{"id":"https://openalex.org/W7163370577","doi":"https://doi.org/10.48550/arxiv.2606.03858","title":"PyraMathBench: Evaluating and Improving Mathematical Capability in Large Language Models","display_name":"PyraMathBench: Evaluating and Improving Mathematical Capability in Large Language Models","publication_year":2026,"publication_date":"2026-06-02","ids":{"openalex":"https://openalex.org/W7163370577","doi":"https://doi.org/10.48550/arxiv.2606.03858"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2606.03858","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03858","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2606.03858","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5137788842","display_name":"Zetian Ouyang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Ouyang, Zetian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137746783","display_name":"Linlin Wang (289071)","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Wang, Linlin","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5137726713","display_name":"Gerard de Melo","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"de Melo, Gerard","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5137775769","display_name":"Liang He","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Liang","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/T10028","display_name":"Topic Modeling","score":0.1500999927520752,"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":0.1500999927520752,"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/T13629","display_name":"Text Readability and Simplification","score":0.11819999665021896,"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":0.11330000311136246,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/interpretability","display_name":"Interpretability","score":0.8772000074386597},{"id":"https://openalex.org/keywords/benchmark","display_name":"Benchmark (surveying)","score":0.6664000153541565},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.6320000290870667},{"id":"https://openalex.org/keywords/key","display_name":"Key (lock)","score":0.5231999754905701},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5073000192642212},{"id":"https://openalex.org/keywords/computational-intelligence","display_name":"Computational intelligence","score":0.37560001015663147},{"id":"https://openalex.org/keywords/cornerstone","display_name":"Cornerstone","score":0.3321000039577484}],"concepts":[{"id":"https://openalex.org/C2781067378","wikidata":"https://www.wikidata.org/wiki/Q17027399","display_name":"Interpretability","level":2,"score":0.8772000074386597},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6906999945640564},{"id":"https://openalex.org/C185798385","wikidata":"https://www.wikidata.org/wiki/Q1161707","display_name":"Benchmark (surveying)","level":2,"score":0.6664000153541565},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.6320000290870667},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.5231999754905701},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5073000192642212},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4311999976634979},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.39910000562667847},{"id":"https://openalex.org/C139502532","wikidata":"https://www.wikidata.org/wiki/Q1122090","display_name":"Computational intelligence","level":2,"score":0.37560001015663147},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3589000105857849},{"id":"https://openalex.org/C2780616401","wikidata":"https://www.wikidata.org/wiki/Q1133673","display_name":"Cornerstone","level":2,"score":0.3321000039577484},{"id":"https://openalex.org/C76969082","wikidata":"https://www.wikidata.org/wiki/Q486902","display_name":"Mathematical model","level":2,"score":0.2994000017642975},{"id":"https://openalex.org/C68859911","wikidata":"https://www.wikidata.org/wiki/Q1503724","display_name":"Pattern matching","level":2,"score":0.2867000102996826},{"id":"https://openalex.org/C137836250","wikidata":"https://www.wikidata.org/wiki/Q984063","display_name":"Optimization problem","level":2,"score":0.28380000591278076},{"id":"https://openalex.org/C169900460","wikidata":"https://www.wikidata.org/wiki/Q2200417","display_name":"Cognition","level":2,"score":0.266400009393692},{"id":"https://openalex.org/C90805587","wikidata":"https://www.wikidata.org/wiki/Q10944557","display_name":"Word (group theory)","level":2,"score":0.26579999923706055},{"id":"https://openalex.org/C2777601683","wikidata":"https://www.wikidata.org/wiki/Q6499736","display_name":"Vocabulary","level":2,"score":0.2565999925136566},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.25529998540878296},{"id":"https://openalex.org/C2986605239","wikidata":"https://www.wikidata.org/wiki/Q925667","display_name":"Numerical models","level":3,"score":0.25049999356269836}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2606.03858","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03858","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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.2606.03858","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2606.03858","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Despite":[0],"the":[1,8,32,89],"pivotal":[2],"role":[3],"of":[4,10,34,80],"numerical":[5,26,75,82],"reasoning":[6],"as":[7],"cornerstone":[9],"mathematical":[11,29],"capabilities":[12],"in":[13,36],"large":[14],"language":[15],"models":[16],"(LLMs)":[17],"across":[18],"applications,":[19],"few":[20],"benchmarks":[21],"evaluate":[22],"LLMs":[23],"by":[24,73],"integrating":[25],"processing":[27],"and":[28,62,77,97,114,129],"reasoning,":[30],"hindering":[31],"interpretability":[33],"failures":[35],"math":[37,52],"tasks.":[38],"We":[39],"introduce":[40],"PyraMathBench,":[41],"a":[42,123],"comprehensive":[43],"hierarchical":[44],"benchmark":[45],"with":[46,127],"32,505":[47],"questions":[48],"derived":[49],"from":[50],"7,404":[51],"word":[53],"problems,":[54],"spanning":[55],"4":[56],"key":[57],"cognitive":[58],"aspects,":[59],"14":[60],"subcategories,":[61],"2":[63],"modalities.":[64],"Experiments":[65],"reveal":[66],"that":[67],"LLMs'":[68,105],"performance":[69],"is":[70],"severely":[71],"compromised":[72],"inadequate":[74],"computation":[76],"weak":[78],"handling":[79],"abstract":[81],"questions.":[83],"To":[84],"address":[85],"this,":[86],"we":[87],"propose":[88],"Smart":[90],"Optimization":[91,101],"&":[92],"Learning-based":[93],"VErsatile":[94],"module":[95],"(SOLVE)":[96],"Interactive":[98],"Relative":[99],"Policy":[100],"(IRPO),":[102],"which":[103],"enhance":[104],"numerical-mathematical":[106],"synergy":[107],"via":[108],"efficient":[109],"tool":[110],"calls":[111],"(fuzzy":[112],"matching":[113],"low-quality":[115],"call":[116],"rejection).":[117],"Comparative":[118],"experiments":[119],"show":[120],"Qwen-2.5":[121],"achieves":[122],"5.0":[124],"score":[125],"improvement":[126],"SOLVE":[128],"IRPO":[130],"training.":[131]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-06-04T00:00:00"}