{"id":"https://openalex.org/W4328007221","doi":"https://doi.org/10.1109/tpami.2022.3231971","title":"Linear Complexity Self-Attention with $3^{\\text{rd}}$ Order Polynomials","display_name":"Linear Complexity Self-Attention with $3^{\\text{rd}}$ Order Polynomials","publication_year":2023,"publication_date":"2023-01-01","ids":{"openalex":"https://openalex.org/W4328007221","doi":"https://doi.org/10.1109/tpami.2022.3231971","pmid":"https://pubmed.ncbi.nlm.nih.gov/37030770"},"language":"en","primary_location":{"id":"doi:10.1109/tpami.2022.3231971","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3231971","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"http://infoscience.epfl.ch/record/308003","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5036945599","display_name":"Francesca Babiloni","orcid":"https://orcid.org/0000-0002-8447-6991"},"institutions":[{"id":"https://openalex.org/I4210160618","display_name":"Huawei Technologies (United Kingdom)","ror":"https://ror.org/056gzgs71","country_code":"GB","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210160618"]},{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":true,"raw_author_name":"Francesca Babiloni","raw_affiliation_strings":["Huawei Technologies Ltd, Noah's Ark Lab, UK","Imperial College London, UK"],"affiliations":[{"raw_affiliation_string":"Huawei Technologies Ltd, Noah's Ark Lab, UK","institution_ids":["https://openalex.org/I4210160618"]},{"raw_affiliation_string":"Imperial College London, UK","institution_ids":["https://openalex.org/I47508984"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085009855","display_name":"Ioannis Marras","orcid":null},"institutions":[{"id":"https://openalex.org/I4210160618","display_name":"Huawei Technologies (United Kingdom)","ror":"https://ror.org/056gzgs71","country_code":"GB","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210160618"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Ioannis Marras","raw_affiliation_strings":["Huawei Technologies Ltd, Noah's Ark Lab, UK"],"affiliations":[{"raw_affiliation_string":"Huawei Technologies Ltd, Noah's Ark Lab, UK","institution_ids":["https://openalex.org/I4210160618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5073110676","display_name":"Jiankang Deng","orcid":"https://orcid.org/0000-0002-3709-6216"},"institutions":[{"id":"https://openalex.org/I4210160618","display_name":"Huawei Technologies (United Kingdom)","ror":"https://ror.org/056gzgs71","country_code":"GB","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210160618"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Jiankang Deng","raw_affiliation_strings":["Huawei Technologies Ltd, Noah's Ark Lab, UK"],"affiliations":[{"raw_affiliation_string":"Huawei Technologies Ltd, Noah's Ark Lab, UK","institution_ids":["https://openalex.org/I4210160618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5068456312","display_name":"Filippos Kokkinos","orcid":"https://orcid.org/0000-0002-4449-6154"},"institutions":[{"id":"https://openalex.org/I4210160618","display_name":"Huawei Technologies (United Kingdom)","ror":"https://ror.org/056gzgs71","country_code":"GB","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210160618"]},{"id":"https://openalex.org/I45129253","display_name":"University College London","ror":"https://ror.org/02jx3x895","country_code":"GB","type":"education","lineage":["https://openalex.org/I124357947","https://openalex.org/I45129253"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Filippos Kokkinos","raw_affiliation_strings":["Huawei Technologies Ltd, Noah's Ark Lab, UK","University College London (UCL), UK"],"affiliations":[{"raw_affiliation_string":"Huawei Technologies Ltd, Noah's Ark Lab, UK","institution_ids":["https://openalex.org/I4210160618"]},{"raw_affiliation_string":"University College London (UCL), UK","institution_ids":["https://openalex.org/I45129253"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5043251921","display_name":"Matteo Maggioni","orcid":"https://orcid.org/0000-0001-8942-320X"},"institutions":[{"id":"https://openalex.org/I4210160618","display_name":"Huawei Technologies (United Kingdom)","ror":"https://ror.org/056gzgs71","country_code":"GB","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210160618"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Matteo Maggioni","raw_affiliation_strings":["Huawei Technologies Ltd, Noah's Ark Lab, UK"],"affiliations":[{"raw_affiliation_string":"Huawei Technologies Ltd, Noah's Ark Lab, UK","institution_ids":["https://openalex.org/I4210160618"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5004562735","display_name":"Grigorios G. Chrysos","orcid":"https://orcid.org/0000-0002-0650-1856"},"institutions":[{"id":"https://openalex.org/I5124864","display_name":"\u00c9cole Polytechnique F\u00e9d\u00e9rale de Lausanne","ror":"https://ror.org/02s376052","country_code":"CH","type":"education","lineage":["https://openalex.org/I2799323385","https://openalex.org/I5124864"]}],"countries":["CH"],"is_corresponding":false,"raw_author_name":"Grigorios Chrysos","raw_affiliation_strings":["Department of Electrical Engineering, Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland"],"affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering, Ecole Polytechnique Federale de Lausanne (EPFL), Switzerland","institution_ids":["https://openalex.org/I5124864"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5109615038","display_name":"Philip Torr","orcid":null},"institutions":[{"id":"https://openalex.org/I40120149","display_name":"University of Oxford","ror":"https://ror.org/052gg0110","country_code":"GB","type":"education","lineage":["https://openalex.org/I40120149"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Philip Torr","raw_affiliation_strings":["Department of Engineering Science, University of Oxford, UK"],"affiliations":[{"raw_affiliation_string":"Department of Engineering Science, University of Oxford, UK","institution_ids":["https://openalex.org/I40120149"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5080553022","display_name":"Stefanos Zafeiriou","orcid":"https://orcid.org/0000-0002-5222-1740"},"institutions":[{"id":"https://openalex.org/I4210160618","display_name":"Huawei Technologies (United Kingdom)","ror":"https://ror.org/056gzgs71","country_code":"GB","type":"company","lineage":["https://openalex.org/I2250955327","https://openalex.org/I4210160618"]},{"id":"https://openalex.org/I47508984","display_name":"Imperial College London","ror":"https://ror.org/041kmwe10","country_code":"GB","type":"education","lineage":["https://openalex.org/I47508984"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Stefanos Zafeiriou","raw_affiliation_strings":["Huawei Technologies Ltd, Noah's Ark Lab, UK","Imperial College London, UK"],"affiliations":[{"raw_affiliation_string":"Huawei Technologies Ltd, Noah's Ark Lab, UK","institution_ids":["https://openalex.org/I4210160618"]},{"raw_affiliation_string":"Imperial College London, UK","institution_ids":["https://openalex.org/I47508984"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":8,"corresponding_author_ids":["https://openalex.org/A5036945599"],"corresponding_institution_ids":["https://openalex.org/I4210160618","https://openalex.org/I47508984"],"apc_list":null,"apc_paid":null,"fwci":3.2497,"has_fulltext":false,"cited_by_count":8,"citation_normalized_percentile":{"value":0.91123963,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"45","issue":"11","first_page":"1","last_page":"12"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10963","display_name":"Advanced Optimization Algorithms Research","score":0.9915000200271606,"subfield":{"id":"https://openalex.org/subfields/2612","display_name":"Numerical Analysis"},"field":{"id":"https://openalex.org/fields/26","display_name":"Mathematics"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10682","display_name":"Quantum Computing Algorithms and Architecture","score":0.991100013256073,"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/T10320","display_name":"Neural Networks and Applications","score":0.9575999975204468,"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/computer-science","display_name":"Computer science","score":0.5215170979499817},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4884883165359497},{"id":"https://openalex.org/keywords/order","display_name":"Order (exchange)","score":0.4811445474624634},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.36452460289001465},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.360421359539032},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3476381301879883},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.33421841263771057},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.32003527879714966}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5215170979499817},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4884883165359497},{"id":"https://openalex.org/C182306322","wikidata":"https://www.wikidata.org/wiki/Q1779371","display_name":"Order (exchange)","level":2,"score":0.4811445474624634},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.36452460289001465},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.360421359539032},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3476381301879883},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.33421841263771057},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.32003527879714966},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C10138342","wikidata":"https://www.wikidata.org/wiki/Q43015","display_name":"Finance","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tpami.2022.3231971","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tpami.2022.3231971","pdf_url":null,"source":{"id":"https://openalex.org/S199944782","display_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","issn_l":"0162-8828","issn":["0162-8828","1939-3539","2160-9292"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310320439","host_organization_name":"IEEE Computer Society","host_organization_lineage":["https://openalex.org/P4310320439","https://openalex.org/P4310319808"],"host_organization_lineage_names":["IEEE Computer Society","Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Pattern Analysis and Machine Intelligence","raw_type":"journal-article"},{"id":"pmid:37030770","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37030770","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on pattern analysis and machine intelligence","raw_type":null},{"id":"pmh:oai:infoscience.epfl.ch:308003","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/308003","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"}],"best_oa_location":{"id":"pmh:oai:infoscience.epfl.ch:308003","is_oa":true,"landing_page_url":"http://infoscience.epfl.ch/record/308003","pdf_url":null,"source":{"id":"https://openalex.org/S4306400487","display_name":"Infoscience (Ecole Polytechnique F\u00e9d\u00e9rale de Lausanne)","issn_l":null,"issn":null,"is_oa":true,"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-nc-nd","license_id":"https://openalex.org/licenses/cc-by-nc-nd","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"WoS","raw_type":"research article"},"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.7900000214576721,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":110,"referenced_works":["https://openalex.org/W78159342","https://openalex.org/W1641020902","https://openalex.org/W1861492603","https://openalex.org/W2024165284","https://openalex.org/W2056370875","https://openalex.org/W2064675550","https://openalex.org/W2097073572","https://openalex.org/W2104657103","https://openalex.org/W2117539524","https://openalex.org/W2120190345","https://openalex.org/W2136163184","https://openalex.org/W2147880316","https://openalex.org/W2170653751","https://openalex.org/W2194775991","https://openalex.org/W2622263826","https://openalex.org/W2752782242","https://openalex.org/W2883502031","https://openalex.org/W2884585870","https://openalex.org/W2889814224","https://openalex.org/W2896457183","https://openalex.org/W2941814890","https://openalex.org/W2947128531","https://openalex.org/W2949846184","https://openalex.org/W2954930822","https://openalex.org/W2955058313","https://openalex.org/W2963091558","https://openalex.org/W2963150697","https://openalex.org/W2963319519","https://openalex.org/W2963495494","https://openalex.org/W2963566548","https://openalex.org/W2963807318","https://openalex.org/W2964019776","https://openalex.org/W2965669158","https://openalex.org/W2981413347","https://openalex.org/W2982220924","https://openalex.org/W2983902802","https://openalex.org/W2991526275","https://openalex.org/W2994821360","https://openalex.org/W3015468748","https://openalex.org/W3023064088","https://openalex.org/W3030520226","https://openalex.org/W3033529678","https://openalex.org/W3034217077","https://openalex.org/W3034345703","https://openalex.org/W3034540350","https://openalex.org/W3035865126","https://openalex.org/W3037798801","https://openalex.org/W3085139254","https://openalex.org/W3094502228","https://openalex.org/W3097065222","https://openalex.org/W3123221884","https://openalex.org/W3123615524","https://openalex.org/W3138516171","https://openalex.org/W3159481202","https://openalex.org/W3167260844","https://openalex.org/W3170874841","https://openalex.org/W3171206729","https://openalex.org/W3177183540","https://openalex.org/W3203784466","https://openalex.org/W3205162917","https://openalex.org/W4214493665","https://openalex.org/W4214634256","https://openalex.org/W4225525539","https://openalex.org/W4286769561","https://openalex.org/W4295838474","https://openalex.org/W4296414724","https://openalex.org/W4298395628","https://openalex.org/W4309793872","https://openalex.org/W4310574272","https://openalex.org/W4312610518","https://openalex.org/W4312820606","https://openalex.org/W4320458252","https://openalex.org/W4323647442","https://openalex.org/W4323654151","https://openalex.org/W4385245566","https://openalex.org/W6639102338","https://openalex.org/W6682082992","https://openalex.org/W6727057065","https://openalex.org/W6729983426","https://openalex.org/W6739622702","https://openalex.org/W6739901393","https://openalex.org/W6754416387","https://openalex.org/W6755207826","https://openalex.org/W6761563299","https://openalex.org/W6761628794","https://openalex.org/W6763197473","https://openalex.org/W6763367864","https://openalex.org/W6771465236","https://openalex.org/W6771571646","https://openalex.org/W6771626834","https://openalex.org/W6776048684","https://openalex.org/W6777028348","https://openalex.org/W6778485988","https://openalex.org/W6779163297","https://openalex.org/W6779577340","https://openalex.org/W6779709467","https://openalex.org/W6783944145","https://openalex.org/W6784333009","https://openalex.org/W6788135285","https://openalex.org/W6789317445","https://openalex.org/W6789463137","https://openalex.org/W6798107787","https://openalex.org/W6802078936","https://openalex.org/W6802868300","https://openalex.org/W6803916128","https://openalex.org/W6810370753","https://openalex.org/W6811190969","https://openalex.org/W6843075173","https://openalex.org/W6849281104","https://openalex.org/W6864424756"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W2073681303","https://openalex.org/W2544423928","https://openalex.org/W2053286651","https://openalex.org/W2181743346","https://openalex.org/W2187401768","https://openalex.org/W2980963558","https://openalex.org/W2181413294","https://openalex.org/W2052122378","https://openalex.org/W4313731559"],"abstract_inverted_index":{"Self-attention":[0],"mechanisms":[1],"and":[2,58,96,115,127,133],"non-local":[3,95,126],"blocks":[4,9,98],"have":[5],"become":[6],"crucial":[7],"building":[8],"for":[10,124],"state-of-the-art":[11,131],"neural":[12],"architectures":[13],"thanks":[14],"to":[15,83,105,158],"their":[16,27,39],"unparalleled":[17],"ability":[18],"in":[19,23,42,130],"capturing":[20],"long-range":[21],"dependencies":[22],"the":[24,32,90,101],"input.":[25],"However":[26],"cost":[28],"is":[29],"quadratic":[30,104],"with":[31],"number":[33],"of":[34,70,88,94,149],"spatial":[35],"positions":[36],"hence":[37],"making":[38],"use":[40],"impractical":[41],"many":[43],"real":[44],"case":[45,69],"applications.":[46],"In":[47],"this":[48,77],"work,":[49],"we":[50,59,80,110],"analyze":[51],"these":[52],"methods":[53],"through":[54],"a":[55,67,71,108,146,155,159],"polynomial":[56,78,85],"lens,":[57],"show":[60],"that":[61,117],"self-attention":[62,97,128],"can":[63,118,138],"be":[64,119],"seen":[65],"as":[66,121],"special":[68],"3":[72],"rd":[73],"order":[74],"polynomial.":[75],"Within":[76],"framework,":[79],"are":[81],"able":[82],"design":[84],"operators":[86],"capable":[87],"accessing":[89],"same":[91],"data":[92],"pattern":[93],"while":[99,153],"reducing":[100],"complexity":[102,156],"from":[103],"linear.":[106],"As":[107],"result,":[109],"propose":[111],"two":[112],"modules":[113,137],"(Poly-NL":[114],"Poly-SA)":[116],"used":[120],"\"drop-in\"":[122],"replacements":[123],"more-complex":[125],"layers":[129],"CNNs":[132],"ViT":[134],"architectures.":[135],"Our":[136],"achieve":[139],"comparable,":[140],"if":[141],"not":[142],"better,":[143],"performance":[144],"across":[145],"wide":[147],"range":[148],"computer":[150],"vision":[151],"tasks":[152],"keeping":[154],"equivalent":[157],"standard":[160],"linear":[161],"layer.":[162]},"counts_by_year":[{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2023-03-22T00:00:00"}