{"id":"https://openalex.org/W7225180346","doi":"https://doi.org/10.48550/arxiv.2611.02346","title":"Pointwise Score Evaluation from Succinct Boolean Descriptions: SAT Equivalence for Strongly Log-Concave Gaussian Mixtures","display_name":"Pointwise Score Evaluation from Succinct Boolean Descriptions: SAT Equivalence for Strongly Log-Concave Gaussian Mixtures","publication_year":2026,"publication_date":"2026-11-02","ids":{"openalex":"https://openalex.org/W7225180346","doi":"https://doi.org/10.48550/arxiv.2611.02346"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2611.02346","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02346","pdf_url":"https://arxiv.org/pdf/2611.02346","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","is_traditional":true,"indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2611.02346","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5123129936","display_name":"Yinzhen Lv","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I165779595","display_name":"The University of Melbourne","ror":"https://ror.org/01ej9dk98","country_code":"AU","type":"education","lineage":["https://openalex.org/I165779595"]}],"countries":["AU"],"is_corresponding":true,"raw_author_name":"Lv, Yinzhen","raw_affiliation_strings":["Faculty of Engineering and Information Technology (FEIT ) The University of Melbourne"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Faculty of Engineering and Information Technology (FEIT ) The University of Melbourne","institution_ids":["https://openalex.org/I165779595"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5123129936"],"corresponding_institution_ids":["https://openalex.org/I165779595"],"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":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":0.38109999895095825,"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":0.38109999895095825,"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/T11596","display_name":"Constraint Satisfaction and Optimization","score":0.07609999924898148,"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/T10374","display_name":"Advanced Graph Theory Research","score":0.07180000096559525,"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/score-based-generative-models","display_name":"score-based generative models","score":0.9350000023841858},{"id":"https://openalex.org/keywords/boolean-satisfiability","display_name":"Boolean satisfiability","score":0.7379999756813049},{"id":"https://openalex.org/keywords/gaussian-mixture-model","display_name":"Gaussian mixture model","score":0.9190000295639038},{"id":"https://openalex.org/keywords/computational-geometry","display_name":"computational geometry","score":0.41999998688697815},{"id":"https://openalex.org/keywords/polynomial-time-approximation","display_name":"polynomial-time approximation","score":0.574999988079071},{"id":"https://openalex.org/keywords/exact-counting","display_name":"exact counting","score":0.7369999885559082},{"id":"https://openalex.org/keywords/mean-estimation","display_name":"mean estimation","score":0.9319999814033508},{"id":"https://openalex.org/keywords/numerical-precision","display_name":"numerical precision","score":0.4449999928474426}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7627000212669373},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.5286999940872192},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.5232999920845032},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.43290001153945923},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.428600013256073},{"id":"https://openalex.org/C187455244","wikidata":"https://www.wikidata.org/wiki/Q942353","display_name":"Boolean function","level":2,"score":0.4255000054836273},{"id":"https://openalex.org/C2777984123","wikidata":"https://www.wikidata.org/wiki/Q9248237","display_name":"Pointwise","level":2,"score":0.4122999906539917},{"id":"https://openalex.org/C7342684","wikidata":"https://www.wikidata.org/wiki/Q520777","display_name":"Boolean data type","level":2,"score":0.37459999322891235},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.3578999936580658},{"id":"https://openalex.org/C156340839","wikidata":"https://www.wikidata.org/wiki/Q2704791","display_name":"Enumeration","level":2,"score":0.33180001378059387},{"id":"https://openalex.org/C67499762","wikidata":"https://www.wikidata.org/wiki/Q4943358","display_name":"Boolean model","level":2,"score":0.32019999623298645},{"id":"https://openalex.org/C74640108","wikidata":"https://www.wikidata.org/wiki/Q1372900","display_name":"Propositional formula","level":5,"score":0.314300000667572},{"id":"https://openalex.org/C111797529","wikidata":"https://www.wikidata.org/wiki/Q17080584","display_name":"Maximum satisfiability problem","level":3,"score":0.3140000104904175},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.30880001187324524},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.3068999946117401},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3027999997138977},{"id":"https://openalex.org/C200415742","wikidata":"https://www.wikidata.org/wiki/Q1350285","display_name":"True quantified Boolean formula","level":2,"score":0.29499998688697815},{"id":"https://openalex.org/C179799912","wikidata":"https://www.wikidata.org/wiki/Q205084","display_name":"Computational complexity theory","level":2,"score":0.2833999991416931},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.28290000557899475},{"id":"https://openalex.org/C179518139","wikidata":"https://www.wikidata.org/wiki/Q5140297","display_name":"Coding (social sciences)","level":2,"score":0.27570000290870667},{"id":"https://openalex.org/C153083717","wikidata":"https://www.wikidata.org/wiki/Q6535263","display_name":"Leverage (statistics)","level":2,"score":0.27059999108314514},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.2696000039577484},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.260699987411499},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.2565999925136566},{"id":"https://openalex.org/C53533937","wikidata":"https://www.wikidata.org/wiki/Q185020","display_name":"Histogram","level":3,"score":0.25600001215934753},{"id":"https://openalex.org/C55439883","wikidata":"https://www.wikidata.org/wiki/Q360812","display_name":"Correctness","level":2,"score":0.2515000104904175}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2611.02346","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02346","pdf_url":"https://arxiv.org/pdf/2611.02346","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.2611.02346","doi":"https://doi.org/10.48550/arxiv.2611.02346","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2611.02346","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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2611.02346","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2611.02346","pdf_url":"https://arxiv.org/pdf/2611.02346","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":[],"study_designs":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7225180346.pdf","grobid_xml":"https://content.openalex.org/works/W7225180346.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4415798607","https://openalex.org/W2522716311","https://openalex.org/W1576973534","https://openalex.org/W7222884613","https://openalex.org/W7162634407","https://openalex.org/W2397828203","https://openalex.org/W4416118738","https://openalex.org/W2145825841","https://openalex.org/W1596339127","https://openalex.org/W4396821265"],"abstract_inverted_index":{"Score-based":[0],"generative":[1],"models":[2],"rely":[3],"on":[4,17],"access":[5,135],"to":[6,92,98,127],"accurate":[7],"scores,":[8],"but":[9],"the":[10,19,88,137,167,178,187],"cost":[11,169],"of":[12,87,101,115,170,189],"computing":[13],"those":[14],"scores":[15,172],"depends":[16],"how":[18,120],"underlying":[20],"distribution":[21,35],"is":[22,36,71,96,113],"represented.":[23],"Can":[24],"smoothness":[25],"and":[26,79,130],"strong":[27,81],"log-concavity":[28],"make":[29],"score":[30,60,90],"evaluation":[31],"efficient":[32,154,192],"when":[33],"a":[34,54,62,68,109,141,190],"specified":[37,56],"by":[38,45],"Boolean":[39,69,102],"constraints?":[40],"I":[41,52,117],"investigate":[42],"this":[43,183],"question":[44],"separating":[46],"geometric":[47],"encoding":[48],"from":[49,153,173],"computational":[50,168],"extraction.":[51],"construct":[53],"succinctly":[55],"Gaussian":[57],"mixture":[58],"whose":[59,111],"at":[61],"fixed":[63],"query":[64],"location":[65],"encodes":[66],"whether":[67],"formula":[70],"satisfiable.":[72],"The":[73],"construction":[74,148],"has":[75],"rational":[76],"component":[77],"means":[78],"uniform":[80],"log-concavity,":[82],"yet":[83],"deterministic":[84],"polynomial-time":[85,99],"approximation":[86,152],"designated":[89],"coordinate":[91],"constant":[93],"absolute":[94],"accuracy":[95],"equivalent":[97],"solvability":[100],"satisfiability.":[103],"This":[104],"equivalence":[105],"remains":[106],"valid":[107],"throughout":[108],"neighborhood":[110],"radius":[112],"independent":[114,133],"dimension.":[116],"further":[118],"characterize":[119],"numerical":[121],"precision":[122],"connects":[123],"bounded":[124],"witness":[125],"enumeration":[126],"exact":[128],"counting,":[129],"show":[131,159],"that":[132,160],"sample":[134],"turns":[136],"same":[138],"target":[139],"into":[140],"dimension-independent":[142],"mean-estimation":[143],"problem.":[144],"An":[145],"explicit":[146],"parity":[147],"also":[149],"separates":[150],"low-degree":[151],"computation.":[155],"Together,":[156],"these":[157],"results":[158],"favorable":[161],"geometry":[162],"alone":[163],"does":[164],"not":[165],"resolve":[166],"extracting":[171],"compact":[174],"descriptions.":[175],"They":[176],"identify":[177],"precise":[179],"extraction":[180],"requirement":[181],"in":[182],"formulation":[184],"while":[185],"leaving":[186],"existence":[188],"general":[191],"evaluator":[193],"open.":[194]},"counts_by_year":[],"updated_date":"2026-11-06T12:05:46.655746","created_date":"2026-11-04T00:00:00"}