{"id":"https://openalex.org/W2112868266","doi":"https://doi.org/10.1162/089976603321891837","title":"The Effect of Noise on a Class of Energy-Based Learning Rules","display_name":"The Effect of Noise on a Class of Energy-Based Learning Rules","publication_year":2003,"publication_date":"2003-06-03","ids":{"openalex":"https://openalex.org/W2112868266","doi":"https://doi.org/10.1162/089976603321891837","mag":"2112868266","pmid":"https://pubmed.ncbi.nlm.nih.gov/12816569"},"language":"en","primary_location":{"id":"doi:10.1162/089976603321891837","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976603321891837","pdf_url":null,"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":false,"oa_status":"closed","oa_url":null,"any_repository_has_fulltext":false},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5058670333","display_name":"Armando Bazzani","orcid":"https://orcid.org/0000-0002-9633-0017"},"institutions":[{"id":"https://openalex.org/I4210148700","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Bologna","ror":"https://ror.org/04j0x0h93","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210148700"]},{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"A. Bazzani","raw_affiliation_strings":["Department of Physics and INFN, University of Bologna, 40126, Bologna, Italy,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and INFN, University of Bologna, 40126, Bologna, Italy,","institution_ids":["https://openalex.org/I4210148700","https://openalex.org/I9360294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5025807854","display_name":"Daniel Remondini","orcid":"https://orcid.org/0000-0003-3185-7456"},"institutions":[{"id":"https://openalex.org/I4210148700","display_name":"Istituto Nazionale di Fisica Nucleare, Sezione di Bologna","ror":"https://ror.org/04j0x0h93","country_code":"IT","type":"facility","lineage":["https://openalex.org/I160013858","https://openalex.org/I4210148700"]},{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"D. Remondini","raw_affiliation_strings":["Department of Physics and INFN, University of Bologna, 40126, Bologna, Italy,"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and INFN, University of Bologna, 40126, Bologna, Italy,","institution_ids":["https://openalex.org/I4210148700","https://openalex.org/I9360294"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5029500893","display_name":"Nathan Intrator","orcid":"https://orcid.org/0000-0002-5635-9835"},"institutions":[{"id":"https://openalex.org/I1314596251","display_name":"Allen Institute for Brain Science","ror":"https://ror.org/00dcv1019","country_code":"US","type":"facility","lineage":["https://openalex.org/I1314596251","https://openalex.org/I4210140341"]},{"id":"https://openalex.org/I27804330","display_name":"Brown University","ror":"https://ror.org/05gq02987","country_code":"US","type":"education","lineage":["https://openalex.org/I27804330"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"N. Intrator","raw_affiliation_strings":["Institute for Brain and Neural Systems, Brown University, Providence, RI 02912, U.S.A"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Institute for Brain and Neural Systems, Brown University, Providence, RI 02912, U.S.A","institution_ids":["https://openalex.org/I27804330","https://openalex.org/I1314596251"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5026341152","display_name":"Gastone Castellani","orcid":"https://orcid.org/0000-0003-4892-925X"},"institutions":[{"id":"https://openalex.org/I9360294","display_name":"University of Bologna","ror":"https://ror.org/01111rn36","country_code":"IT","type":"education","lineage":["https://openalex.org/I9360294"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"G. C. Castellani","raw_affiliation_strings":["Department of Physics and DIMORFIPA, University of Bologna, 40126, Bologna, Italy,","Department of Physics and DIMORFIPA, University of Bologna, 40126, Bologna, Italy#TAB#"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and DIMORFIPA, University of Bologna, 40126, Bologna, Italy,","institution_ids":["https://openalex.org/I9360294"]},{"raw_affiliation_string":"Department of Physics and DIMORFIPA, University of Bologna, 40126, Bologna, Italy#TAB#","institution_ids":["https://openalex.org/I9360294"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.4688,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.75343546,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"15","issue":"7","first_page":"1621","last_page":"1640"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9998000264167786,"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":0.9998000264167786,"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/T10581","display_name":"Neural dynamics and brain function","score":0.9991000294685364,"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"}},{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.994700014591217,"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/robustness","display_name":"Robustness (evolution)","score":0.7736744284629822},{"id":"https://openalex.org/keywords/kurtosis","display_name":"Kurtosis","score":0.7390464544296265},{"id":"https://openalex.org/keywords/curse-of-dimensionality","display_name":"Curse of dimensionality","score":0.6685702800750732},{"id":"https://openalex.org/keywords/subspace-topology","display_name":"Subspace topology","score":0.5467135906219482},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5004284381866455},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.46986421942710876},{"id":"https://openalex.org/keywords/noise","display_name":"Noise (video)","score":0.4424586296081543},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3848493993282318},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3751818537712097},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.3523247241973877},{"id":"https://openalex.org/keywords/statistical-physics","display_name":"Statistical physics","score":0.3377380967140198},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16967588663101196},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.11058363318443298}],"concepts":[{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.7736744284629822},{"id":"https://openalex.org/C166963901","wikidata":"https://www.wikidata.org/wiki/Q287251","display_name":"Kurtosis","level":2,"score":0.7390464544296265},{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.6685702800750732},{"id":"https://openalex.org/C32834561","wikidata":"https://www.wikidata.org/wiki/Q660730","display_name":"Subspace topology","level":2,"score":0.5467135906219482},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5004284381866455},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.46986421942710876},{"id":"https://openalex.org/C99498987","wikidata":"https://www.wikidata.org/wiki/Q2210247","display_name":"Noise (video)","level":3,"score":0.4424586296081543},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3848493993282318},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3751818537712097},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.3523247241973877},{"id":"https://openalex.org/C121864883","wikidata":"https://www.wikidata.org/wiki/Q677916","display_name":"Statistical physics","level":1,"score":0.3377380967140198},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16967588663101196},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.11058363318443298},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D004560","descriptor_name":"Electricity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D004560","descriptor_name":"Electricity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D004560","descriptor_name":"Electricity","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D004734","descriptor_name":"Energy Metabolism","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D004734","descriptor_name":"Energy Metabolism","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D004734","descriptor_name":"Energy Metabolism","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D007858","descriptor_name":"Learning","qualifier_ui":"Q000502","qualifier_name":"physiology","is_major_topic":false},{"descriptor_ui":"D007858","descriptor_name":"Learning","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":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D016011","descriptor_name":"Normal Distribution","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1162/089976603321891837","is_oa":false,"landing_page_url":"https://doi.org/10.1162/089976603321891837","pdf_url":null,"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:12816569","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/12816569","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}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Affordable and clean energy","id":"https://metadata.un.org/sdg/7","score":0.9100000262260437}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":14,"referenced_works":["https://openalex.org/W1733248925","https://openalex.org/W1964724001","https://openalex.org/W2000292661","https://openalex.org/W2001553466","https://openalex.org/W2030145020","https://openalex.org/W2059010387","https://openalex.org/W2061405268","https://openalex.org/W2083046441","https://openalex.org/W2092401580","https://openalex.org/W2105262671","https://openalex.org/W2116837363","https://openalex.org/W2167275700","https://openalex.org/W2432567885","https://openalex.org/W4249925659"],"related_works":["https://openalex.org/W4381516319","https://openalex.org/W1506384729","https://openalex.org/W2037499216","https://openalex.org/W4225568567","https://openalex.org/W4286378979","https://openalex.org/W2075698830","https://openalex.org/W3127045225","https://openalex.org/W3216026256","https://openalex.org/W2059891554","https://openalex.org/W3125756894"],"abstract_inverted_index":{"Westudy":[0],"the":[1,31,46,52,76,81,102,112,126],"selectivity":[2,53],"properties":[3],"of":[4,17,30,41,62,80,97,105,114,125],"neurons":[5],"based":[6],"on":[7,69],"BCM":[8,82,106,127],"and":[9,107],"kurtosis":[10,108],"energy":[11,42],"functions":[12],"in":[13,111],"a":[14,38,59,95,115,122],"general":[15],"case":[16,113],"noisy":[18],"high-dimensional":[19],"input":[20,117],"space.":[21],"The":[22],"proposed":[23],"approach,":[24],"which":[25,51,65],"is":[26,54],"used":[27],"for":[28,129],"characterization":[29],"stable":[32],"states,":[33],"can":[34],"be":[35],"generalized":[36],"to":[37,78],"whole":[39],"class":[40],"functions.":[43],"We":[44,56,73,99],"characterize":[45],"critical":[47],"noise":[48,79],"levels":[49],"beyond":[50],"destroyed.":[55],"also":[57],"perform":[58],"quantitative":[60],"analysis":[61],"such":[63],"transitions,":[64],"shows":[66],"interesting":[67],"dependency":[68],"data":[70,131],"set":[71,132],"size.":[72],"observe":[74],"that":[75],"robustness":[77,124],"neuron":[83],"(Bienenstock,":[84],"Cooper,":[85,91],"&":[86,90],"Munro,":[87],"1982;":[88],"Intrator":[89],"1992)":[92],"increases":[93],"as":[94],"function":[96],"dimensionality.":[98],"explicitly":[100],"compute":[101],"separability":[103],"limit":[104],"learning":[109],"rules":[110],"bimodal":[116],"distribution.":[118],"Numerical":[119],"simulations":[120],"show":[121],"stronger":[123],"rule":[128],"practical":[130],"size":[133],"when":[134],"compared":[135],"with":[136],"kurtosis.":[137]},"counts_by_year":[{"year":2020,"cited_by_count":1},{"year":2015,"cited_by_count":1},{"year":2013,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}