{"id":"https://openalex.org/W4388870647","doi":"https://doi.org/10.1162/neco_a_01723","title":"Computing With Residue Numbers in High-Dimensional Representation","display_name":"Computing With Residue Numbers in High-Dimensional Representation","publication_year":2024,"publication_date":"2024-11-18","ids":{"openalex":"https://openalex.org/W4388870647","doi":"https://doi.org/10.1162/neco_a_01723","pmid":"https://pubmed.ncbi.nlm.nih.gov/37986727"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_01723","is_oa":true,"landing_page_url":"https://doi.org/10.1162/neco_a_01723","pdf_url":"https://direct.mit.edu/neco/article-pdf/37/1/1/2483438/neco_a_01723.pdf","source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"bronze","oa_url":"https://direct.mit.edu/neco/article-pdf/37/1/1/2483438/neco_a_01723.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5046062578","display_name":"Christopher J. Kymn","orcid":null},"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":"Christopher J. Kymn","raw_affiliation_strings":["Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A. cjkymn@berkeley.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A. cjkymn@berkeley.edu","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5065925392","display_name":"Denis Kleyko","orcid":"https://orcid.org/0000-0002-6032-6155"},"institutions":[{"id":"https://openalex.org/I26437253","display_name":"\u00d6rebro University","ror":"https://ror.org/05kytsw45","country_code":"SE","type":"education","lineage":["https://openalex.org/I26437253"]},{"id":"https://openalex.org/I2800664555","display_name":"RISE Research Institutes of Sweden","ror":"https://ror.org/03nnxqz81","country_code":"SE","type":"other","lineage":["https://openalex.org/I2800664555"]}],"countries":["SE"],"is_corresponding":false,"raw_author_name":"Denis Kleyko","raw_affiliation_strings":["Centre for Applied Autonomous Sensor Systems, Orebro University, Orebro SE-701 82, Sweden","Intelligent Systems Lab, Research Institutes of Sweden, 164 40 Kista, Sweden denis.kleyko@oru.se"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Centre for Applied Autonomous Sensor Systems, Orebro University, Orebro SE-701 82, Sweden","institution_ids":["https://openalex.org/I26437253"]},{"raw_affiliation_string":"Intelligent Systems Lab, Research Institutes of Sweden, 164 40 Kista, Sweden denis.kleyko@oru.se","institution_ids":["https://openalex.org/I2800664555"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5013958028","display_name":"E. Paxon Frady","orcid":"https://orcid.org/0000-0001-8248-4544"},"institutions":[{"id":"https://openalex.org/I1343180700","display_name":"Intel (United States)","ror":"https://ror.org/01ek73717","country_code":"US","type":"company","lineage":["https://openalex.org/I1343180700"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"E. Paxon Frady","raw_affiliation_strings":["Neuromorphic Computing Lab, Intel, Santa Clara, CA 95054, U.S.A. e.paxon.frady@intel.com"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Neuromorphic Computing Lab, Intel, Santa Clara, CA 95054, U.S.A. e.paxon.frady@intel.com","institution_ids":["https://openalex.org/I1343180700"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5001274542","display_name":"Connor Bybee","orcid":"https://orcid.org/0000-0001-6685-1228"},"institutions":[{"id":"https://openalex.org/I4210145836","display_name":"Center for Theoretical Biological Physics","ror":"https://ror.org/04hfg7v94","country_code":"US","type":"facility","lineage":["https://openalex.org/I12912129","https://openalex.org/I181547552","https://openalex.org/I2801539370","https://openalex.org/I4210145836","https://openalex.org/I44461941","https://openalex.org/I74775410"]},{"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":"Connor Bybee","raw_affiliation_strings":["Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A. bybee@berkeley.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A. bybee@berkeley.edu","institution_ids":["https://openalex.org/I4210145836","https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025002766","display_name":"Pentti Kanerva","orcid":"https://orcid.org/0000-0003-4879-6143"},"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":"Pentti Kanerva","raw_affiliation_strings":["Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A. pkanerva@csli.stanford.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A. pkanerva@csli.stanford.edu","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5085896415","display_name":"Friedrich T. Sommer","orcid":"https://orcid.org/0000-0002-6738-9263"},"institutions":[{"id":"https://openalex.org/I1343180700","display_name":"Intel (United States)","ror":"https://ror.org/01ek73717","country_code":"US","type":"company","lineage":["https://openalex.org/I1343180700"]},{"id":"https://openalex.org/I4210145836","display_name":"Center for Theoretical Biological Physics","ror":"https://ror.org/04hfg7v94","country_code":"US","type":"facility","lineage":["https://openalex.org/I12912129","https://openalex.org/I181547552","https://openalex.org/I2801539370","https://openalex.org/I4210145836","https://openalex.org/I44461941","https://openalex.org/I74775410"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Friedrich T. Sommer","raw_affiliation_strings":["Neuromorphic Computing Lab, Intel, Santa Clara, CA 95054, U.S.A. fsommer@berkeley.edu","Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A","Neuromorphic Computing Lab, Intel, Santa Clara, CA 95054, U.S.A. sommer@berkeley.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Neuromorphic Computing Lab, Intel, Santa Clara, CA 95054, U.S.A. fsommer@berkeley.edu","institution_ids":["https://openalex.org/I1343180700"]},{"raw_affiliation_string":"Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A","institution_ids":["https://openalex.org/I4210145836"]},{"raw_affiliation_string":"Neuromorphic Computing Lab, Intel, Santa Clara, CA 95054, U.S.A. sommer@berkeley.edu","institution_ids":["https://openalex.org/I1343180700"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5032674291","display_name":"Bruno A. Olshausen","orcid":null},"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":"Bruno A. Olshausen","raw_affiliation_strings":["Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A. baolshausen@berkeley.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Redwood Center for Theoretical Neuroscience, University of California, Berkeley, CA 94720, U.S.A. baolshausen@berkeley.edu","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":7,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.8249,"has_fulltext":true,"cited_by_count":10,"citation_normalized_percentile":{"value":0.84547551,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":94,"max":99},"biblio":{"volume":"37","issue":"1","first_page":"1","last_page":"37"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.9979000091552734,"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"}},"topics":[{"id":"https://openalex.org/T12808","display_name":"Ferroelectric and Negative Capacitance Devices","score":0.9979000091552734,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":0.9897000193595886,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9689000248908997,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/parallelizable-manifold","display_name":"Parallelizable manifold","score":0.675706684589386},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5559939742088318},{"id":"https://openalex.org/keywords/residue-number-system","display_name":"Residue number system","score":0.5253214836120605},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.5187445282936096},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.4519120156764984},{"id":"https://openalex.org/keywords/algebraic-operation","display_name":"Algebraic operation","score":0.44079694151878357},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.41843628883361816},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.3798266649246216},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.30146488547325134}],"concepts":[{"id":"https://openalex.org/C148047603","wikidata":"https://www.wikidata.org/wiki/Q1014612","display_name":"Parallelizable manifold","level":2,"score":0.675706684589386},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5559939742088318},{"id":"https://openalex.org/C71480937","wikidata":"https://www.wikidata.org/wiki/Q3086516","display_name":"Residue number system","level":2,"score":0.5253214836120605},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.5187445282936096},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.4519120156764984},{"id":"https://openalex.org/C136003732","wikidata":"https://www.wikidata.org/wiki/Q3854337","display_name":"Algebraic operation","level":3,"score":0.44079694151878357},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.41843628883361816},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.3798266649246216},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.30146488547325134},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1162/neco_a_01723","is_oa":true,"landing_page_url":"https://doi.org/10.1162/neco_a_01723","pdf_url":"https://direct.mit.edu/neco/article-pdf/37/1/1/2483438/neco_a_01723.pdf","source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:37986727","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/37986727","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":"ArXiv","raw_type":null},{"id":"pmid:39556514","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/39556514","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":"Neural computation","raw_type":null},{"id":"pmh:oai:escholarship.org:ark:/13030/qt0k08p180","is_oa":true,"landing_page_url":"https://escholarship.org/uc/item/0k08p180","pdf_url":"https://escholarship.org/content/qt0k08p180/qt0k08p180.pdf","source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Neural Computation, vol 37, iss 1","raw_type":"article"},{"id":"pmh:oai:pubmedcentral.nih.gov:10659444","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/10659444","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC10659444/pdf/nihpp-2311.04872v1.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"ArXiv","raw_type":"Text"},{"id":"pmh:oai:pubmedcentral.nih.gov:11647909","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/11647909","pdf_url":"https://pmc.ncbi.nlm.nih.gov/articles/PMC11647909/pdf/neco-37-1-01723.pdf","source":{"id":"https://openalex.org/S2764455111","display_name":"PubMed Central","issn_l":null,"issn":null,"is_oa":true,"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":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Neural Comput","raw_type":"Text"}],"best_oa_location":{"id":"doi:10.1162/neco_a_01723","is_oa":true,"landing_page_url":"https://doi.org/10.1162/neco_a_01723","pdf_url":"https://direct.mit.edu/neco/article-pdf/37/1/1/2483438/neco_a_01723.pdf","source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1452086972","display_name":null,"funder_award_id":"JUMP 2.0","funder_id":"https://openalex.org/F4320306087","funder_display_name":"Semiconductor Research Corporation"},{"id":"https://openalex.org/G5278088920","display_name":"A Low-Power Artificial Intelligence Framework based on Vector Symbolic Architectures","funder_award_id":"839179","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G6279555096","display_name":null,"funder_award_id":"R01-EB026955","funder_id":"https://openalex.org/F4320332161","funder_display_name":"National Institutes of Health"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320306078","display_name":"U.S. Department of Defense","ror":"https://ror.org/0447fe631"},{"id":"https://openalex.org/F4320306087","display_name":"Semiconductor Research Corporation","ror":"https://ror.org/047z4n946"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320332161","display_name":"National Institutes of Health","ror":"https://ror.org/01cwqze88"},{"id":"https://openalex.org/F4320332180","display_name":"Defense Advanced Research Projects Agency","ror":"https://ror.org/02caytj08"},{"id":"https://openalex.org/F4320333566","display_name":"National Defense Science and Engineering Graduate","ror":null},{"id":"https://openalex.org/F4320337363","display_name":"National Institute of Biomedical Imaging and Bioengineering","ror":"https://ror.org/00372qc85"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4388870647.pdf","grobid_xml":"https://content.openalex.org/works/W4388870647.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W1129461654","https://openalex.org/W1503602982","https://openalex.org/W1965963207","https://openalex.org/W1970792572","https://openalex.org/W2001915754","https://openalex.org/W2016903065","https://openalex.org/W2030477952","https://openalex.org/W2030805642","https://openalex.org/W2052091366","https://openalex.org/W2052176331","https://openalex.org/W2070862086","https://openalex.org/W2077554996","https://openalex.org/W2078023722","https://openalex.org/W2089097360","https://openalex.org/W2121176637","https://openalex.org/W2128712494","https://openalex.org/W2145889472","https://openalex.org/W2155309852","https://openalex.org/W2157306293","https://openalex.org/W2160654481","https://openalex.org/W2186649876","https://openalex.org/W2401610261","https://openalex.org/W2796260258","https://openalex.org/W2805904203","https://openalex.org/W2895910969","https://openalex.org/W2921525502","https://openalex.org/W2963650979","https://openalex.org/W2969945374","https://openalex.org/W2973650171","https://openalex.org/W3048915709","https://openalex.org/W3093755763","https://openalex.org/W3094277857","https://openalex.org/W3184456550","https://openalex.org/W3214202924","https://openalex.org/W4205399426","https://openalex.org/W4225381310","https://openalex.org/W4225389525","https://openalex.org/W4225400039","https://openalex.org/W4229484196","https://openalex.org/W4235583970","https://openalex.org/W4293216350","https://openalex.org/W4308481194","https://openalex.org/W4311674792","https://openalex.org/W4362459302","https://openalex.org/W4376604041","https://openalex.org/W6629390021","https://openalex.org/W6636444753","https://openalex.org/W6673130433","https://openalex.org/W6677940039","https://openalex.org/W6681302627","https://openalex.org/W6683294121","https://openalex.org/W6739901393","https://openalex.org/W6743441366","https://openalex.org/W6747920752","https://openalex.org/W6753567080","https://openalex.org/W6779753539","https://openalex.org/W6780179280","https://openalex.org/W6782191332","https://openalex.org/W6792264366","https://openalex.org/W6797705112","https://openalex.org/W6810623501","https://openalex.org/W6867098464","https://openalex.org/W7039442881"],"related_works":["https://openalex.org/W196064004","https://openalex.org/W2372854171","https://openalex.org/W3143745619","https://openalex.org/W1484338948","https://openalex.org/W4211175933","https://openalex.org/W1815267262","https://openalex.org/W2049562662","https://openalex.org/W2392216692","https://openalex.org/W2162655755","https://openalex.org/W2185957598"],"abstract_inverted_index":{",":[0],"a":[1,29,67,113],"computing":[2],"framework":[3,91,111],"that":[4,31],"unifies":[5],"residue":[6,20],"number":[7],"systems":[8],"with":[9,38,51],"an":[10,52],"algebra":[11],"defined":[12],"over":[13,66,105],"random,":[14],"high-dimensional":[15,26,57],"vectors.":[16],"We":[17,85],"show":[18],"how":[19],"numbers":[21],"can":[22,59],"be":[23,36],"represented":[24],"as":[25],"vectors":[27],"in":[28,97,123],"manner":[30],"allows":[32],"algebraic":[33],"operations":[34,41,119],"to":[35,83,92],"performed":[37],"component-wise,":[39],"parallelizable":[40],"on":[42,63],"the":[43,87,110,117,124],"vector":[44],"elements.":[45],"The":[46],"resulting":[47],"framework,":[48],"when":[49],"combined":[50],"efficient":[53],"method":[54],"for":[55,89,116,133],"factorizing":[56],"vectors,":[58],"represent":[60],"and":[61,78,100,126,135],"operate":[62],"numerical":[64,137],"values":[65],"large":[68],"dynamic":[69],"range":[70],"using":[71],"vastly":[72],"fewer":[73],"resources":[74],"than":[75],"previous":[76],"methods,":[77],"it":[79,127],"exhibits":[80],"impressive":[81],"robustness":[82],"noise.":[84],"demonstrate":[86],"potential":[88],"this":[90],"solve":[93],"computationally":[94],"difficult":[95],"problems":[96],"visual":[98],"perception":[99],"combinatorial":[101],"optimization,":[102],"showing":[103],"improvement":[104],"baseline":[106],"methods.":[107],"More":[108],"broadly,":[109],"provides":[112],"possible":[114],"account":[115],"computational":[118],"of":[120],"grid":[121],"cells":[122],"brain,":[125],"suggests":[128],"new":[129],"machine":[130],"learning":[131],"architectures":[132],"representing":[134],"manipulating":[136],"data.":[138]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":2}],"updated_date":"2026-06-23T13:55:30.953635","created_date":"2023-11-22T00:00:00"}