{"id":"https://openalex.org/W7135073871","doi":"https://doi.org/10.48550/arxiv.2603.10396","title":"Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilities","display_name":"Verbalizing LLM's Higher-order Uncertainty via Imprecise Probabilities","publication_year":2026,"publication_date":"2026-03-11","ids":{"openalex":"https://openalex.org/W7135073871","doi":"https://doi.org/10.48550/arxiv.2603.10396"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.10396","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10396","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":null,"license_id":null,"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.2603.10396","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5128868671","display_name":"Anita Yang","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Yang, Anita","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035023688","display_name":"Krikamol Muandet","orcid":"https://orcid.org/0000-0002-4182-5282"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Muandet, Krikamol","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5000098655","display_name":"Michele Caprio","orcid":"https://orcid.org/0000-0002-7569-097X"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Caprio, Michele","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051223998","display_name":"Siu Lun Chau","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Chau, Siu Lun","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5128872452","display_name":"Masaki Adachi","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Adachi, Masaki","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5128868671"],"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":0.4478999972343445,"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":0.4478999972343445,"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":0.06560000032186508,"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/T11147","display_name":"Misinformation and Its Impacts","score":0.05550000071525574,"subfield":{"id":"https://openalex.org/subfields/3312","display_name":"Sociology and Political Science"},"field":{"id":"https://openalex.org/fields/33","display_name":"Social Sciences"},"domain":{"id":"https://openalex.org/domains/2","display_name":"Social Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/credibility","display_name":"Credibility","score":0.7312999963760376},{"id":"https://openalex.org/keywords/probabilistic-logic","display_name":"Probabilistic logic","score":0.6917999982833862},{"id":"https://openalex.org/keywords/indeterminacy","display_name":"Indeterminacy (philosophy)","score":0.6489999890327454},{"id":"https://openalex.org/keywords/expert-elicitation","display_name":"Expert elicitation","score":0.6129000186920166},{"id":"https://openalex.org/keywords/uncertainty-quantification","display_name":"Uncertainty quantification","score":0.510200023651123},{"id":"https://openalex.org/keywords/uncertainty-analysis","display_name":"Uncertainty analysis","score":0.4277999997138977},{"id":"https://openalex.org/keywords/measurement-uncertainty","display_name":"Measurement uncertainty","score":0.35679998993873596}],"concepts":[{"id":"https://openalex.org/C2780224610","wikidata":"https://www.wikidata.org/wiki/Q1530061","display_name":"Credibility","level":2,"score":0.7312999963760376},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.6917999982833862},{"id":"https://openalex.org/C2777366796","wikidata":"https://www.wikidata.org/wiki/Q6017758","display_name":"Indeterminacy (philosophy)","level":2,"score":0.6489999890327454},{"id":"https://openalex.org/C72161134","wikidata":"https://www.wikidata.org/wiki/Q5421219","display_name":"Expert elicitation","level":2,"score":0.6129000186920166},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5809000134468079},{"id":"https://openalex.org/C32230216","wikidata":"https://www.wikidata.org/wiki/Q7882499","display_name":"Uncertainty quantification","level":2,"score":0.510200023651123},{"id":"https://openalex.org/C177803969","wikidata":"https://www.wikidata.org/wiki/Q29205","display_name":"Uncertainty analysis","level":2,"score":0.4277999997138977},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3662000000476837},{"id":"https://openalex.org/C137209882","wikidata":"https://www.wikidata.org/wiki/Q1403517","display_name":"Measurement uncertainty","level":2,"score":0.35679998993873596},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.34549999237060547},{"id":"https://openalex.org/C2777868144","wikidata":"https://www.wikidata.org/wiki/Q7239817","display_name":"Preference elicitation","level":3,"score":0.31360000371932983},{"id":"https://openalex.org/C176147448","wikidata":"https://www.wikidata.org/wiki/Q1889114","display_name":"Sensitivity analysis","level":3,"score":0.311599999666214},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.28540000319480896},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.2768000066280365},{"id":"https://openalex.org/C2778067643","wikidata":"https://www.wikidata.org/wiki/Q166507","display_name":"Interval (graph theory)","level":2,"score":0.272599995136261},{"id":"https://openalex.org/C149782125","wikidata":"https://www.wikidata.org/wiki/Q160039","display_name":"Econometrics","level":1,"score":0.27000001072883606},{"id":"https://openalex.org/C120936955","wikidata":"https://www.wikidata.org/wiki/Q2155640","display_name":"Empirical research","level":2,"score":0.2655999958515167},{"id":"https://openalex.org/C116834253","wikidata":"https://www.wikidata.org/wiki/Q2039217","display_name":"Identification (biology)","level":2,"score":0.2533999979496002}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.10396","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10396","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"article"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2603.10396","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.10396","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":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"article"},"sustainable_development_goals":[{"score":0.7508062720298767,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Despite":[0],"the":[1,24,29,95],"growing":[2],"demand":[3],"for":[4,69],"eliciting":[5,72],"uncertainty":[6,32,59,77,79,88,128],"from":[7,130],"large":[8],"language":[9],"models":[10],"(LLMs),":[11],"empirical":[12],"evidence":[13],"suggests":[14],"that":[15,44],"LLM":[16],"behavior":[17],"is":[18],"not":[19],"always":[20],"adequately":[21],"captured":[22],"by":[23],"elicitation":[25,60],"techniques":[26,61],"developed":[27],"under":[28],"classical":[30],"probabilistic":[31],"framework.":[33],"This":[34],"mismatch":[35],"leads":[36],"to":[37,83,107],"systematic":[38],"failure":[39],"modes,":[40],"particularly":[41],"in":[42,63,94],"settings":[43],"involve":[45],"ambiguous":[46],"question-answering,":[47],"in-context":[48],"learning,":[49],"and":[50,71,104,110,116,134],"self-reflection.":[51],"To":[52],"address":[53],"this,":[54],"we":[55],"propose":[56],"novel":[57],"prompt-based":[58],"grounded":[62],"\\emph{imprecise":[64],"probabilities},":[65],"a":[66,84],"principled":[67],"framework":[68],"repesenting":[70],"higher-order":[73],"uncertainty.":[74],"Here,":[75],"first-order":[76],"captures":[78],"over":[80],"possible":[81],"responses":[82],"prompt,":[85],"while":[86],"second-order":[87],"(uncertainty":[89],"about":[90],"uncertainty)":[91],"quantifies":[92],"indeterminacy":[93],"underlying":[96],"probability":[97],"model":[98],"itself.":[99],"We":[100],"introduce":[101],"general-purpose":[102],"prompting":[103],"post-processing":[105],"procedures":[106],"directly":[108],"elicit":[109],"quantify":[111],"both":[112],"orders":[113],"of":[114],"uncertainty,":[115],"demonstrate":[117],"their":[118],"effectiveness":[119],"across":[120],"diverse":[121],"settings.":[122],"Our":[123],"approach":[124],"enables":[125],"more":[126],"faithful":[127],"reporting":[129],"LLMs,":[131],"improving":[132],"credibility":[133],"supporting":[135],"downstream":[136],"decision-making.":[137]},"counts_by_year":[],"updated_date":"2026-03-13T14:25:03.468858","created_date":"2026-03-13T00:00:00"}