{"id":"https://openalex.org/W2122879428","doi":"https://doi.org/10.1162/neco.2008.04-08-750","title":"On the Asymptotic Equivalence Between Differential Hebbian and Temporal Difference Learning","display_name":"On the Asymptotic Equivalence Between Differential Hebbian and Temporal Difference Learning","publication_year":2008,"publication_date":"2008-11-19","ids":{"openalex":"https://openalex.org/W2122879428","doi":"https://doi.org/10.1162/neco.2008.04-08-750","mag":"2122879428","pmid":"https://pubmed.ncbi.nlm.nih.gov/19018698"},"language":"en","primary_location":{"id":"doi:10.1162/neco.2008.04-08-750","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco.2008.04-08-750","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/A5111954344","display_name":"Christoph Kolodziejski","orcid":null},"institutions":[{"id":"https://openalex.org/I4210087171","display_name":"Bernstein Center for Computational Neuroscience G\u00f6ttingen","ror":"https://ror.org/003g6b432","country_code":"DE","type":"government","lineage":["https://openalex.org/I4210087171","https://openalex.org/I4210092532"]},{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Christoph Kolodziejski","raw_affiliation_strings":["Bernstein Center for Computational Neuroscience, University of G\u00f6ttingen, 37073 G\u00f6ttingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bernstein Center for Computational Neuroscience, University of G\u00f6ttingen, 37073 G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I4210087171","https://openalex.org/I74656192"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5091850362","display_name":"Bernd Porr","orcid":"https://orcid.org/0000-0001-8157-998X"},"institutions":[{"id":"https://openalex.org/I7882870","display_name":"University of Glasgow","ror":"https://ror.org/00vtgdb53","country_code":"GB","type":"education","lineage":["https://openalex.org/I7882870"]}],"countries":["GB"],"is_corresponding":false,"raw_author_name":"Bernd Porr","raw_affiliation_strings":["Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow, Scotland"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Electronics and Electrical Engineering, University of Glasgow, Glasgow, Scotland","institution_ids":["https://openalex.org/I7882870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023811677","display_name":"Florentin W\u00f6rg\u00f6tter","orcid":null},"institutions":[{"id":"https://openalex.org/I4210087171","display_name":"Bernstein Center for Computational Neuroscience G\u00f6ttingen","ror":"https://ror.org/003g6b432","country_code":"DE","type":"government","lineage":["https://openalex.org/I4210087171","https://openalex.org/I4210092532"]},{"id":"https://openalex.org/I74656192","display_name":"University of G\u00f6ttingen","ror":"https://ror.org/01y9bpm73","country_code":"DE","type":"education","lineage":["https://openalex.org/I74656192"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Florentin W\u00f6rg\u00f6tter","raw_affiliation_strings":["Bernstein Center for Computational Neuroscience, University of G\u00f6ttingen, 37073 G\u00f6ttingen, Germany"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Bernstein Center for Computational Neuroscience, University of G\u00f6ttingen, 37073 G\u00f6ttingen, Germany","institution_ids":["https://openalex.org/I4210087171","https://openalex.org/I74656192"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.5992,"has_fulltext":false,"cited_by_count":13,"citation_normalized_percentile":{"value":0.67992755,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":97},"biblio":{"volume":"21","issue":"4","first_page":"1173","last_page":"1202"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9991999864578247,"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"}},"topics":[{"id":"https://openalex.org/T10581","display_name":"Neural dynamics and brain function","score":0.9991999864578247,"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/T10621","display_name":"Gene Regulatory Network Analysis","score":0.993399977684021,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}},{"id":"https://openalex.org/T11178","display_name":"Receptor Mechanisms and Signaling","score":0.9864000082015991,"subfield":{"id":"https://openalex.org/subfields/1312","display_name":"Molecular Biology"},"field":{"id":"https://openalex.org/fields/13","display_name":"Biochemistry, Genetics and Molecular Biology"},"domain":{"id":"https://openalex.org/domains/1","display_name":"Life Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/hebbian-theory","display_name":"Hebbian theory","score":0.9114018678665161},{"id":"https://openalex.org/keywords/temporal-difference-learning","display_name":"Temporal difference learning","score":0.6282851099967957},{"id":"https://openalex.org/keywords/reinforcement-learning","display_name":"Reinforcement learning","score":0.5580466389656067},{"id":"https://openalex.org/keywords/correlation","display_name":"Correlation","score":0.5555077791213989},{"id":"https://openalex.org/keywords/equivalence","display_name":"Equivalence (formal languages)","score":0.535412073135376},{"id":"https://openalex.org/keywords/perspective","display_name":"Perspective (graphical)","score":0.5083624720573425},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.48224884271621704},{"id":"https://openalex.org/keywords/leabra","display_name":"Leabra","score":0.4431454837322235},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.43233299255371094},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.39551034569740295},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3834036588668823},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.15044665336608887},{"id":"https://openalex.org/keywords/generalization-error","display_name":"Generalization error","score":0.11424204707145691},{"id":"https://openalex.org/keywords/wake-sleep-algorithm","display_name":"Wake-sleep algorithm","score":0.10518491268157959}],"concepts":[{"id":"https://openalex.org/C111437709","wikidata":"https://www.wikidata.org/wiki/Q1277874","display_name":"Hebbian theory","level":3,"score":0.9114018678665161},{"id":"https://openalex.org/C196340769","wikidata":"https://www.wikidata.org/wiki/Q7698910","display_name":"Temporal difference learning","level":3,"score":0.6282851099967957},{"id":"https://openalex.org/C97541855","wikidata":"https://www.wikidata.org/wiki/Q830687","display_name":"Reinforcement learning","level":2,"score":0.5580466389656067},{"id":"https://openalex.org/C117220453","wikidata":"https://www.wikidata.org/wiki/Q5172842","display_name":"Correlation","level":2,"score":0.5555077791213989},{"id":"https://openalex.org/C2780069185","wikidata":"https://www.wikidata.org/wiki/Q7977945","display_name":"Equivalence (formal languages)","level":2,"score":0.535412073135376},{"id":"https://openalex.org/C12713177","wikidata":"https://www.wikidata.org/wiki/Q1900281","display_name":"Perspective (graphical)","level":2,"score":0.5083624720573425},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.48224884271621704},{"id":"https://openalex.org/C97108695","wikidata":"https://www.wikidata.org/wiki/Q6508265","display_name":"Leabra","level":5,"score":0.4431454837322235},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.43233299255371094},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.39551034569740295},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3834036588668823},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.15044665336608887},{"id":"https://openalex.org/C117765406","wikidata":"https://www.wikidata.org/wiki/Q5362437","display_name":"Generalization error","level":3,"score":0.11424204707145691},{"id":"https://openalex.org/C17061570","wikidata":"https://www.wikidata.org/wiki/Q7960888","display_name":"Wake-sleep algorithm","level":4,"score":0.10518491268157959},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D000818","descriptor_name":"Animals","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001703","descriptor_name":"Biophysics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001703","descriptor_name":"Biophysics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001703","descriptor_name":"Biophysics","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":"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":"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":"D012054","descriptor_name":"Reinforcement, Psychology","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012054","descriptor_name":"Reinforcement, Psychology","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D012054","descriptor_name":"Reinforcement, Psychology","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D013997","descriptor_name":"Time Factors","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":3,"locations":[{"id":"doi:10.1162/neco.2008.04-08-750","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco.2008.04-08-750","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:19018698","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19018698","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:eprints.gla.ac.uk:34905","is_oa":false,"landing_page_url":"http://eprints.gla.ac.uk/34905/","pdf_url":null,"source":{"id":"https://openalex.org/S4210235606","display_name":"ENLIGHTEN (Jurnal Bimbingan dan Konseling Islam)","issn_l":"2622-8912","issn":["2622-8912","2622-8920"],"is_oa":false,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Articles"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":53,"referenced_works":["https://openalex.org/W32403112","https://openalex.org/W1515851193","https://openalex.org/W1535810436","https://openalex.org/W1542305729","https://openalex.org/W1557517019","https://openalex.org/W1652173018","https://openalex.org/W1814308503","https://openalex.org/W1820996291","https://openalex.org/W1823057531","https://openalex.org/W1965227651","https://openalex.org/W1979215131","https://openalex.org/W1985623473","https://openalex.org/W1986246844","https://openalex.org/W2031688164","https://openalex.org/W2038605385","https://openalex.org/W2040598998","https://openalex.org/W2060052647","https://openalex.org/W2061405268","https://openalex.org/W2066759495","https://openalex.org/W2069258922","https://openalex.org/W2073003335","https://openalex.org/W2089132957","https://openalex.org/W2098378004","https://openalex.org/W2100644648","https://openalex.org/W2100677568","https://openalex.org/W2109059823","https://openalex.org/W2109152498","https://openalex.org/W2113077545","https://openalex.org/W2116577160","https://openalex.org/W2121863487","https://openalex.org/W2122925692","https://openalex.org/W2126404188","https://openalex.org/W2128084896","https://openalex.org/W2135094859","https://openalex.org/W2139418546","https://openalex.org/W2143873689","https://openalex.org/W2148201341","https://openalex.org/W2150339816","https://openalex.org/W2153564253","https://openalex.org/W2154145851","https://openalex.org/W2176864480","https://openalex.org/W2185212694","https://openalex.org/W2235056388","https://openalex.org/W2282055800","https://openalex.org/W2432567885","https://openalex.org/W3041202696","https://openalex.org/W4212774754","https://openalex.org/W4214717370","https://openalex.org/W4241521318","https://openalex.org/W4242770316","https://openalex.org/W4247206283","https://openalex.org/W4248400504","https://openalex.org/W4251206009"],"related_works":["https://openalex.org/W4306291900","https://openalex.org/W3114310175","https://openalex.org/W4287549639","https://openalex.org/W2899454144","https://openalex.org/W2137674257","https://openalex.org/W2145352734","https://openalex.org/W4321853849","https://openalex.org/W4389086722","https://openalex.org/W1978872345","https://openalex.org/W2122879428"],"abstract_inverted_index":{"In":[0],"this":[1],"theoretical":[2],"contribution,":[3],"we":[4],"provide":[5],"mathematical":[6],"proof":[7],"that":[8],"two":[9],"of":[10,15,44,60],"the":[11,30,38,45,58],"most":[12,43],"important":[13],"classes":[14],"network":[16],"learning-correlation-based":[17],"differential":[18],"Hebbian":[19],"learning":[20,31,48],"and":[21],"reward-based":[22],"temporal":[23],"difference":[24],"learning-are":[25],"asymptotically":[26],"equivalent":[27],"when":[28],"timing":[29],"with":[32],"a":[33,51],"modulatory":[34],"signal.":[35],"This":[36],"opens":[37],"opportunity":[39],"to":[40,57],"consistently":[41],"reformulate":[42],"abstract":[46],"reinforcement":[47],"framework":[49],"from":[50],"correlation-based":[52],"perspective":[53],"more":[54],"closely":[55],"related":[56],"biophysics":[59],"neurons.":[61]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2016,"cited_by_count":1},{"year":2014,"cited_by_count":3},{"year":2013,"cited_by_count":1},{"year":2012,"cited_by_count":1}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}