{"id":"https://openalex.org/W7154368717","doi":"https://doi.org/10.48550/arxiv.2604.11188","title":"MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis","display_name":"MathAgent: Adversarial Evolution of Constraint Graphs for Mathematical Reasoning Data Synthesis","publication_year":2026,"publication_date":"2026-04-13","ids":{"openalex":"https://openalex.org/W7154368717","doi":"https://doi.org/10.48550/arxiv.2604.11188"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2604.11188","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11188","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":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.2604.11188","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5048944308","display_name":"Zixiong Yu","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Yu, Zixiong","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133559801","display_name":"Jun Rao","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rao, Jun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5074712456","display_name":"Guhan Chen","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chen, Guhan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133616258","display_name":"Songtao Tian","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Tian, Songtao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133552652","display_name":"Bohan Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Bohan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133594607","display_name":"Jiansheng Wei","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wei, Jiansheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5133620102","display_name":"Min Zhang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Min","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5133624508","display_name":"Xiaojun Meng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meng, Xiaojun","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/T13523","display_name":"Mathematics, Computing, and Information Processing","score":0.19609999656677246,"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":0.19609999656677246,"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/T11948","display_name":"Machine Learning in Materials Science","score":0.1565999984741211,"subfield":{"id":"https://openalex.org/subfields/2505","display_name":"Materials Chemistry"},"field":{"id":"https://openalex.org/fields/25","display_name":"Materials 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":0.05920000001788139,"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/constraint","display_name":"Constraint (computer-aided design)","score":0.46810001134872437},{"id":"https://openalex.org/keywords/graph","display_name":"Graph","score":0.42309999465942383},{"id":"https://openalex.org/keywords/synthetic-data","display_name":"Synthetic data","score":0.41920000314712524},{"id":"https://openalex.org/keywords/simple","display_name":"Simple (philosophy)","score":0.41620001196861267},{"id":"https://openalex.org/keywords/executor","display_name":"Executor","score":0.3517000079154968},{"id":"https://openalex.org/keywords/core","display_name":"Core (optical fiber)","score":0.3163999915122986},{"id":"https://openalex.org/keywords/encoding","display_name":"Encoding (memory)","score":0.3116999864578247},{"id":"https://openalex.org/keywords/natural-language","display_name":"Natural language","score":0.30320000648498535},{"id":"https://openalex.org/keywords/constraint-programming","display_name":"Constraint programming","score":0.30309998989105225}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.7283999919891357},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5990999937057495},{"id":"https://openalex.org/C2776036281","wikidata":"https://www.wikidata.org/wiki/Q48769818","display_name":"Constraint (computer-aided design)","level":2,"score":0.46810001134872437},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.46459999680519104},{"id":"https://openalex.org/C132525143","wikidata":"https://www.wikidata.org/wiki/Q141488","display_name":"Graph","level":2,"score":0.42309999465942383},{"id":"https://openalex.org/C160920958","wikidata":"https://www.wikidata.org/wiki/Q7662746","display_name":"Synthetic data","level":2,"score":0.41920000314712524},{"id":"https://openalex.org/C2780586882","wikidata":"https://www.wikidata.org/wiki/Q7520643","display_name":"Simple (philosophy)","level":2,"score":0.41620001196861267},{"id":"https://openalex.org/C180591056","wikidata":"https://www.wikidata.org/wiki/Q654437","display_name":"Executor","level":2,"score":0.3517000079154968},{"id":"https://openalex.org/C2164484","wikidata":"https://www.wikidata.org/wiki/Q5170150","display_name":"Core (optical fiber)","level":2,"score":0.3163999915122986},{"id":"https://openalex.org/C125411270","wikidata":"https://www.wikidata.org/wiki/Q18653","display_name":"Encoding (memory)","level":2,"score":0.3116999864578247},{"id":"https://openalex.org/C195324797","wikidata":"https://www.wikidata.org/wiki/Q33742","display_name":"Natural language","level":2,"score":0.30320000648498535},{"id":"https://openalex.org/C173404611","wikidata":"https://www.wikidata.org/wiki/Q528588","display_name":"Constraint programming","level":3,"score":0.30309998989105225},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.30149999260902405},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.30059999227523804},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.3005000054836273},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.3003000020980835},{"id":"https://openalex.org/C192209626","wikidata":"https://www.wikidata.org/wiki/Q190909","display_name":"Focus (optics)","level":2,"score":0.28839999437332153},{"id":"https://openalex.org/C67186912","wikidata":"https://www.wikidata.org/wiki/Q367664","display_name":"Data modeling","level":2,"score":0.2874999940395355},{"id":"https://openalex.org/C162319229","wikidata":"https://www.wikidata.org/wiki/Q175263","display_name":"Data structure","level":2,"score":0.2856999933719635},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.265500009059906},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.2646999955177307},{"id":"https://openalex.org/C205606062","wikidata":"https://www.wikidata.org/wiki/Q5249645","display_name":"Decoupling (probability)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C2781089630","wikidata":"https://www.wikidata.org/wiki/Q21856745","display_name":"Realization (probability)","level":2,"score":0.2644999921321869},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.26190000772476196},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2606000006198883},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.25760000944137573},{"id":"https://openalex.org/C90312973","wikidata":"https://www.wikidata.org/wiki/Q7449052","display_name":"Semantic data model","level":2,"score":0.2547999918460846}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2604.11188","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11188","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":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.2604.11188","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2604.11188","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":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":{"Synthesizing":[0],"high-quality":[1,117],"mathematical":[2,159],"reasoning":[3],"data":[4,18,42,118],"without":[5],"human":[6],"priors":[7],"remains":[8],"a":[9,36,50,62,69,105,123],"significant":[10],"challenge.":[11],"Current":[12],"approaches":[13],"typically":[14],"rely":[15],"on":[16,108,122,145],"seed":[17],"mutation":[19],"or":[20],"simple":[21],"prompt":[22],"engineering,":[23],"often":[24],"suffering":[25],"from":[26,101],"mode":[27],"collapse":[28],"and":[29,111,133],"limited":[30],"logical":[31,113],"complexity.":[32],"This":[33,96],"paper":[34],"proposes":[35],"hierarchical":[37],"synthesis":[38,43],"framework":[39],"that":[40,137],"formulates":[41],"as":[44,61],"an":[45],"unsupervised":[46],"optimization":[47],"problem":[48],"over":[49],"constraint":[51],"graph":[52],"followed":[53],"by":[54],"semantic":[55],"instantiation,":[56],"rather":[57],"than":[58],"treating":[59],"it":[60],"direct":[63],"text":[64],"generation":[65,77],"task.":[66],"We":[67],"introduce":[68],"Legislator-Executor":[70],"paradigm:":[71],"The":[72],"Legislator":[73],"adversarially":[74],"evolves":[75],"structured":[76],"blueprints":[78],"encoding":[79],"the":[80,83,86,129],"constraints":[81],"of":[82,98,125,152],"problem,":[84],"while":[85],"Executor":[87],"instantiates":[88],"these":[89],"specifications":[90],"into":[91],"diverse":[92,112],"natural":[93],"language":[94],"scenarios.":[95],"decoupling":[97],"skeleton":[99],"design":[100],"linguistic":[102],"realization":[103],"enables":[104],"prioritized":[106],"focus":[107],"constructing":[109],"complex":[110],"structures,":[114],"thereby":[115],"guiding":[116],"synthesis.":[119],"Experiments":[120],"conducted":[121],"total":[124],"10":[126],"models":[127,143],"across":[128,157],"Qwen,":[130],"Llama,":[131],"Mistral,":[132],"Gemma":[134],"series":[135],"demonstrate":[136],"our":[138],"method":[139],"achieves":[140],"notable":[141],"results:":[142],"fine-tuned":[144],"1K":[146],"synthesized":[147],"samples":[148],"outperform":[149],"widely-used":[150],"datasets":[151],"comparable":[153],"scale":[154],"(LIMO,":[155],"s1K)":[156],"eight":[158],"benchmarks,":[160],"exhibiting":[161],"superior":[162],"out-of-distribution":[163],"generalization.":[164]},"counts_by_year":[],"updated_date":"2026-07-28T07:46:37.118299","created_date":"2026-04-15T00:00:00"}