{"id":"https://openalex.org/W7160857720","doi":"https://doi.org/10.48550/arxiv.2605.07698","title":"Future Validity is the Missing Statistic: From Impossibility to $\u03a6$-Estimation for Grammar-Faithful Speculative Decoding","display_name":"Future Validity is the Missing Statistic: From Impossibility to $\u03a6$-Estimation for Grammar-Faithful Speculative Decoding","publication_year":2026,"publication_date":"2026-05-08","ids":{"openalex":"https://openalex.org/W7160857720","doi":"https://doi.org/10.48550/arxiv.2605.07698"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.07698","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07698","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":"Preprint"},"type":"preprint","indexed_in":["datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://doi.org/10.48550/arxiv.2605.07698","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5113392171","display_name":"Wenhua Nie","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Nie, Wenhua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135874424","display_name":"Zijie Meng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Meng, Zijie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5101570585","display_name":"Kun Zou","orcid":"https://orcid.org/0009-0008-0575-5142"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zou, Kun","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135842995","display_name":"Zheng Lin","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Lin, Zheng","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135901887","display_name":"Ziwei Li","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Li, Ziwei","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135859879","display_name":"Haoran Zheng","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zheng, Haoran","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135833922","display_name":"Jyh-Shing Roger Jang","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Jang, Jyh-Shing Roger","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5135836631","display_name":"Hao Zhang","orcid":"https://orcid.org/0000-0003-0067-5238"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zhang, Hao","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/T10181","display_name":"Natural Language Processing Techniques","score":0.6984999775886536,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.6984999775886536,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.10029999911785126,"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/T10028","display_name":"Topic Modeling","score":0.041200000792741776,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hash-function","display_name":"Hash function","score":0.3849000036716461},{"id":"https://openalex.org/keywords/impossibility","display_name":"Impossibility","score":0.3725000023841858},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.336899995803833},{"id":"https://openalex.org/keywords/decoding-methods","display_name":"Decoding methods","score":0.32010000944137573},{"id":"https://openalex.org/keywords/matching","display_name":"Matching (statistics)","score":0.31450000405311584},{"id":"https://openalex.org/keywords/distribution","display_name":"Distribution (mathematics)","score":0.31349998712539673},{"id":"https://openalex.org/keywords/recursion","display_name":"Recursion (computer science)","score":0.30959999561309814},{"id":"https://openalex.org/keywords/json","display_name":"JSON","score":0.3034000098705292},{"id":"https://openalex.org/keywords/perfect-hash-function","display_name":"Perfect hash function","score":0.30239999294281006}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6255999803543091},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4472000002861023},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4415999948978424},{"id":"https://openalex.org/C99138194","wikidata":"https://www.wikidata.org/wiki/Q183427","display_name":"Hash function","level":2,"score":0.3849000036716461},{"id":"https://openalex.org/C2776261394","wikidata":"https://www.wikidata.org/wiki/Q315562","display_name":"Impossibility","level":2,"score":0.3725000023841858},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.336899995803833},{"id":"https://openalex.org/C57273362","wikidata":"https://www.wikidata.org/wiki/Q576722","display_name":"Decoding methods","level":2,"score":0.32010000944137573},{"id":"https://openalex.org/C165064840","wikidata":"https://www.wikidata.org/wiki/Q1321061","display_name":"Matching (statistics)","level":2,"score":0.31450000405311584},{"id":"https://openalex.org/C110121322","wikidata":"https://www.wikidata.org/wiki/Q865811","display_name":"Distribution (mathematics)","level":2,"score":0.31349998712539673},{"id":"https://openalex.org/C168773036","wikidata":"https://www.wikidata.org/wiki/Q264164","display_name":"Recursion (computer science)","level":2,"score":0.30959999561309814},{"id":"https://openalex.org/C2780416260","wikidata":"https://www.wikidata.org/wiki/Q2063","display_name":"JSON","level":2,"score":0.3034000098705292},{"id":"https://openalex.org/C87431388","wikidata":"https://www.wikidata.org/wiki/Q2070573","display_name":"Perfect hash function","level":4,"score":0.30239999294281006},{"id":"https://openalex.org/C186644900","wikidata":"https://www.wikidata.org/wiki/Q194152","display_name":"Parsing","level":2,"score":0.3021000027656555},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.29840001463890076},{"id":"https://openalex.org/C98763669","wikidata":"https://www.wikidata.org/wiki/Q176645","display_name":"Markov chain","level":2,"score":0.2964000105857849},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.28929999470710754},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2874999940395355},{"id":"https://openalex.org/C110157686","wikidata":"https://www.wikidata.org/wiki/Q922122","display_name":"Broadcasting (networking)","level":2,"score":0.27649998664855957},{"id":"https://openalex.org/C60582962","wikidata":"https://www.wikidata.org/wiki/Q83886","display_name":"Viterbi algorithm","level":3,"score":0.27129998803138733},{"id":"https://openalex.org/C46681722","wikidata":"https://www.wikidata.org/wiki/Q4725589","display_name":"Alias","level":2,"score":0.2687999904155731},{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.26750001311302185},{"id":"https://openalex.org/C2779960059","wikidata":"https://www.wikidata.org/wiki/Q7113681","display_name":"Overhead (engineering)","level":2,"score":0.2639999985694885},{"id":"https://openalex.org/C113174947","wikidata":"https://www.wikidata.org/wiki/Q2859736","display_name":"Tree (set theory)","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C184337299","wikidata":"https://www.wikidata.org/wiki/Q1437428","display_name":"Semantics (computer science)","level":2,"score":0.2623000144958496},{"id":"https://openalex.org/C29248071","wikidata":"https://www.wikidata.org/wiki/Q163310","display_name":"Turing machine","level":3,"score":0.26190000772476196},{"id":"https://openalex.org/C53893814","wikidata":"https://www.wikidata.org/wiki/Q7378909","display_name":"Rule-based machine translation","level":2,"score":0.257099986076355},{"id":"https://openalex.org/C177264268","wikidata":"https://www.wikidata.org/wiki/Q1514741","display_name":"Set (abstract data type)","level":2,"score":0.25290000438690186}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.07698","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07698","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":"Preprint"}],"best_oa_location":{"id":"doi:10.48550/arxiv.2605.07698","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07698","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":"Preprint"},"sustainable_development_goals":[{"id":"https://metadata.un.org/sdg/4","score":0.7785615921020508,"display_name":"Quality Education"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Grammar-constrained":[0],"generation":[1],"is":[2,17,89,132],"often":[3],"combined":[4],"with":[5,31,65,97,119,155],"local":[6,32,100],"vocabulary":[7],"masking":[8,101],"and":[9,37,145,167,184],"speculative":[10,29,60],"decoding,":[11],"but":[12],"the":[13,19,42,49,55,67,75,82,94,124],"resulting":[14,125],"sampling":[15],"law":[16],"not":[18],"grammar-conditional":[20,50],"distribution":[21,45,51,88],"users":[22],"usually":[23],"intend.":[24],"We":[25,73],"show":[26],"that":[27],"any":[28],"decoder":[30,113],"mask":[33],"access,":[34],"Leviathan":[35],"rejection,":[36],"rollback":[38],"soundness":[39],"samples":[40,115],"from":[41,117],"locally":[43],"projected":[44],"$\u03bc^{\\mathrm{proj}}$":[46],"rather":[47],"than":[48],"$\u03bc^\\star$.":[52],"This":[53],"extends":[54],"GAD":[56],"impossibility":[57],"result":[58],"to":[59,103,106,173,181],"decoding;":[61],"on":[62,142],"Dyck":[63,144,151],"grammars":[64,183],"Qwen3-8B,":[66],"total-variation":[68,126],"gap":[69],"can":[70],"reach":[71],"0.996.":[72],"identify":[74],"future-validity":[76],"function":[77],"$\u03a6_t(y)=\\Pr_p[\\mathrm{valid\\":[78],"completion}\\mid":[79],"y]$":[80],"as":[81],"missing":[83],"correction":[84,169],"statistic.":[85],"The":[86],"target":[87],"a":[90],"Doob":[91],"transform":[92],"of":[93],"base":[95],"model":[96],"$h=\u03a6$,":[98],"while":[99],"corresponds":[102],"setting":[104],"$h$":[105],"one.":[107],"With":[108],"exact":[109,129,160],"$\u03a6$,":[110,121],"our":[111],"oracle":[112],"FVO-Spec":[114],"exactly":[116],"$\u03bc^\\star$;":[118],"approximate":[120],"we":[122,138],"bound":[123],"error.":[127],"Because":[128],"future":[130],"validity":[131],"hard":[133],"for":[134],"general":[135],"context-free":[136],"grammars,":[137],"evaluate":[139],"estimator":[140],"hierarchies":[141],"tractable":[143],"finite":[146],"JSON":[147,171],"languages.":[148],"OneStep":[149],"reduces":[150,163],"TV":[152],"by":[153,165],"14%":[154],"under":[156],"1%":[157],"throughput":[158],"overhead,":[159],"dynamic":[161],"programming":[162],"it":[164],"97%,":[166],"finite-language":[168],"closes":[170],"gaps":[172],"numerical":[174],"precision.":[175],"All":[176],"fidelity":[177],"claims":[178],"are":[179],"scoped":[180],"enumerable":[182],"token":[185],"tries.":[186]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-05-12T00:00:00"}