{"id":"https://openalex.org/W7160878427","doi":"https://doi.org/10.48550/arxiv.2605.07105","title":"Theoretical Limits of Language Model Alignment","display_name":"Theoretical Limits of Language Model Alignment","publication_year":2026,"publication_date":"2026-05-08","ids":{"openalex":"https://openalex.org/W7160878427","doi":"https://doi.org/10.48550/arxiv.2605.07105"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2605.07105","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07105","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.2605.07105","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5092145397","display_name":"Lucas Monteiro Paes","orcid":"https://orcid.org/0000-0003-0129-1420"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Paes, Lucas Monteiro","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5052836067","display_name":"Natalie Mackraz","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mackraz, Natalie","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5112911728","display_name":"Barry-John Theobald","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Theobald, Barry-John","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5035740107","display_name":"Federico Danieli","orcid":"https://orcid.org/0000-0002-0866-2485"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Danieli, Federico","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.2313999980688095,"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/T12026","display_name":"Explainable Artificial Intelligence (XAI)","score":0.2313999980688095,"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":0.1088000014424324,"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/T10883","display_name":"Ethics and Social Impacts of AI","score":0.06710000336170197,"subfield":{"id":"https://openalex.org/subfields/3311","display_name":"Safety Research"},"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/inference","display_name":"Inference","score":0.5936999917030334},{"id":"https://openalex.org/keywords/estimator","display_name":"Estimator","score":0.5575000047683716},{"id":"https://openalex.org/keywords/covariance","display_name":"Covariance","score":0.4307999908924103},{"id":"https://openalex.org/keywords/base","display_name":"Base (topology)","score":0.4059999883174896},{"id":"https://openalex.org/keywords/proxy","display_name":"Proxy (statistics)","score":0.390500009059906},{"id":"https://openalex.org/keywords/statistical-model","display_name":"Statistical model","score":0.3440000116825104},{"id":"https://openalex.org/keywords/divergence","display_name":"Divergence (linguistics)","score":0.3416000008583069},{"id":"https://openalex.org/keywords/language-model","display_name":"Language model","score":0.34139999747276306}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6539999842643738},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5936999917030334},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.5575000047683716},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.4307999908924103},{"id":"https://openalex.org/C42058472","wikidata":"https://www.wikidata.org/wiki/Q810214","display_name":"Base (topology)","level":2,"score":0.4059999883174896},{"id":"https://openalex.org/C2780148112","wikidata":"https://www.wikidata.org/wiki/Q1432581","display_name":"Proxy (statistics)","level":2,"score":0.390500009059906},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.3440000116825104},{"id":"https://openalex.org/C207390915","wikidata":"https://www.wikidata.org/wiki/Q1230525","display_name":"Divergence (linguistics)","level":2,"score":0.3416000008583069},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.34139999747276306},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3230000138282776},{"id":"https://openalex.org/C51485801","wikidata":"https://www.wikidata.org/wiki/Q16966861","display_name":"Efficient frontier","level":3,"score":0.32260000705718994},{"id":"https://openalex.org/C90559484","wikidata":"https://www.wikidata.org/wiki/Q778379","display_name":"Expression (computer science)","level":2,"score":0.31940001249313354},{"id":"https://openalex.org/C137635306","wikidata":"https://www.wikidata.org/wiki/Q182667","display_name":"Pareto principle","level":2,"score":0.3122999966144562},{"id":"https://openalex.org/C8505890","wikidata":"https://www.wikidata.org/wiki/Q605095","display_name":"Budget constraint","level":2,"score":0.3109999895095825},{"id":"https://openalex.org/C93959086","wikidata":"https://www.wikidata.org/wiki/Q6888345","display_name":"Model selection","level":2,"score":0.3050000071525574},{"id":"https://openalex.org/C134261354","wikidata":"https://www.wikidata.org/wiki/Q938438","display_name":"Statistical inference","level":2,"score":0.29919999837875366},{"id":"https://openalex.org/C72169020","wikidata":"https://www.wikidata.org/wiki/Q194404","display_name":"Monotonic function","level":2,"score":0.2987000048160553},{"id":"https://openalex.org/C49937458","wikidata":"https://www.wikidata.org/wiki/Q2599292","display_name":"Probabilistic logic","level":2,"score":0.2962000072002411},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.2921999990940094},{"id":"https://openalex.org/C2986314615","wikidata":"https://www.wikidata.org/wiki/Q36829","display_name":"Pareto optimal","level":3,"score":0.28940001130104065},{"id":"https://openalex.org/C2777472644","wikidata":"https://www.wikidata.org/wiki/Q16968992","display_name":"Approximate inference","level":3,"score":0.2736999988555908},{"id":"https://openalex.org/C81917197","wikidata":"https://www.wikidata.org/wiki/Q628760","display_name":"Selection (genetic algorithm)","level":2,"score":0.2732999920845032},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.2628999948501587},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.25920000672340393},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.25459998846054077}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2605.07105","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07105","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.2605.07105","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2605.07105","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":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Language":[0],"model":[1,5,137],"(LM)":[2],"alignment":[3,22,74,133,157,236,248],"improves":[4],"outputs":[6],"to":[7,144,245],"reflect":[8],"human":[9],"preferences":[10],"while":[11,217],"preserving":[12],"the":[13,16,30,43,54,69,77,96,108,123,145,151,162,169,196,214,235],"capabilities":[14],"of":[15,57,72,164],"base":[17,124,136],"model.":[18],"The":[19],"most":[20],"common":[21],"approaches":[23,213],"are":[24,243],"(i)":[25],"reinforcement":[26],"learning,":[27],"which":[28,41],"maximizes":[29],"expected":[31,80],"reward":[32,58,81,98,147,165,178,181],"under":[33,60,122],"a":[34,61,84,92,102,120,127,184],"KL-divergence":[35,86],"constraint,":[36],"and":[37,155,167,206,208,219,238],"(ii)":[38],"best-of-$N$":[39,211],"alignment,":[40],"selects":[42],"highest-reward":[44],"output":[45],"among":[46],"$N$":[47],"independent":[48],"samples.":[49],"Despite":[50],"their":[51],"widespread":[52],"use,":[53],"fundamental":[55],"limits":[56,71],"improvement":[59],"KL":[62,170],"budget":[63],"remain":[64,221],"poorly":[65],"understood.":[66],"We":[67,114,140,174],"characterize":[68],"information-theoretic":[70],"KL-regularized":[73],"by":[75,101],"deriving":[76],"maximum":[78],"achievable":[79,132],"gain":[82],"for":[83,95,187,200,203],"fixed":[85],"budget.":[87],"Our":[88,224],"first":[89],"result":[90],"provides":[91],"closed-form":[93],"expression":[94,118],"optimal":[97,247],"improvement,":[99],"governed":[100],"Jeffreys":[103],"divergence":[104],"term":[105],"rather":[106],"than":[107],"$\\sqrt{\\texttt{KL}}$":[109],"used":[110,190],"in":[111,191,234],"prior":[112],"analyses.":[113],"further":[115],"reformulate":[116],"this":[117,188],"as":[119],"covariance":[121],"model,":[125],"yielding":[126],"practical":[128],"estimator":[129],"that":[130,150,177,210,240],"predicts":[131],"gains":[134],"from":[135],"samples":[138],"alone.":[139],"extend":[141],"our":[142],"analysis":[143],"proxy":[146,156],"setting,":[148],"showing":[149],"gap":[152],"between":[153],"ideal":[154],"(reward":[158],"hacking)":[159],"grows":[160],"with":[161],"magnitude":[163],"error":[166],"when":[168],"penalty":[171],"factor":[172],"decreases.":[173],"then":[175],"prove":[176],"ensembling":[179],"mitigates":[180],"hacking,":[182],"providing":[183],"theoretical":[185,215,225],"justification":[186],"technique":[189],"practice.":[192],"Empirically,":[193],"we":[194],"compute":[195],"KL-reward":[197],"Pareto":[198],"frontier":[199],"two":[201],"tasks":[202],"LMs,":[204],"safety":[205],"summarization,":[207],"show":[209],"closely":[212],"limit,":[216],"PPO":[218],"GRPO":[220],"substantially":[222],"suboptimal.":[223],"results":[226],"shed":[227],"light":[228],"on":[229],"several":[230],"empirically":[231],"observed":[232],"phenomena":[233],"literature":[237],"suggest":[239],"algorithmic":[241],"improvements":[242],"needed":[244],"achieve":[246],"without":[249],"high":[250],"inference":[251],"costs.":[252]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2026-05-12T00:00:00"}