{"id":"https://openalex.org/W7128074936","doi":"https://doi.org/10.48550/arxiv.2602.05062","title":"Scaling Laws for Embedding Dimension in Information Retrieval","display_name":"Scaling Laws for Embedding Dimension in Information Retrieval","publication_year":2026,"publication_date":"2026-02-04","ids":{"openalex":"https://openalex.org/W7128074936","doi":"https://doi.org/10.48550/arxiv.2602.05062"},"language":null,"primary_location":{"id":"pmh:doi:10.48550/arxiv.2602.05062","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","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":null,"any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5066490162","display_name":"Julian Killingback","orcid":"https://orcid.org/0000-0003-2280-8759"},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Killingback, Julian","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125146698","display_name":"Mahta Rafiee","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Rafiee, Mahta","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"middle","author":{"id":"https://openalex.org/A5125219225","display_name":"Madine Manas","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Manas, Madine","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5125200565","display_name":"Hamed Zamani","orcid":null},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Zamani, Hamed","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/T10286","display_name":"Information Retrieval and Search Behavior","score":0.8062000274658203,"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/T10286","display_name":"Information Retrieval and Search Behavior","score":0.8062000274658203,"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/T10320","display_name":"Neural Networks and Applications","score":0.02449999935925007,"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/T10824","display_name":"Image Retrieval and Classification Techniques","score":0.017000000923871994,"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/embedding","display_name":"Embedding","score":0.8539000153541565},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.5490999817848206},{"id":"https://openalex.org/keywords/metric","display_name":"Metric (unit)","score":0.48750001192092896},{"id":"https://openalex.org/keywords/scaling","display_name":"Scaling","score":0.47870001196861267},{"id":"https://openalex.org/keywords/multidimensional-scaling","display_name":"Multidimensional scaling","score":0.3840999901294708},{"id":"https://openalex.org/keywords/range","display_name":"Range (aeronautics)","score":0.3564000129699707},{"id":"https://openalex.org/keywords/similarity","display_name":"Similarity (geometry)","score":0.34610000252723694},{"id":"https://openalex.org/keywords/similitude","display_name":"Similitude","score":0.33899998664855957}],"concepts":[{"id":"https://openalex.org/C41608201","wikidata":"https://www.wikidata.org/wiki/Q980509","display_name":"Embedding","level":2,"score":0.8539000153541565},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5774999856948853},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.5490999817848206},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.535099983215332},{"id":"https://openalex.org/C176217482","wikidata":"https://www.wikidata.org/wiki/Q860554","display_name":"Metric (unit)","level":2,"score":0.48750001192092896},{"id":"https://openalex.org/C99844830","wikidata":"https://www.wikidata.org/wiki/Q102441924","display_name":"Scaling","level":2,"score":0.47870001196861267},{"id":"https://openalex.org/C91682802","wikidata":"https://www.wikidata.org/wiki/Q620538","display_name":"Multidimensional scaling","level":2,"score":0.3840999901294708},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3564999997615814},{"id":"https://openalex.org/C204323151","wikidata":"https://www.wikidata.org/wiki/Q905424","display_name":"Range (aeronautics)","level":2,"score":0.3564000129699707},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3528999984264374},{"id":"https://openalex.org/C103278499","wikidata":"https://www.wikidata.org/wiki/Q254465","display_name":"Similarity (geometry)","level":3,"score":0.34610000252723694},{"id":"https://openalex.org/C143271835","wikidata":"https://www.wikidata.org/wiki/Q254515","display_name":"Similitude","level":2,"score":0.33899998664855957},{"id":"https://openalex.org/C70518039","wikidata":"https://www.wikidata.org/wiki/Q16000077","display_name":"Dimensionality reduction","level":2,"score":0.334199994802475},{"id":"https://openalex.org/C124101348","wikidata":"https://www.wikidata.org/wiki/Q172491","display_name":"Data mining","level":1,"score":0.3131999969482422},{"id":"https://openalex.org/C2780801425","wikidata":"https://www.wikidata.org/wiki/Q5164392","display_name":"Construct (python library)","level":2,"score":0.3037000000476837},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2913999855518341},{"id":"https://openalex.org/C2988430800","wikidata":"https://www.wikidata.org/wiki/Q428971","display_name":"Scaling law","level":3,"score":0.289900004863739},{"id":"https://openalex.org/C30732413","wikidata":"https://www.wikidata.org/wiki/Q17092636","display_name":"Intrinsic dimension","level":3,"score":0.2793000042438507},{"id":"https://openalex.org/C149189445","wikidata":"https://www.wikidata.org/wiki/Q5283894","display_name":"Divergence-from-randomness model","level":3,"score":0.2750000059604645},{"id":"https://openalex.org/C2778755073","wikidata":"https://www.wikidata.org/wiki/Q10858537","display_name":"Scale (ratio)","level":2,"score":0.2705000042915344},{"id":"https://openalex.org/C161156560","wikidata":"https://www.wikidata.org/wiki/Q1638872","display_name":"Document retrieval","level":2,"score":0.2567000091075897},{"id":"https://openalex.org/C46686674","wikidata":"https://www.wikidata.org/wiki/Q466303","display_name":"Boosting (machine learning)","level":2,"score":0.25429999828338623}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:doi:10.48550/arxiv.2602.05062","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},{"id":"doi:10.48550/arxiv.2602.05062","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2602.05062","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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:doi:10.48550/arxiv.2602.05062","is_oa":true,"landing_page_url":null,"pdf_url":null,"source":{"id":"https://openalex.org/S4406922384","display_name":"Open MIND","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Article"},"sustainable_development_goals":[{"score":0.5345513820648193,"display_name":"Peace, Justice and strong institutions","id":"https://metadata.un.org/sdg/16"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":0,"referenced_works":[],"related_works":[],"abstract_inverted_index":{"Dense":[0],"retrieval,":[1],"which":[2],"encodes":[3],"queries":[4],"and":[5,23,48,54,71,112,128,137,186,253,266,276],"documents":[6],"into":[7,248],"a":[8,119,138,147,161,179,260],"single":[9,69],"dense":[10,34,92],"vector,":[11],"has":[12,63],"become":[13,57],"the":[14,32,40,44,78,82,123,157,198,221,249],"dominant":[15],"neural":[16],"retrieval":[17,35,88,93,107,129],"approach":[18],"due":[19],"to":[20,68,77,103,145,166,203,269],"its":[21],"simplicity":[22],"compatibility":[24],"with":[25,197,210,220,231,234,273],"fast":[26],"approximate":[27],"nearest":[28],"neighbor":[29],"algorithms.":[30],"As":[31],"tasks":[33,195],"performs":[36],"grow":[37],"in":[38],"complexity,":[39],"fundamental":[41,102],"limitations":[42,66,250],"of":[43,84,122,140,150,251],"underlying":[45],"data":[46,215],"structure":[47],"similarity":[49],"metric":[50],"--":[51,56],"namely":[52],"vectors":[53,70],"inner-products":[55,72],"more":[58],"apparent.":[59],"Prior":[60],"recent":[61],"work":[62,244],"shown":[64],"theoretical":[65],"inherent":[67],"that":[73,109,156,192,216,226],"are":[74],"generally":[75],"tied":[76],"embedding":[79,85,97,126,151,174,184,206,236,267],"dimension.":[80],"Given":[81],"importance":[83],"dimension":[86,98,127,185,268],"for":[87,170,183,193,238,263],"capacity,":[89],"understanding":[90],"how":[91],"performance":[94,171,201,227,232,272],"changes":[95],"as":[96,176,178,205,256,258],"is":[99,101,217,228],"scaled":[100],"building":[104],"next":[105],"generation":[106],"models":[108],"balance":[110],"effectiveness":[111],"efficiency.":[113],"In":[114],"this":[115],"work,":[116],"we":[117,224],"conduct":[118],"comprehensive":[120],"analysis":[121,190],"relationship":[124],"between":[125],"performance.":[130],"Our":[131,189],"experiments":[132],"include":[133],"two":[134],"model":[135,141,187,265],"families":[136],"range":[139],"sizes":[142],"from":[143],"each":[144],"construct":[146],"detailed":[148],"picture":[149],"scaling":[152,158,168],"behavior.":[153],"We":[154,241],"find":[155,225],"behavior":[159,255],"fits":[160],"power":[162],"law,":[163],"allowing":[164],"us":[165],"derive":[167],"laws":[169],"given":[172],"only":[173],"dimension,":[175],"well":[177,257],"joint":[180],"law":[181],"accounting":[182],"size.":[188],"shows":[191],"evaluation":[194,214],"aligned":[196,219],"training":[199,222],"task,":[200,223],"continues":[202],"improve":[204],"size":[207],"increases,":[208],"though":[209],"diminishing":[211],"returns.":[212],"For":[213],"less":[218,229],"predictable,":[230],"degrading":[233],"larger":[235],"dimensions":[237],"certain":[239],"tasks.":[240],"hope":[242],"our":[243],"provides":[245],"additional":[246],"insight":[247],"embeddings":[252],"their":[254],"offers":[259],"practical":[261],"guide":[262],"selecting":[264],"achieve":[270],"optimal":[271],"reduced":[274],"storage":[275],"compute":[277],"costs.":[278]},"counts_by_year":[],"updated_date":"2026-07-01T06:00:48.157686","created_date":"2026-02-07T00:00:00"}