{"id":"https://openalex.org/W7221784497","doi":"https://doi.org/10.48550/arxiv.2610.17971","title":"Rarity Determines Minimax Rates of Semantic Entropy From Weak Pairwise Judgments With a Known Channel","display_name":"Rarity Determines Minimax Rates of Semantic Entropy From Weak Pairwise Judgments With a Known Channel","publication_year":2026,"publication_date":"2026-10-13","ids":{"openalex":"https://openalex.org/W7221784497","doi":"https://doi.org/10.48550/arxiv.2610.17971"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2610.17971","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17971","pdf_url":"https://arxiv.org/pdf/2610.17971","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/2610.17971","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5158705884","display_name":"Xiaoli Yu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I10535382","display_name":"Chongqing University of Posts and Telecommunications","ror":"https://ror.org/03dgaqz26","country_code":"CN","type":"education","lineage":["https://openalex.org/I10535382"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yu, Xiaoli","raw_affiliation_strings":["School of Cyber Security and Information Law Chongqing University of Posts and Telecommunications Chongqing 400065 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Cyber Security and Information Law Chongqing University of Posts and Telecommunications Chongqing 400065 , China","institution_ids":["https://openalex.org/I10535382"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5158714332","display_name":"Jiamiao Liu","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I151075929","display_name":"Army Medical University","ror":"https://ror.org/05w21nn13","country_code":"CN","type":"education","lineage":["https://openalex.org/I151075929"]},{"id":"https://openalex.org/I4210117763","display_name":"Xinqiao Hospital","ror":"https://ror.org/02d217z27","country_code":"CN","type":"healthcare","lineage":["https://openalex.org/I4210117763"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Liu, Jiamiao","raw_affiliation_strings":["Department of Information , Xinqiao Hospital Army Medical University (Third Military Medical University) Chongqing 400037 , China"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Information , Xinqiao Hospital Army Medical University (Third Military Medical University) Chongqing 400037 , China","institution_ids":["https://openalex.org/I151075929","https://openalex.org/I4210117763"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"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":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.3765000104904175,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10136","display_name":"Statistical Methods and Inference","score":0.3765000104904175,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13500","display_name":"Probability and Statistical Research","score":0.3118000030517578,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T13141","display_name":"Statistical Methods and Applications","score":0.05649999901652336,"subfield":{"id":"https://openalex.org/subfields/2613","display_name":"Statistics and Probability"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/semantic-entropy","display_name":"semantic entropy","score":0.8180000185966492},{"id":"https://openalex.org/keywords/language-model-evaluation","display_name":"language model evaluation","score":0.5},{"id":"https://openalex.org/keywords/minimax-rates","display_name":"minimax rates","score":0.6430000066757202},{"id":"https://openalex.org/keywords/entropy-estimation","display_name":"entropy estimation","score":0.42399999499320984},{"id":"https://openalex.org/keywords/spanning-trees","display_name":"spanning trees","score":0.5249999761581421},{"id":"https://openalex.org/keywords/lower-bounds","display_name":"lower bounds","score":0.44600000977516174}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.7652000188827515},{"id":"https://openalex.org/C184898388","wikidata":"https://www.wikidata.org/wiki/Q1435712","display_name":"Pairwise comparison","level":2,"score":0.6416000127792358},{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.5435000061988831},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.5364999771118164},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.5239999890327454},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.428600013256073},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4023999869823456},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.38440001010894775},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.37439998984336853},{"id":"https://openalex.org/C21031990","wikidata":"https://www.wikidata.org/wiki/Q355020","display_name":"Probability measure","level":2,"score":0.3506999909877777},{"id":"https://openalex.org/C9679016","wikidata":"https://www.wikidata.org/wiki/Q1417473","display_name":"Principle of maximum entropy","level":2,"score":0.3375999927520752},{"id":"https://openalex.org/C62438384","wikidata":"https://www.wikidata.org/wiki/Q331350","display_name":"Simplex","level":2,"score":0.33070001006126404},{"id":"https://openalex.org/C43711488","wikidata":"https://www.wikidata.org/wiki/Q7534783","display_name":"Skew","level":2,"score":0.3140999972820282},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.2994999885559082},{"id":"https://openalex.org/C144237770","wikidata":"https://www.wikidata.org/wiki/Q747534","display_name":"Mathematical economics","level":1,"score":0.29010000824928284},{"id":"https://openalex.org/C80899671","wikidata":"https://www.wikidata.org/wiki/Q1304193","display_name":"Vertex (graph theory)","level":3,"score":0.2888000011444092},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.288100004196167},{"id":"https://openalex.org/C149441793","wikidata":"https://www.wikidata.org/wiki/Q200726","display_name":"Probability distribution","level":2,"score":0.28610000014305115},{"id":"https://openalex.org/C125252325","wikidata":"https://www.wikidata.org/wiki/Q1345213","display_name":"Entropy rate","level":4,"score":0.27459999918937683},{"id":"https://openalex.org/C50817715","wikidata":"https://www.wikidata.org/wiki/Q79895177","display_name":"Regret","level":2,"score":0.2736000120639801},{"id":"https://openalex.org/C2776436953","wikidata":"https://www.wikidata.org/wiki/Q5163215","display_name":"Consistency (knowledge bases)","level":2,"score":0.271699994802475},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.2653999924659729},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.26010000705718994},{"id":"https://openalex.org/C108650721","wikidata":"https://www.wikidata.org/wiki/Q1783253","display_name":"Counterfactual thinking","level":2,"score":0.2565000057220459},{"id":"https://openalex.org/C159254197","wikidata":"https://www.wikidata.org/wiki/Q1144915","display_name":"Lexicographical order","level":2,"score":0.2535000145435333},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.2535000145435333},{"id":"https://openalex.org/C2776809875","wikidata":"https://www.wikidata.org/wiki/Q1375963","display_name":"Converse","level":2,"score":0.2517000138759613},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.2508000135421753},{"id":"https://openalex.org/C2780522230","wikidata":"https://www.wikidata.org/wiki/Q1140419","display_name":"Ambiguity","level":2,"score":0.2508000135421753}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2610.17971","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17971","pdf_url":"https://arxiv.org/pdf/2610.17971","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.2610.17971","doi":"https://doi.org/10.48550/arxiv.2610.17971","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2610.17971","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2610.17971","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/2610.17971","pdf_url":"https://arxiv.org/pdf/2610.17971","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":[{"id":"https://openalex.org/G2443899004","display_name":null,"funder_award_id":"2025YQB034","funder_id":"https://openalex.org/F4320327581","funder_display_name":"Army Medical University"}],"funders":[{"id":"https://openalex.org/F4320327581","display_name":"Army Medical University","ror":null}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W7221784497.pdf","grobid_xml":"https://content.openalex.org/works/W7221784497.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W7223574291","https://openalex.org/W2965294095","https://openalex.org/W617976673","https://openalex.org/W2963608890","https://openalex.org/W2788378756","https://openalex.org/W7097996655","https://openalex.org/W2786072821","https://openalex.org/W7096218137","https://openalex.org/W2752114013","https://openalex.org/W2398570102"],"abstract_inverted_index":{"The":[0,17,146,196],"semantic":[1],"entropy":[2,9,24,211],"of":[3,10,13,30,38,90,129,171,178,181],"a":[4,31,41,53,74,88,120],"language":[5],"model":[6],"is":[7,25,66,83,103,128,212],"the":[8,11,23,28,36,79,91,95,101,124,184,189,200,205,210],"meanings":[12,18,37,62,108,118],"its":[14],"sampled":[15],"answers.":[16],"are":[19],"never":[20],"observed,":[21],"and":[22,55,64,71,93,137,193,204],"estimated":[26],"from":[27,69],"verdicts":[29,173],"pairwise":[32],"equivalence":[33],"judge.":[34],"Given":[35],"$n$":[39],"answers,":[40,182],"known":[42],"channel":[43],"declares":[44],"each":[45],"pair":[46],"equivalent":[47],"independently,":[48],"with":[49,77,114,208],"probability":[50,122],"$q+\u0394$":[51],"within":[52],"meaning":[54],"$q$":[56,65],"across":[57],"meanings.":[58],"At":[59],"most":[60,116],"$K$":[61],"occur,":[63],"bounded":[67],"away":[68],"$0$":[70],"$1$.":[72],"For":[73],"weak":[75],"judge,":[76],"$n\u0394^2\\to0$,":[78],"global":[80,201],"minimax":[81,125],"rate":[82,202],"set":[84,104,192],"by":[85,105],"distributions":[86,113],"near":[87],"vertex":[89],"simplex":[92],"overstates":[94],"difficulty":[96,102],"elsewhere.":[97],"We":[98],"show":[99],"that":[100],"how":[106],"many":[107],"can":[109],"be":[110],"rare.":[111],"Over":[112],"at":[115,142],"$s$":[117,165],"below":[119],"fixed":[121,153],"$\u03c4<1/(K-s)$,":[123],"squared":[126],"risk":[127],"order":[130],"$N^{-1/s}$":[131],"for":[132,135,139],"$s\\ge2$,":[133],"$N^{-1}\\log^2(e+N)$":[134],"$s=1$":[136],"$N^{-1}$":[138],"$s=0$,":[140],"capped":[141],"one,":[143],"where":[144],"$N=n^K\u0394^{2K-2}$.":[145],"matching":[147],"lower":[148],"bounds":[149],"hold":[150],"on":[151],"every":[152,179],"polynomial":[154],"window":[155],"$n\u0394^2\\le":[156],"n^{-\u03ba}$.":[157],"One":[158],"estimator":[159],"attains":[160],"these":[161],"rates":[162],"without":[163],"knowing":[164],"or":[166],"$\u03c4$:":[167],"it":[168],"averages":[169],"products":[170],"centered":[172],"along":[174],"all":[175],"spanning":[176],"trees":[177],"$k$-set":[180],"projects":[183],"resulting":[185],"power":[186],"sums":[187],"onto":[188],"valid":[190],"moment":[191],"inverts":[194],"them.":[195],"case":[197],"$s=K-1$":[198],"gives":[199],"$N^{-1/(K-1)}$":[203],"consistency":[206],"threshold:":[207],"$\u0394=n^{-\u03b3}$":[209],"uniformly":[213],"consistently":[214],"estimable":[215],"exactly":[216],"when":[217],"$\u03b3":[218]},"counts_by_year":[],"updated_date":"2026-10-28T10:33:24.094632","created_date":"2026-10-15T00:00:00"}
