},{"id":"https://openalex.org/keywords/automated-reasoning","display_name":"Automated reasoning","score":0.29120001196861267},{"id":"https://openalex.org/keywords/non-monotonic-logic","display_name":"Non-monotonic logic","score":0.2759000062942505}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.637499988079071},{"id":"https://openalex.org/C85847156","wikidata":"https://www.wikidata.org/wiki/Q59015987","display_name":"Verifiable secret sharing","level":3,"score":0.6194999814033508},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48570001125335693},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.391400009393692},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3869999945163727},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3513000011444092},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.3248000144958496},{"id":"https://openalex.org/C22367795","wikidata":"https://www.wikidata.org/wiki/Q7625208","display_name":"Structured prediction","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3005000054836273},{"id":"https://openalex.org/C195344581","wikidata":"https://www.wikidata.org/wiki/Q2555318","display_name":"Automated reasoning","level":2,"score":0.29120001196861267},{"id":"https://openalex.org/C159032336","wikidata":"https://www.wikidata.org/wiki/Q2488768","display_name":"Non-monotonic logic","level":2,"score":0.2759000062942505},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2728999853134155},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.2676999866962433},{"id":"https://openalex.org/C2777686260","wikidata":"https://www.wikidata.org/wiki/Q144037","display_name":"Calculus (dental)","level":2,"score":0.2669999897480011},{"id":"https://openalex.org/C161301231","wikidata":"https://www.wikidata.org/wiki/Q3478658","display_name":"Knowledge representation and reasoning","level":2,"score":0.2538999915122986}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.18653/v1/2026.findings-eacl.93","is_oa":true,"landing_page_url":"https://doi.org/10.18653/v1/2026.findings-eacl.93","pdf_url":"https://aclanthology.org/2026.findings-eacl.93.pdf","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Findings of the Association for Computational Linguistics: EACL 2026","raw_type":"proceedings-article"}],"best_oa_location":{"id":"doi:10.18653/v1/2026.findings-eacl.93","is_oa":true,"landing_page_url":"https://doi.org/10.18653/v1/2026.findings-eacl.93","pdf_url":"https://aclanthology.org/2026.findings-eacl.93.pdf","source":null,"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Findings of the Association for Computational Linguistics: EACL 2026","raw_type":"proceedings-article"},"sustainable_development_goals":[],"awards":[],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7140132769.pdf","grobid_xml":"https://content.openalex.org/works/W7140132769.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"The":[0],"advancement":[1],"of":[2,13,53,62,84,118,175,183,235,260,263,275,365,381,400,423,436,471,491],"reasoning":[3,15,170],"capabilities":[4],"in":[5,18,48,457],"Large":[6],"Language":[7],"Models":[8],"(LLMs)":[9],"requires":[10],"substantial":[11],"amounts":[12],"high-quality":[14],"data,":[16],"particularly":[17],"mathematics.Existing":[19],"data":[20,25,145,151,160],"synthesis":[21,127],"methods,":[22,128],"such":[23,401,413,467],"as":[24,97,420],"augmentation":[26],"from":[27],"annotated":[28],"training":[29,159],"sets":[30],"or":[31,339],"direct":[32],"question":[33],"generation":[34,57,112,172],"based":[35],"on":[36,146],"relevant":[37],"knowledge":[38],"points":[39],"and":[40,58,74,87,148,168,193,216,228,268,272,297,354,378,394,426,432,449],"documents,":[41],"have":[42,386],"expanded":[43],"datasets":[44],"but":[45],"face":[46],"challenges":[47],"mastering":[49],"the":[50,54,60,63,116,119,141,158,199,207,233,258,261,273,349,355,362,369,372,376,387,398,408,421,433,465,488],"internal":[51],"logic":[52],"problem":[55,111],"during":[56],"ensuring":[59,115],"verifiability":[61,117],"solutions.To":[64],"address":[65],"these":[66],"issues,":[67],"we":[68,316],"propose":[69],"RV-Syn,":[70],"a":[71,81,136,165,236,345,458],"novel":[72],"Rational":[73],"Verifiable":[75],"mathematical":[76,85],"Synthesis":[77],"approach.RV-Syn":[78],"first":[79],"constructs":[80],"structured":[82],"library":[83],"operations":[86],"then":[88],"composes":[89],"them":[90],"into":[91,105],"executable":[92],"computational":[93],"graphs,":[94],"which":[95],"serve":[96],"verifiable":[98],"solution":[99],"blueprints.These":[100],"graphs":[101],"are":[102,218,289,332],"subsequently":[103],"back-translated":[104],"complex":[106,265],"problems,":[107],"enabling":[108,164],"solution-guided,":[109],"logic-aware":[110],"while":[113],"inherently":[114],"solving":[120],"process.Experimental":[121],"results":[122],"show":[123],"RV-Syn":[124,185],"surpasses":[125],"existing":[126],"including":[129],"those":[130],"involving":[131],"humancrafted":[132],"problems.Our":[133],"method":[134],"achieves":[135],"6.3%":[137],"performance":[138],"gain":[139],"over":[140],"previous":[142],"state-of-theart":[143],"synthetic":[144],"LLaMA-3-8B":[147],"demonstrates":[149],"superior":[150],"efficiency,":[152],"outperforming":[153],"others":[154],"with":[155,368],"only":[156,330],"half":[157],"(50k":[161],"vs.":[162],"100k),":[163],"more":[166],"scalable":[167],"robust":[169],"dataset":[171],"framework.(1)":[173],"Lack":[174,182],"Reasoning":[176],"Depth":[177],"(2)":[178],"Logical":[179],"Inconsistency":[180],"(3)":[181],"Ground-Truth":[184],"Synthesized":[186],"problem:":[187,205,255,343,406,453],"Michael":[188],"starts":[189],"counting":[190],"at":[191,224],"32,":[192],"he":[194,203],"counts":[195],"by":[196,286,348,392],"fives.What":[197],"is":[198,222,232,270,278,335,397,444,487],"12th":[200],"number":[201,490],"that":[202,257,291,325,333,385,414,438,468],"counts?Synthesized":[204],"Consider":[206],"piecewise":[208],"function":[209],"f(x)":[210],"defined":[211,347],"as:":[212],"Where":[213],"a,":[214],"b,":[215],"c":[217],"constants.The":[219],"derivative":[220],"f'(x)":[221],"continuous":[223],"x":[225,229,267,377],"=":[226,230,242,295,301,320,430],"2":[227,243,251,292,294,311,314,412,415,428,440],"-2.What":[231],"value":[234],"+":[237,239,244,293,299,306,310,313,321,326,334,442],"b":[238],"c?":[240],"(Contradiction)":[241],",":[245],">":[246,411],"2,":[247,250,337,352],"-5,":[248],"-2":[249,441],"-,":[252],"<":[253],"-2,Synthesized":[254],"Suppose":[256],"sum":[259,274],"squares":[262],"two":[264,424,437],"numbers":[266,374],"y":[269,379],"7":[271,296,322],"their":[276],"cubes":[277],"10.List":[279],"all":[280,460],"possible":[281],"values":[282],"for":[283],"x+y,":[284],"separated":[285],"commas.":[287],"Completion:We":[288],"given":[290],"3":[298,300,305,307,393],"7.We":[302],"can":[303,317,417],"factor":[304],"to":[308,482],"get":[309],"-":[312,443],".Thus,":[315],"write":[318],"10":[319],".It":[323],"follows":[324],"must":[327],"divide":[328],"10.The":[329],"possibilities":[331],"1,":[336,359],"5":[338],"10.":[340],"(Incorrect":[341],"Answer)Synthesized":[342],"Given":[344,454],"line":[346,367],"point":[350,364,384],"(1,":[351,358],"3)":[353],"direction":[356],"vector":[357],"-1),":[360],"find":[361],"intersection":[363,383],"this":[366,382],"xy-plane.Then,":[370],"count":[371,399],"prime":[373,402],"between":[375],"coordinates":[380],"same":[388],"remainder":[389],"when":[390],"divided":[391],"5.":[395],"What":[396],"numbers?":[403],"Multi-hopGround-Truth:":[404],"0Synthesized":[405],"Find":[407],"smallest":[409],"integer":[410],"-1":[416,429],"be":[418],"expressed":[419],"product":[422],"integers":[425],"(i.e.,":[427],"),":[431],"highest":[434],"power":[435],"divides":[439],"an":[445],"even":[446],"number.":[447],"Enumeration":[448],"Iterative":[450],"LoopGround-Truth:":[451],"3Synthesized":[452],"eleven":[455],"coins":[456,466,473],"row,":[459],"initially":[461],"headsup.To":[462],"win,":[463],"arrange":[464],"every":[469],"pair":[470],"adjacent":[472,485],"shows":[474],"different":[475],"faces":[476],"(e.g.,":[477],"heads-tails-heads...).Each":[478],"move":[479],"allows":[480],"you":[481],"flip":[483],"there":[484],"coins.What":[486],"minimum":[489],"moves":[492],"required?":[493]},"counts_by_year":[],"updated_date":"2026-07-14T23:27:15.235271","created_date":"2026-02-19T00:00:00"}