{"id":"https://openalex.org/W7147270067","doi":"https://doi.org/10.48550/arxiv.2603.28061","title":"Testing Sparse Functions over the Reals","display_name":"Testing Sparse Functions over the Reals","publication_year":2026,"publication_date":"2026-03-30","ids":{"openalex":"https://openalex.org/W7147270067","doi":"https://doi.org/10.48550/arxiv.2603.28061"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.28061","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28061","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":"article"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2603.28061","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5132587087","display_name":"Vipul Arora","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Arora, Vipul","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5132579688","display_name":"Arnab Bhattacharyya","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bhattacharyya, Arnab","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5017159940","display_name":"Philips George John","orcid":"https://orcid.org/0000-0003-2324-8933"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"John, Philips George","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5080670450","display_name":"Sayantan Sen","orcid":"https://orcid.org/0000-0001-5875-5252"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Sen, Sayantan","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5132587087"],"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.8012999892234802,"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.8012999892234802,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.09470000118017197,"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/T11435","display_name":"Polynomial and algebraic computation","score":0.020600000396370888,"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/property-testing","display_name":"Property testing","score":0.67330002784729},{"id":"https://openalex.org/keywords/property","display_name":"Property (philosophy)","score":0.6128000020980835},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5697000026702881},{"id":"https://openalex.org/keywords/domain","display_name":"Domain (mathematical analysis)","score":0.49059998989105225},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.4875999987125397},{"id":"https://openalex.org/keywords/prime","display_name":"Prime (order theory)","score":0.45249998569488525}],"concepts":[{"id":"https://openalex.org/C123842658","wikidata":"https://www.wikidata.org/wiki/Q2918980","display_name":"Property testing","level":2,"score":0.67330002784729},{"id":"https://openalex.org/C189950617","wikidata":"https://www.wikidata.org/wiki/Q937228","display_name":"Property (philosophy)","level":2,"score":0.6128000020980835},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5735999941825867},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5697000026702881},{"id":"https://openalex.org/C36503486","wikidata":"https://www.wikidata.org/wiki/Q11235244","display_name":"Domain (mathematical analysis)","level":2,"score":0.49059998989105225},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.4875999987125397},{"id":"https://openalex.org/C184992742","wikidata":"https://www.wikidata.org/wiki/Q7243229","display_name":"Prime (order theory)","level":2,"score":0.45249998569488525},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4447999894618988},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.42719998955726624},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.37470000982284546},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3594000041484833},{"id":"https://openalex.org/C136119220","wikidata":"https://www.wikidata.org/wiki/Q1000660","display_name":"Algebra over a field","level":2,"score":0.3513000011444092},{"id":"https://openalex.org/C18762648","wikidata":"https://www.wikidata.org/wiki/Q42213","display_name":"Work (physics)","level":2,"score":0.3458999991416931},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.34049999713897705},{"id":"https://openalex.org/C77170095","wikidata":"https://www.wikidata.org/wiki/Q1753188","display_name":"Linearity","level":2,"score":0.3287999927997589},{"id":"https://openalex.org/C87007009","wikidata":"https://www.wikidata.org/wiki/Q210832","display_name":"Statistical hypothesis testing","level":2,"score":0.2770000100135803}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.28061","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28061","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":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.28061","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.28061","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":"article"},"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":{"Over":[0],"the":[1,21,29,32,50,60,78,96,109,137,154,157,162,165,173],"last":[2],"three":[3,102,190],"decades,":[4],"function":[5,26,138],"testing":[6,27,53,76,90,186],"has":[7],"been":[8,46],"extensively":[9],"studied":[10],"over":[11,28,108],"Boolean,":[12],"finite":[13],"fields,":[14],"and":[15,34,64,70,77,85,117,181],"discrete":[16],"settings.":[17],"However,":[18],"to":[19,127,134],"encode":[20],"real-world":[22],"applications":[23],"more":[24],"succinctly,":[25],"reals":[30],"(where":[31],"domain":[33],"range,":[35],"both":[36],"are":[37,169],"reals)":[38],"is":[39,147,159],"of":[40,52,57,80,106,142,188],"prime":[41],"importance.":[42],"Recently,":[43],"there":[44],"have":[45],"some":[47,128,140],"works":[48],"in":[49,161],"direction":[51],"for":[54,89,185],"algebraic":[55],"representations":[56,105],"such":[58],"functions:":[59],"work":[61,79,94],"by":[62],"Fleming":[63],"Yoshida":[65,86],"(ITCS":[66],"20),":[67],"Arora,":[68,81],"Kelman,":[69,84],"Meir":[71],"(SOSA":[72],"25)":[73],"on":[74],"linearity":[75],"Bhattacharyya,":[82],"Fleming,":[83],"(SODA":[87],"23)":[88],"low-degree":[91],"polynomials.":[92],"Our":[93],"follows":[95],"same":[97],"avenue,":[98],"wherein":[99],"we":[100,132,168],"study":[101],"well-studied":[103],"sparse":[104],"functions,":[107],"reals,":[110],"namely":[111],"(i)":[112],"$k$-linearity,":[113],"(ii)":[114],"$k$-sparse":[115],"polynomials,":[116],"(iii)":[118],"$k$-junta.":[119],"In":[120],"this":[121],"setting,":[122],"given":[123],"approximate":[124],"query":[125],"access":[126],"$f:\\mathbb{R}^n":[129],"\\rightarrow":[130],"\\mathbb{R}$,":[131],"want":[133],"decide":[135],"if":[136,145],"satisfies":[139],"property":[141],"interest,":[143],"or":[144],"it":[146],"far":[148],"from":[149,172],"all":[150],"functions":[151],"that":[152,167],"satisfy":[153],"property.":[155],"Here,":[156],"distance":[158],"measured":[160],"$\\ell_1$-metric,":[163],"under":[164],"assumption":[166],"drawing":[170],"samples":[171],"Standard":[174],"Gaussian":[175],"distribution.":[176],"We":[177],"present":[178],"efficient":[179],"testers":[180],"$\u03a9(k)$":[182],"lower":[183],"bounds":[184],"each":[187],"these":[189],"properties.":[191]},"counts_by_year":[],"updated_date":"2026-04-02T13:53:19.096889","created_date":"2026-04-02T00:00:00"}
