{"id":"https://openalex.org/W1918371587","doi":"https://doi.org/10.1371/journal.pcbi.1004439","title":"A Three-Threshold Learning Rule Approaches the Maximal Capacity of Recurrent Neural Networks","display_name":"A Three-Threshold Learning Rule Approaches the Maximal Capacity of Recurrent Neural Networks","publication_year":2015,"publication_date":"2015-08-20","ids":{"openalex":"https://openalex.org/W1918371587","doi":"https://doi.org/10.1371/journal.pcbi.1004439","mag":"1918371587","pmid":"https://pubmed.ncbi.nlm.nih.gov/26291608"},"language":"en","primary_location":{"id":"doi:10.1371/journal.pcbi.1004439","is_oa":true,"landing_page_url":"https://doi.org/10.1371/journal.pcbi.1004439","pdf_url":"https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1004439&type=printable","source":{"id":"https://openalex.org/S86033158","display_name":"PLoS Computational Biology","issn_l":"1553-734X","issn":["1553-734X","1553-7358"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315706","host_organization_name":"Public Library of Science","host_organization_lineage":["https://openalex.org/P4310315706"],"host_organization_lineage_names":["Public Library of Science"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLOS Computational Biology","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","datacite","doaj","pubmed"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1004439&type=printable","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5087092502","display_name":"Alireza Alemi","orcid":"https://orcid.org/0000-0002-5811-775X"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]},{"id":"https://openalex.org/I4210123319","display_name":"Italian institute for Genomic Medicine","ror":"https://ror.org/036054d36","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210123319"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Alireza Alemi","raw_affiliation_strings":["Human Genetics Foundation (HuGeF), Turin, Italy; DISAT, Politecnico di Torino, Turin, Italy","DISAT, Politecnico di Torino, Turin, Italy","Human Genetics Foundation (HuGeF), Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Human Genetics Foundation (HuGeF), Turin, Italy; DISAT, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856","https://openalex.org/I4210123319"]},{"raw_affiliation_string":"DISAT, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Human Genetics Foundation (HuGeF), Turin, Italy","institution_ids":["https://openalex.org/I4210123319"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5028083013","display_name":"Carlo Baldassi","orcid":"https://orcid.org/0000-0002-5451-8388"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]},{"id":"https://openalex.org/I4210123319","display_name":"Italian institute for Genomic Medicine","ror":"https://ror.org/036054d36","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210123319"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Carlo Baldassi","raw_affiliation_strings":["Human Genetics Foundation (HuGeF), Turin, Italy; DISAT, Politecnico di Torino, Turin, Italy","DISAT, Politecnico di Torino, Turin, Italy","Human Genetics Foundation (HuGeF), Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Human Genetics Foundation (HuGeF), Turin, Italy; DISAT, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856","https://openalex.org/I4210123319"]},{"raw_affiliation_string":"DISAT, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Human Genetics Foundation (HuGeF), Turin, Italy","institution_ids":["https://openalex.org/I4210123319"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5047235486","display_name":"Nicolas Brunel","orcid":"https://orcid.org/0000-0002-2272-3248"},"institutions":[{"id":"https://openalex.org/I40347166","display_name":"University of Chicago","ror":"https://ror.org/024mw5h28","country_code":"US","type":"education","lineage":["https://openalex.org/I40347166"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Nicolas Brunel","raw_affiliation_strings":["Departments of Statistics and Neurobiology, University of Chicago, Chicago, Illinois, United States of America"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Statistics and Neurobiology, University of Chicago, Chicago, Illinois, United States of America","institution_ids":["https://openalex.org/I40347166"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5041685522","display_name":"Riccardo Zecchina","orcid":"https://orcid.org/0000-0002-1221-5207"},"institutions":[{"id":"https://openalex.org/I177477856","display_name":"Politecnico di Torino","ror":"https://ror.org/00bgk9508","country_code":"IT","type":"education","lineage":["https://openalex.org/I177477856"]},{"id":"https://openalex.org/I4210123319","display_name":"Italian institute for Genomic Medicine","ror":"https://ror.org/036054d36","country_code":"IT","type":"nonprofit","lineage":["https://openalex.org/I4210123319"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Riccardo Zecchina","raw_affiliation_strings":["Human Genetics Foundation (HuGeF), Turin, Italy; DISAT, Politecnico di Torino, Turin, Italy","DISAT, Politecnico di Torino, Turin, Italy","Human Genetics Foundation (HuGeF), Turin, Italy"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Human Genetics Foundation (HuGeF), Turin, Italy; DISAT, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856","https://openalex.org/I4210123319"]},{"raw_affiliation_string":"DISAT, Politecnico di Torino, Turin, Italy","institution_ids":["https://openalex.org/I177477856"]},{"raw_affiliation_string":"Human Genetics Foundation (HuGeF), Turin, Italy","institution_ids":["https://openalex.org/I4210123319"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5087092502"],"corresponding_institution_ids":["https://openalex.org/I177477856","https://openalex.org/I4210123319"],"apc_list":{"value":2655,"currency":"USD","value_usd":2655},"apc_paid":{"value":2655,"currency":"USD","value_usd":2655},"fwci":4.0656,"has_fulltext":true,"cited_by_count":24,"citation_normalized_percentile":{"value":0.94304845,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"11","issue":"8","first_page":"e1004439","last_page":"e1004439"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998999834060669,"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/T10320","display_name":"Neural Networks and Applications","score":0.9998999834060669,"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":0.9991999864578247,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9990000128746033,"subfield":{"id":"https://openalex.org/subfields/2805","display_name":"Cognitive Neuroscience"},"field":{"id":"https://openalex.org/fields/28","display_name":"Neuroscience"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5227670669555664},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4463141858577728},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.40769606828689575}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5227670669555664},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4463141858577728},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.40769606828689575}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D003198","descriptor_name":"Computer Simulation","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D008568","descriptor_name":"Memory","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D008568","descriptor_name":"Memory","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D008568","descriptor_name":"Memory","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D008959","descriptor_name":"Models, Neurological","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D009415","descriptor_name":"Nerve Net","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009415","descriptor_name":"Nerve Net","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009415","descriptor_name":"Nerve Net","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D009474","descriptor_name":"Neurons","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D019295","descriptor_name":"Computational Biology","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D019295","descriptor_name":"Computational Biology","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D019295","descriptor_name":"Computational Biology","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":12,"locations":[{"id":"doi:10.1371/journal.pcbi.1004439","is_oa":true,"landing_page_url":"https://doi.org/10.1371/journal.pcbi.1004439","pdf_url":"https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1004439&type=printable","source":{"id":"https://openalex.org/S86033158","display_name":"PLoS Computational Biology","issn_l":"1553-734X","issn":["1553-734X","1553-7358"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315706","host_organization_name":"Public Library of Science","host_organization_lineage":["https://openalex.org/P4310315706"],"host_organization_lineage_names":["Public Library of Science"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLOS Computational Biology","raw_type":"journal-article"},{"id":"pmid:26291608","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/26291608","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":"PLoS computational biology","raw_type":null},{"id":"pmh:oai:arXiv.org:1508.00429","is_oa":true,"landing_page_url":"http://arxiv.org/abs/1508.00429","pdf_url":"https://arxiv.org/pdf/1508.00429","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,"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":"pmh:oai:porto.polito.it:2634737","is_oa":true,"landing_page_url":"http://porto.polito.it/2634737/1/A_Three_Threshold_Learning_Rule_Approaches_the_Maximal_Capacity_of_Recurrent_Neural_Networks.pdf","pdf_url":"http://porto.polito.it/2634737/1/A_Three_Threshold_Learning_Rule_Approaches_the_Maximal_Capacity_of_Recurrent_Neural_Networks.pdf","source":{"id":"https://openalex.org/S4306402038","display_name":"PORTO Publications Open Repository TOrino (Politecnico di Torino)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I177477856","host_organization_name":"Politecnico di Torino","host_organization_lineage":["https://openalex.org/I177477856"],"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":"ISSN:1553-734X","raw_type":"info:eu-repo/semantics/article"},{"id":"pmh:oai:europepmc.org:3521326","is_oa":true,"landing_page_url":"https://www.ncbi.nlm.nih.gov/pmc/articles/4546407","pdf_url":null,"source":{"id":"https://openalex.org/S4306400806","display_name":"Europe PMC (PubMed Central)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1303153112","host_organization_name":"European Bioinformatics Institute","host_organization_lineage":["https://openalex.org/I1303153112"],"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":"Text"},{"id":"pmh:oai:uchicago.tind.io:7698","is_oa":true,"landing_page_url":"http://knowledge.uchicago.edu/record/7698","pdf_url":null,"source":{"id":"https://openalex.org/S4306402460","display_name":"Knowledge@UChicago (University of Chicago)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I40347166","host_organization_name":"University of Chicago","host_organization_lineage":["https://openalex.org/I40347166"],"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":"http://knowledge.uchicago.edu/record/7698","raw_type":"Text"},{"id":"pmh:doi:10.6082/bw01q-czf59","is_oa":true,"landing_page_url":"https://knowledge.uchicago.edu/communities/physical-sciences-division/","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":"JournalArticle"},{"id":"pmh:oai:RePEc:plo:pcbi00:1004439","is_oa":false,"landing_page_url":"https://journals.plos.org/ploscompbiol/article?id=10.1371/journal.pcbi.1004439","pdf_url":null,"source":{"id":"https://openalex.org/S4306401271","display_name":"RePEc: Research Papers in Economics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I77793887","host_organization_name":"Federal Reserve Bank of St. Louis","host_organization_lineage":["https://openalex.org/I77793887"],"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":"article"},{"id":"pmh:oai:doaj.org/article:3f1adf5ca18a47ad86d6f2a4bd89ae2a","is_oa":true,"landing_page_url":"https://doaj.org/article/3f1adf5ca18a47ad86d6f2a4bd89ae2a","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","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-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"PLoS Computational Biology, Vol 11, Iss 8, p e1004439 (2015)","raw_type":"article"},{"id":"pmh:oai:dukespace.lib.duke.edu:10161/15109","is_oa":true,"landing_page_url":"http://hdl.handle.net/10161/15109","pdf_url":null,"source":{"id":"https://openalex.org/S4306400687","display_name":"DukeSpace (Duke University)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I170897317","host_organization_name":"Duke University","host_organization_lineage":["https://openalex.org/I170897317"],"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":"","raw_type":"Journal Article"},{"id":"doi:10.6082/bw01q-czf59","is_oa":true,"landing_page_url":"https://doi.org/10.6082/bw01q-czf59","pdf_url":null,"source":{"id":"https://openalex.org/S7407053018","display_name":"University of Chicago","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"},{"id":"doi:10.6082/en6xb-wgg35","is_oa":true,"landing_page_url":"https://doi.org/10.6082/en6xb-wgg35","pdf_url":null,"source":{"id":"https://openalex.org/S7407053018","display_name":"University of Chicago","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":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"JournalArticle"}],"best_oa_location":{"id":"doi:10.1371/journal.pcbi.1004439","is_oa":true,"landing_page_url":"https://doi.org/10.1371/journal.pcbi.1004439","pdf_url":"https://journals.plos.org/ploscompbiol/article/file?id=10.1371/journal.pcbi.1004439&type=printable","source":{"id":"https://openalex.org/S86033158","display_name":"PLoS Computational Biology","issn_l":"1553-734X","issn":["1553-734X","1553-7358"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310315706","host_organization_name":"Public Library of Science","host_organization_lineage":["https://openalex.org/P4310315706"],"host_organization_lineage_names":["Public Library of Science"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"PLOS Computational Biology","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W1918371587.pdf","grobid_xml":"https://content.openalex.org/works/W1918371587.grobid-xml"},"referenced_works_count":62,"referenced_works":["https://openalex.org/W82110254","https://openalex.org/W1488411625","https://openalex.org/W1670642870","https://openalex.org/W1733248925","https://openalex.org/W1794719084","https://openalex.org/W1797772348","https://openalex.org/W1884390770","https://openalex.org/W1939596644","https://openalex.org/W1966104725","https://openalex.org/W1985392528","https://openalex.org/W1995341919","https://openalex.org/W1999813559","https://openalex.org/W2002249797","https://openalex.org/W2004547450","https://openalex.org/W2012074763","https://openalex.org/W2014881118","https://openalex.org/W2016201172","https://openalex.org/W2030450972","https://openalex.org/W2037990198","https://openalex.org/W2040715937","https://openalex.org/W2043161845","https://openalex.org/W2043699248","https://openalex.org/W2048087827","https://openalex.org/W2060910814","https://openalex.org/W2065737959","https://openalex.org/W2067415178","https://openalex.org/W2070900790","https://openalex.org/W2072804750","https://openalex.org/W2076551955","https://openalex.org/W2077758457","https://openalex.org/W2080277460","https://openalex.org/W2080792322","https://openalex.org/W2081484203","https://openalex.org/W2090765114","https://openalex.org/W2098328927","https://openalex.org/W2101222204","https://openalex.org/W2101620490","https://openalex.org/W2103019454","https://openalex.org/W2112408199","https://openalex.org/W2113345172","https://openalex.org/W2128084896","https://openalex.org/W2128965713","https://openalex.org/W2129386380","https://openalex.org/W2133671888","https://openalex.org/W2135369850","https://openalex.org/W2147981220","https://openalex.org/W2155051950","https://openalex.org/W2155754335","https://openalex.org/W2161819335","https://openalex.org/W2168462263","https://openalex.org/W2168965695","https://openalex.org/W2274928822","https://openalex.org/W2322002063","https://openalex.org/W3013179879","https://openalex.org/W3097930016","https://openalex.org/W3124563337","https://openalex.org/W4214871172","https://openalex.org/W4231160605","https://openalex.org/W4253613142","https://openalex.org/W4253667136","https://openalex.org/W4298069009","https://openalex.org/W6639350175"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Understanding":[0],"the":[1,29,37,44,47,53,62,72,121,124,142,157,160,169,174,188,217,234,243,248,256,259,268,275,280,285],"theoretical":[2,22],"foundations":[3],"of":[4,46,55,108,156,159,202,216,219,245,250,258,270,277,279,287],"how":[5],"memories":[6],"are":[7,130,151],"encoded":[8],"and":[9,43,116,172,198,208,264,274],"retrieved":[10],"in":[11,18],"neural":[12,31,85],"populations":[13],"is":[14,28,36,191,228],"a":[15,56,83,138,154,200],"central":[16],"challenge":[17],"neuroscience.":[19],"A":[20],"popular":[21],"scenario":[23],"for":[24,82,141,213],"modeling":[25],"memory":[26,125],"function":[27,155],"attractor":[30],"network":[32,86,106,122,201],"scenario,":[33],"whose":[34],"prototype":[35],"Hopfield":[38],"model.":[39],"The":[40,104,221],"model":[41],"simplicity":[42],"locality":[45],"synaptic":[48,144,261],"update":[49],"rules":[50],"come":[51],"at":[52],"cost":[54],"poor":[57],"storage":[58,90,211,222],"capacity,":[59],"compared":[60],"with":[61,65,112,163,284],"capacity":[63,91,212,223,246],"achieved":[64],"perceptron":[66,73],"learning":[67,74,80],"algorithms.":[68],"Here,":[69],"by":[70,237],"transforming":[71],"rule,":[75],"we":[76,254],"present":[77],"an":[78,93,193],"online":[79,132],"rule":[81,207],"recurrent":[84,114],"that":[87,266],"achieves":[88],"near-maximal":[89],"without":[92],"explicit":[94],"supervisory":[95],"error":[96],"signal,":[97],"relying":[98],"only":[99],"upon":[100],"locally":[101],"accessible":[102],"information.":[103],"fully-connected":[105],"consists":[107],"excitatory":[109],"binary":[110,203],"neurons":[111,204],"plastic":[113],"connections":[115],"non-plastic":[117],"inhibitory":[118],"feedback":[119],"stabilizing":[120],"dynamics;":[123],"patterns":[126],"to":[127,148,165,230,233],"be":[128,231],"memorized":[129],"presented":[131],"as":[133,153],"strong":[134],"afferent":[135],"currents,":[136],"producing":[137],"bimodal":[139],"distribution":[140],"neuron":[143],"inputs.":[145,252],"Synapses":[146],"corresponding":[147],"active":[149],"inputs":[150],"modified":[152],"value":[158,235],"local":[161,189],"fields":[162],"respect":[164],"three":[166],"thresholds.":[167],"Above":[168],"highest":[170],"threshold,":[171,176],"below":[173],"lowest":[175],"no":[177],"plasticity":[178],"occurs.":[179],"In":[180],"between":[181],"these":[182],"two":[183],"thresholds,":[184],"potentiation/depression":[185],"occurs":[186],"when":[187],"field":[190],"above/below":[192],"intermediate":[194],"threshold.":[195],"We":[196,240],"simulated":[197],"analyzed":[199],"implementing":[205],"this":[206],"measured":[209,242],"its":[210],"different":[214],"sizes":[215],"basins":[218],"attraction.":[220],"obtained":[224],"through":[225],"numerical":[226],"simulations":[227],"shown":[229],"close":[232],"predicted":[236],"analytical":[238],"calculations.":[239],"also":[241],"dependence":[244],"on":[247],"strength":[249],"external":[251],"Finally,":[253],"quantified":[255],"statistics":[257],"resulting":[260],"connectivity":[262],"matrix,":[263],"found":[265],"both":[267],"fraction":[269],"zero":[271],"weight":[272,281],"synapses":[273],"degree":[276],"symmetry":[278],"matrix":[282],"increase":[283],"number":[286],"stored":[288],"patterns.":[289]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":2},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":4},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":3},{"year":2017,"cited_by_count":1},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":1}],"updated_date":"2026-08-11T07:18:39.950985","created_date":"2025-10-10T00:00:00"}