{"id":"https://openalex.org/W7138293750","doi":"https://doi.org/10.48550/arxiv.2603.13314","title":"Linear Predictability of Attention Heads in Large Language Models","display_name":"Linear Predictability of Attention Heads in Large Language Models","publication_year":2026,"publication_date":"2026-03-04","ids":{"openalex":"https://openalex.org/W7138293750","doi":"https://doi.org/10.48550/arxiv.2603.13314"},"language":null,"primary_location":{"id":"doi:10.48550/arxiv.2603.13314","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13314","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.2603.13314","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5018462126","display_name":"Khalid Shaikh","orcid":null},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Shaikh, Khalid","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5126169316","display_name":"Asmit Kumar Singh","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Singh, Asmit Kumar","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5129644118","display_name":"Rebecca Christopher Dsouza","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Dsouza, Rebecca Christopher","raw_affiliation_strings":[],"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5120679449","display_name":"Shikhar Shiromani","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Shiromani, Shikhar","raw_affiliation_strings":[],"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5018462126"],"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/T14347","display_name":"Big Data and Digital Economy","score":0.18490000069141388,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T14347","display_name":"Big Data and Digital Economy","score":0.18490000069141388,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.07180000096559525,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10036","display_name":"Advanced Neural Network Applications","score":0.06809999793767929,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/approx","display_name":"Approx","score":0.6771000027656555},{"id":"https://openalex.org/keywords/predictability","display_name":"Predictability","score":0.5942999720573425},{"id":"https://openalex.org/keywords/inference","display_name":"Inference","score":0.5651999711990356},{"id":"https://openalex.org/keywords/exploit","display_name":"Exploit","score":0.5512999892234802},{"id":"https://openalex.org/keywords/redundancy","display_name":"Redundancy (engineering)","score":0.53329998254776},{"id":"https://openalex.org/keywords/language-model","display_name":"Language model","score":0.4652000069618225},{"id":"https://openalex.org/keywords/linear-model","display_name":"Linear model","score":0.4410000145435333},{"id":"https://openalex.org/keywords/offset","display_name":"Offset (computer science)","score":0.3862999975681305}],"concepts":[{"id":"https://openalex.org/C2777894999","wikidata":"https://www.wikidata.org/wiki/Q4781758","display_name":"Approx","level":2,"score":0.6771000027656555},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6330000162124634},{"id":"https://openalex.org/C197640229","wikidata":"https://www.wikidata.org/wiki/Q2534066","display_name":"Predictability","level":2,"score":0.5942999720573425},{"id":"https://openalex.org/C2776214188","wikidata":"https://www.wikidata.org/wiki/Q408386","display_name":"Inference","level":2,"score":0.5651999711990356},{"id":"https://openalex.org/C165696696","wikidata":"https://www.wikidata.org/wiki/Q11287","display_name":"Exploit","level":2,"score":0.5512999892234802},{"id":"https://openalex.org/C152124472","wikidata":"https://www.wikidata.org/wiki/Q1204361","display_name":"Redundancy (engineering)","level":2,"score":0.53329998254776},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.47119998931884766},{"id":"https://openalex.org/C137293760","wikidata":"https://www.wikidata.org/wiki/Q3621696","display_name":"Language model","level":2,"score":0.4652000069618225},{"id":"https://openalex.org/C163175372","wikidata":"https://www.wikidata.org/wiki/Q3339222","display_name":"Linear model","level":2,"score":0.4410000145435333},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4032999873161316},{"id":"https://openalex.org/C175291020","wikidata":"https://www.wikidata.org/wiki/Q1156822","display_name":"Offset (computer science)","level":2,"score":0.3862999975681305},{"id":"https://openalex.org/C77553402","wikidata":"https://www.wikidata.org/wiki/Q13222579","display_name":"Upper and lower bounds","level":2,"score":0.37610000371932983},{"id":"https://openalex.org/C2776459999","wikidata":"https://www.wikidata.org/wiki/Q2119376","display_name":"Fidelity","level":2,"score":0.36730000376701355},{"id":"https://openalex.org/C28490314","wikidata":"https://www.wikidata.org/wiki/Q189436","display_name":"Speech recognition","level":1,"score":0.3237999975681305},{"id":"https://openalex.org/C57493831","wikidata":"https://www.wikidata.org/wiki/Q3134666","display_name":"Projection (relational algebra)","level":2,"score":0.28459998965263367},{"id":"https://openalex.org/C28719098","wikidata":"https://www.wikidata.org/wiki/Q44946","display_name":"Point (geometry)","level":2,"score":0.28110000491142273},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2806999981403351},{"id":"https://openalex.org/C2777036070","wikidata":"https://www.wikidata.org/wiki/Q18393452","display_name":"Random projection","level":2,"score":0.27900001406669617},{"id":"https://openalex.org/C178650346","wikidata":"https://www.wikidata.org/wiki/Q201984","display_name":"Covariance","level":2,"score":0.27309998869895935},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.27140000462532043},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.2678000032901764},{"id":"https://openalex.org/C69710193","wikidata":"https://www.wikidata.org/wiki/Q14946576","display_name":"Vernier scale","level":2,"score":0.2667999863624573},{"id":"https://openalex.org/C131109320","wikidata":"https://www.wikidata.org/wiki/Q581012","display_name":"Linear prediction","level":2,"score":0.2614000141620636},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2515999972820282},{"id":"https://openalex.org/C311688","wikidata":"https://www.wikidata.org/wiki/Q2393193","display_name":"Time complexity","level":2,"score":0.25029999017715454}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.48550/arxiv.2603.13314","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13314","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.2603.13314","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2603.13314","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":{"Large":[0],"language":[1],"model":[2],"(LLM)":[3],"inference":[4],"is":[5,107,113,130,215],"increasingly":[6],"bottlenecked":[7],"by":[8,132,166],"the":[9,14,38,66,174,178],"Key-Value":[10],"(KV)":[11],"cache,":[12],"yet":[13],"fine-grained":[15],"structure":[16],"of":[17,45,57,61,155],"attention-head":[18],"activations":[19],"remains":[20],"poorly":[21],"understood.":[22],"We":[23,146],"show":[24],"that":[25,212],"pretrained":[26],"Transformers":[27],"exhibit":[28],"a":[29,35,54,58,133],"pervasive":[30],"inter-head":[31],"linear":[32,55,142,182],"structure:":[33],"for":[34,91,141,164],"given":[36],"token,":[37],"Query,":[39],"Key,":[40],"and":[41,73,98,129,172,199,204,209],"Value":[42],"(QKV)":[43],"vectors":[44],"an":[46],"attention":[47],"head":[48],"can":[49],"often":[50],"be":[51],"reconstructed":[52],"as":[53,123],"combination":[56],"small":[59],"number":[60],"peer":[62],"heads,":[63],"typically":[64],"within":[65],"same":[67],"layer.":[68],"Across":[69],"Llama-3.1-8B,":[70],"Falcon3-10B,":[71],"OLMo-2-7B,":[72],"Qwen3-32B,":[74],"just":[75],"2-5":[76],"reference":[77],"heads":[78,82,176],"recover":[79],"many":[80],"target":[81],"with":[83,95,188],"high":[84,138],"fidelity":[85],"(e.g.,":[86],"mean":[87],"R^2":[88,100],"approx":[89],"0.76":[90],"Keys":[92,214],"on":[93,103,177,197,207],"C4":[94],"five":[96,202],"references,":[97],"frequently":[99],">":[101],"0.85":[102],"GSM8K).":[104],"This":[105],"predictability":[106],"learned":[108],"rather":[109],"than":[110,219],"architectural:":[111],"it":[112],"largely":[114],"absent":[115],"at":[116,144],"random":[117],"initialization,":[118],"rises":[119],"rapidly":[120],"during":[121],"pretraining":[122],"we":[124,160,210],"track":[125],"through":[126],"OLMo-2":[127],"checkpoints,":[128],"supported":[131],"theoretical":[134],"lower":[135],"bound":[136],"showing":[137],"mean-squared":[139],"error":[140],"prediction":[143],"initialization.":[145],"further":[147],"connect":[148],"this":[149,162],"emergence":[150],"to":[151],"increasing":[152],"intra-layer":[153],"alignment":[154],"Key":[156],"projection":[157],"subspaces.":[158],"Finally,":[159],"exploit":[161],"redundancy":[163],"efficiency":[165],"caching":[167],"only":[168],"reference-head":[169],"KV":[170],"states":[171],"reconstructing":[173,213,220],"remaining":[175],"fly":[179],"via":[180],"lightweight":[181],"maps,":[183],"achieving":[184],"2x":[185],"KV-cache":[186],"reduction":[187],"model-dependent":[189],"accuracy":[190],"trade-offs":[191],"(4.5-5.5":[192],"percentage":[193],"point":[194],"average":[195],"drop":[196],"Falcon3-10B":[198],"Qwen3-32B":[200],"across":[201],"benchmarks,":[203],"larger":[205],"drops":[206],"Llama-3.1-8B),":[208],"find":[211],"substantially":[216],"less":[217],"harmful":[218],"Values.":[221]},"counts_by_year":[],"updated_date":"2026-03-18T06:31:55.123368","created_date":"2026-03-18T00:00:00"}