{"id":"https://openalex.org/W4416360693","doi":"https://doi.org/10.48550/arxiv.2511.12869","title":"On the Fundamental Limits of LLMs at Scale","display_name":"On the Fundamental Limits of LLMs at Scale","publication_year":2025,"publication_date":"2025-11-17","ids":{"openalex":"https://openalex.org/W4416360693","doi":"https://doi.org/10.48550/arxiv.2511.12869"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2511.12869","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.12869","pdf_url":"https://arxiv.org/pdf/2511.12869","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/2511.12869","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5027027201","display_name":"Muhammad Ahmed Mohsin","orcid":"https://orcid.org/0009-0005-2766-0345","observed_orcids":["https://orcid.org/0009-0005-2766-0345"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Mohsin, Muhammad Ahmed","raw_affiliation_strings":["Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Umer, Muhammad","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Umer, Muhammad","raw_affiliation_strings":["Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Bilal, Ahsan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I8692664","display_name":"University of Oklahoma","ror":"https://ror.org/02aqsxs83","country_code":"US","type":"education","lineage":["https://openalex.org/I8692664"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bilal, Ahsan","raw_affiliation_strings":["The University of Oklahoma"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"The University of Oklahoma","institution_ids":["https://openalex.org/I8692664"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5135295510","display_name":"Zeeshan Memon","orcid":"https://orcid.org/0009-0005-7526-0231","observed_orcids":["https://orcid.org/0009-0005-7526-0231"]},"institutions":[{"id":"https://openalex.org/I150468666","display_name":"Emory University","ror":"https://ror.org/03czfpz43","country_code":"US","type":"education","lineage":["https://openalex.org/I150468666"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Memon, Zeeshan","raw_affiliation_strings":["Emory University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Emory University","institution_ids":["https://openalex.org/I150468666"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Qadir, Muhammad Ibtsaam","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I219193219","display_name":"Purdue University West Lafayette","ror":"https://ror.org/02dqehb95","country_code":"US","type":"education","lineage":["https://openalex.org/I219193219"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Qadir, Muhammad Ibtsaam","raw_affiliation_strings":["Purdue University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Purdue University","institution_ids":["https://openalex.org/I219193219"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5034455446","display_name":"Sagnik Bhattacharya","orcid":"https://orcid.org/0000-0003-0385-1225","observed_orcids":["https://orcid.org/0000-0003-0385-1225"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Bhattacharya, Sagnik","raw_affiliation_strings":["Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5124967394","display_name":"Hassan Rizwan","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I103635307","display_name":"University of California, Riverside","ror":"https://ror.org/03nawhv43","country_code":"US","type":"education","lineage":["https://openalex.org/I103635307"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Rizwan, Hassan","raw_affiliation_strings":["UC Riverside"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UC Riverside","institution_ids":["https://openalex.org/I103635307"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5116053905","display_name":"Abhiram Rao Gorle","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Gorle, Abhiram R.","raw_affiliation_strings":["Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5120363346","display_name":"Maahe Zehra Kazmi","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Kazmi, Maahe Zehra","raw_affiliation_strings":["UC Berkeley"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"UC Berkeley","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Amir, Nukhba","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I24542750","display_name":"Khyber Medical University","ror":"https://ror.org/00nv6q035","country_code":"PK","type":"education","lineage":["https://openalex.org/I24542750"]}],"countries":["PK"],"is_corresponding":false,"raw_author_name":"Amir, Nukhba","raw_affiliation_strings":["Khyber Medical University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Khyber Medical University","institution_ids":["https://openalex.org/I24542750"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Subhan, Ali","orcid":null,"observed_orcids":[]},"institutions":[{"id":"https://openalex.org/I170486558","display_name":"Universitat Pompeu Fabra","ror":"https://ror.org/04n0g0b29","country_code":"ES","type":"education","lineage":["https://openalex.org/I170486558"]}],"countries":["ES"],"is_corresponding":false,"raw_author_name":"Subhan, Ali","raw_affiliation_strings":["Universtat Pompeu Fabra"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Universtat Pompeu Fabra","institution_ids":["https://openalex.org/I170486558"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039655720","display_name":"Muhammad Usman Rafique","orcid":"https://orcid.org/0000-0001-5504-5482","observed_orcids":["https://orcid.org/0000-0001-5504-5482"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rafique, Muhammad Usman","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5108370761","display_name":"Zhaofeng He","orcid":"https://orcid.org/0000-0003-3043-2122","observed_orcids":["https://orcid.org/0000-0003-3043-2122"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"He, Zihao","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062022071","display_name":"Punit Mehta","orcid":null,"observed_orcids":[]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Mehta, Pulkit","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5057961688","display_name":"Muhammad Ali Jamshed","orcid":"https://orcid.org/0000-0002-2141-9025","observed_orcids":["https://orcid.org/0000-0002-2141-9025"]},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jamshed, Muhammad Ali","raw_affiliation_strings":["University of Glasgow"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"University of Glasgow","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5029146230","display_name":"J.M. Cioffi","orcid":"https://orcid.org/0000-0003-1353-8101","observed_orcids":["https://orcid.org/0000-0003-1353-8101"]},"institutions":[{"id":"https://openalex.org/I97018004","display_name":"Stanford University","ror":"https://ror.org/00f54p054","country_code":"US","type":"education","lineage":["https://openalex.org/I97018004"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Cioffi, John M.","raw_affiliation_strings":["Stanford University"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Stanford University","institution_ids":["https://openalex.org/I97018004"]}]}],"institutions":[],"countries_distinct_count":4,"institutions_distinct_count":9,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":30,"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":0.8715999722480774,"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":0.8715999722480774,"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/T10181","display_name":"Natural Language Processing Techniques","score":0.06639999896287918,"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/T12002","display_name":"Computability, Logic, AI Algorithms","score":0.007400000002235174,"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/large-language-models","display_name":"large language models","score":0.9309999942779541},{"id":"https://openalex.org/keywords/scaling-limits","display_name":"scaling limits","score":0.8569999933242798},{"id":"https://openalex.org/keywords/hallucinations","display_name":"hallucinations","score":0.8539999723434448},{"id":"https://openalex.org/keywords/context-compression","display_name":"context compression","score":0.984000027179718},{"id":"https://openalex.org/keywords/matrix-diagonalization","display_name":"diagonalization","score":0.6520000100135803},{"id":"https://openalex.org/keywords/undecidability","display_name":"undecidability","score":0.7910000085830688},{"id":"https://openalex.org/keywords/sample-complexity","display_name":"sample complexity","score":0.746999979019165},{"id":"https://openalex.org/keywords/semantic-drift","display_name":"semantic drift","score":0.746999979019165},{"id":"https://openalex.org/keywords/cross-modal-alignment","display_name":"cross-modal alignment","score":0.8059999942779541},{"id":"https://openalex.org/keywords/sparse-attention","display_name":"sparse attention","score":0.5849999785423279},{"id":"https://openalex.org/keywords/hierarchical-attention","display_name":"hierarchical attention","score":0.7440000176429749}],"concepts":[{"id":"https://openalex.org/C192034797","wikidata":"https://www.wikidata.org/wiki/Q3502995","display_name":"Undecidable problem","level":3,"score":0.8468000292778015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.617900013923645},{"id":"https://openalex.org/C153269930","wikidata":"https://www.wikidata.org/wiki/Q430001","display_name":"Decidability","level":2,"score":0.5788999795913696},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.5770999789237976},{"id":"https://openalex.org/C152062344","wikidata":"https://www.wikidata.org/wiki/Q818888","display_name":"Computability","level":2,"score":0.5724999904632568},{"id":"https://openalex.org/C188441871","wikidata":"https://www.wikidata.org/wiki/Q7554146","display_name":"Softmax function","level":3,"score":0.5467000007629395},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.48820000886917114},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.4697999954223633},{"id":"https://openalex.org/C168773769","wikidata":"https://www.wikidata.org/wiki/Q1350299","display_name":"Satisfiability","level":2,"score":0.4489000141620636},{"id":"https://openalex.org/C167729594","wikidata":"https://www.wikidata.org/wiki/Q17736","display_name":"Axiom","level":2,"score":0.4244000017642975},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.41749998927116394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.391400009393692},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.3723999857902527},{"id":"https://openalex.org/C117160843","wikidata":"https://www.wikidata.org/wiki/Q338652","display_name":"Sublinear function","level":2,"score":0.34209999442100525},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.33889999985694885},{"id":"https://openalex.org/C6943359","wikidata":"https://www.wikidata.org/wiki/Q875276","display_name":"Boolean satisfiability problem","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.3273000121116638},{"id":"https://openalex.org/C164226766","wikidata":"https://www.wikidata.org/wiki/Q7293202","display_name":"Rank (graph theory)","level":2,"score":0.31790000200271606},{"id":"https://openalex.org/C31170391","wikidata":"https://www.wikidata.org/wiki/Q188619","display_name":"Hierarchy","level":2,"score":0.31220000982284546},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3050999939441681},{"id":"https://openalex.org/C166052673","wikidata":"https://www.wikidata.org/wiki/Q83021","display_name":"Empirical evidence","level":2,"score":0.3043999969959259},{"id":"https://openalex.org/C45340560","wikidata":"https://www.wikidata.org/wiki/Q215382","display_name":"Disjoint sets","level":2,"score":0.30309998989105225},{"id":"https://openalex.org/C87117476","wikidata":"https://www.wikidata.org/wiki/Q362383","display_name":"Cardinality (data modeling)","level":2,"score":0.2930000126361847},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.28999999165534973},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.27799999713897705},{"id":"https://openalex.org/C197657726","wikidata":"https://www.wikidata.org/wiki/Q174733","display_name":"Bipartite graph","level":3,"score":0.2741999924182892},{"id":"https://openalex.org/C2778112365","wikidata":"https://www.wikidata.org/wiki/Q3511065","display_name":"Sequence (biology)","level":2,"score":0.2727000117301941},{"id":"https://openalex.org/C2776359362","wikidata":"https://www.wikidata.org/wiki/Q2145286","display_name":"Representation (politics)","level":3,"score":0.26899999380111694},{"id":"https://openalex.org/C114289077","wikidata":"https://www.wikidata.org/wiki/Q3284399","display_name":"Statistical model","level":2,"score":0.26759999990463257},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.2662000060081482},{"id":"https://openalex.org/C74912251","wikidata":"https://www.wikidata.org/wiki/Q6815727","display_name":"Memory footprint","level":2,"score":0.26420000195503235},{"id":"https://openalex.org/C2777508537","wikidata":"https://www.wikidata.org/wiki/Q7936620","display_name":"Visual reasoning","level":2,"score":0.25270000100135803},{"id":"https://openalex.org/C102993220","wikidata":"https://www.wikidata.org/wiki/Q387196","display_name":"Description logic","level":2,"score":0.25209999084472656},{"id":"https://openalex.org/C136979486","wikidata":"https://www.wikidata.org/wiki/Q773483","display_name":"Existential quantification","level":2,"score":0.25200000405311584}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2511.12869","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.12869","pdf_url":"https://arxiv.org/pdf/2511.12869","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.2511.12869","doi":"https://doi.org/10.48550/arxiv.2511.12869","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2511.12869","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:2511.12869","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2511.12869","pdf_url":"https://arxiv.org/pdf/2511.12869","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":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4416360693.pdf","grobid_xml":"https://content.openalex.org/works/W4416360693.grobid-xml"},"referenced_works_count":166,"referenced_works":["https://openalex.org/W1686946872","https://openalex.org/W2902442580","https://openalex.org/W2940744433","https://openalex.org/W2986922898","https://openalex.org/W3001279689","https://openalex.org/W3015468748","https://openalex.org/W3020712669","https://openalex.org/W3027879771","https://openalex.org/W3035214886","https://openalex.org/W3039017601","https://openalex.org/W3085139254","https://openalex.org/W3118838679","https://openalex.org/W3170863103","https://openalex.org/W3172942063","https://openalex.org/W3196318247","https://openalex.org/W3199748991","https://openalex.org/W4225909425","https://openalex.org/W4226082499","https://openalex.org/W4229026446","https://openalex.org/W4287888039","https://openalex.org/W4312261477","https://openalex.org/W4315705838","https://openalex.org/W4319165821","https://openalex.org/W4322718191","https://openalex.org/W4327810158","https://openalex.org/W4365211686","https://openalex.org/W4382603041","https://openalex.org/W4384648639","https://openalex.org/W4385573586","https://openalex.org/W4385718077","https://openalex.org/W4385774107","https://openalex.org/W4386942462","https://openalex.org/W4387323904","https://openalex.org/W4387355694","https://openalex.org/W4387356039","https://openalex.org/W4387432095","https://openalex.org/W4387838903","https://openalex.org/W4388514134","https://openalex.org/W4388555916","https://openalex.org/W4388774693","https://openalex.org/W4388927764","https://openalex.org/W4388979610","https://openalex.org/W4389326242","https://openalex.org/W4389518953","https://openalex.org/W4389520747","https://openalex.org/W4390041933","https://openalex.org/W4391158659","https://openalex.org/W4391800042","https://openalex.org/W4391876619","https://openalex.org/W4392575321","https://openalex.org/W4393027756","https://openalex.org/W4393905017","https://openalex.org/W4393942918","https://openalex.org/W4394708144","https://openalex.org/W4394862623","https://openalex.org/W4395484131","https://openalex.org/W4396624257","https://openalex.org/W4398229669","https://openalex.org/W4399062487","https://openalex.org/W4399453666","https://openalex.org/W4399759481","https://openalex.org/W4400023197","https://openalex.org/W4400949264","https://openalex.org/W4401042382","https://openalex.org/W4401042459","https://openalex.org/W4401042735","https://openalex.org/W4401043267","https://openalex.org/W4401306886","https://openalex.org/W4402364937","https://openalex.org/W4402670703","https://openalex.org/W4402671034","https://openalex.org/W4402671334","https://openalex.org/W4402672106","https://openalex.org/W4402672112","https://openalex.org/W4402704598","https://openalex.org/W4402753774","https://openalex.org/W4403381960","https://openalex.org/W4403443663","https://openalex.org/W4403578737","https://openalex.org/W4403702484","https://openalex.org/W4403749280","https://openalex.org/W4403795513","https://openalex.org/W4403818822","https://openalex.org/W4403920471","https://openalex.org/W4404305023","https://openalex.org/W4404307372","https://openalex.org/W4404314417","https://openalex.org/W4404330874","https://openalex.org/W4404569914","https://openalex.org/W4404648721","https://openalex.org/W4404781621","https://openalex.org/W4404781668","https://openalex.org/W4404781848","https://openalex.org/W4404782094","https://openalex.org/W4404782801","https://openalex.org/W4404782813","https://openalex.org/W4404782840","https://openalex.org/W4404783013","https://openalex.org/W4404783032","https://openalex.org/W4404783366","https://openalex.org/W4404792833","https://openalex.org/W4405023779","https://openalex.org/W4405140008","https://openalex.org/W4405766390","https://openalex.org/W4405903187","https://openalex.org/W4406033435","https://openalex.org/W4406231018","https://openalex.org/W4406841238","https://openalex.org/W4407231747","https://openalex.org/W4407424718","https://openalex.org/W4407759168","https://openalex.org/W4407794264","https://openalex.org/W4409368309","https://openalex.org/W4409661400","https://openalex.org/W4410964376","https://openalex.org/W4411119292","https://openalex.org/W4411119852","https://openalex.org/W4411120025","https://openalex.org/W4412376969","https://openalex.org/W4412610890","https://openalex.org/W4412722243","https://openalex.org/W4412944984","https://openalex.org/W4412945011","https://openalex.org/W4413147337","https://openalex.org/W4413358888","https://openalex.org/W4414586223","https://openalex.org/W4414631650","https://openalex.org/W4414973451","https://openalex.org/W4415063194","https://openalex.org/W4415101139","https://openalex.org/W4415273274","https://openalex.org/W4415308082","https://openalex.org/W4415311663","https://openalex.org/W4415427951","https://openalex.org/W4415796627","https://openalex.org/W4416034285","https://openalex.org/W4416034722","https://openalex.org/W4416035636","https://openalex.org/W4416035762","https://openalex.org/W4416036398","https://openalex.org/W4416050957","https://openalex.org/W4416091752","https://openalex.org/W4416112531","https://openalex.org/W4416390973","https://openalex.org/W4416556574","https://openalex.org/W4417097899","https://openalex.org/W4417156095","https://openalex.org/W4417253743","https://openalex.org/W4417258166","https://openalex.org/W4417287872","https://openalex.org/W6910741274","https://openalex.org/W6929293117","https://openalex.org/W6929399311","https://openalex.org/W6947954562","https://openalex.org/W6948199246","https://openalex.org/W6966921795","https://openalex.org/W6967033044","https://openalex.org/W7133191918","https://openalex.org/W7133214447","https://openalex.org/W7133227460","https://openalex.org/W7134182271","https://openalex.org/W7139083851","https://openalex.org/W7140093517","https://openalex.org/W7166805633","https://openalex.org/W7166832077","https://openalex.org/W7171977352"],"related_works":["https://openalex.org/W4405765899","https://openalex.org/W7169498256","https://openalex.org/W7171631767","https://openalex.org/W4415977047","https://openalex.org/W7162298793","https://openalex.org/W6910515245","https://openalex.org/W7164457048","https://openalex.org/W7105749967","https://openalex.org/W7213301781","https://openalex.org/W7214537689"],"abstract_inverted_index":{"Large":[0],"Language":[1],"Models":[2],"(LLMs)":[3],"have":[4],"benefited":[5],"enormously":[6],"from":[7,181],"scaling,":[8],"yet":[9],"these":[10,37],"gains":[11],"are":[12],"bounded":[13],"by":[14,62],"five":[15],"fundamental":[16],"limitations:":[17],"(1)":[18],"hallucination,":[19],"(2)":[20],"context":[21],"compression,":[22],"(3)":[23],"reasoning":[24],"degradation,":[25],"(4)":[26],"retrieval":[27,176],"fragility,":[28],"and":[29,55,79,102,118,134,144,161,184,187,200,211,220,229],"(5)":[30],"multimodal":[31,189],"misalignment.":[32],"While":[33],"existing":[34],"surveys":[35],"describe":[36],"phenomena":[38],"empirically,":[39],"they":[40],"lack":[41],"a":[42,64],"rigorous":[43],"theoretical":[44,72,218],"synthesis":[45],"connecting":[46],"them":[47],"to":[48,156,203],"the":[49,70],"foundational":[50],"limits":[51,179],"of":[52,74,85],"computation,":[53],"information,":[54],"learning.":[56],"This":[57],"work":[58],"closes":[59],"that":[60,68],"gap":[61],"presenting":[63],"unified,":[65],"proof-informed":[66],"framework":[67],"formalizes":[69],"innate":[71],"ceilings":[73],"LLM":[75],"scaling.":[76],"First,":[77],"computability":[78],"uncomputability":[80],"imply":[81],"an":[82],"irreducible":[83],"residue":[84],"error:":[86],"for":[87,112],"any":[88],"computably":[89],"enumerable":[90],"model":[91,99],"family,":[92],"diagonalization":[93],"guarantees":[94],"inputs":[95],"on":[96,125],"which":[97],"some":[98],"must":[100],"fail,":[101],"undecidable":[103],"queries":[104],"(e.g.,":[105],"halting-style":[106],"tasks)":[107],"induce":[108],"infinite":[109],"failure":[110],"sets":[111],"all":[113],"computable":[114],"predictors.":[115],"Second,":[116],"information-theoretic":[117],"statistical":[119],"constraints":[120],"bound":[121],"attainable":[122],"accuracy":[123],"even":[124],"decidable":[126],"tasks,":[127],"finite":[128],"description":[129],"length":[130],"enforces":[131],"compression":[132],"error,":[133],"long-tail":[135],"factual":[136],"knowledge":[137],"requires":[138],"prohibitive":[139],"sample":[140],"complexity.":[141],"Third,":[142],"geometric":[143],"computational":[145],"effects":[146],"compress":[147],"long":[148],"contexts":[149],"far":[150],"below":[151],"their":[152],"nominal":[153],"size":[154],"due":[155],"positional":[157,227],"under-training,":[158],"encoding":[159],"attenuation,":[160],"softmax":[162],"crowding.":[163],"We":[164],"further":[165],"show":[166],"how":[167,175,188],"likelihood-based":[168],"training":[169],"favors":[170],"pattern":[171],"completion":[172],"over":[173],"inference,":[174],"under":[177],"token":[178],"suffers":[180],"semantic":[182],"drift":[183],"coupling":[185],"noise,":[186],"scaling":[190,206],"inherits":[191],"shallow":[192],"cross-modal":[193],"alignment.":[194],"Across":[195],"sections,":[196],"we":[197],"pair":[198],"theorems":[199],"empirical":[201],"evidence":[202],"outline":[204],"where":[205,208,212],"helps,":[207],"it":[209,213],"saturates,":[210],"cannot":[214],"progress,":[215],"providing":[216],"both":[217],"foundations":[219],"practical":[221],"mitigation":[222],"paths":[223],"like":[224],"bounded-oracle":[225],"retrieval,":[226],"curricula,":[228],"sparse":[230],"or":[231],"hierarchical":[232],"attention.":[233]},"counts_by_year":[{"year":2026,"cited_by_count":30}],"updated_date":"2026-11-09T13:22:03.289127","created_date":"2025-11-19T00:00:00"}