{"id":"https://openalex.org/W2170558536","doi":"https://doi.org/10.1109/tnn.2008.2012257","title":"Spurious Valleys in the Error Surface of Recurrent Networks\u2014Analysis and Avoidance","display_name":"Spurious Valleys in the Error Surface of Recurrent Networks\u2014Analysis and Avoidance","publication_year":2009,"publication_date":"2009-03-10","ids":{"openalex":"https://openalex.org/W2170558536","doi":"https://doi.org/10.1109/tnn.2008.2012257","mag":"2170558536","pmid":"https://pubmed.ncbi.nlm.nih.gov/19273043"},"language":"en","primary_location":{"id":"doi:10.1109/tnn.2008.2012257","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2008.2012257","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks","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/A5016380482","display_name":"Jason Horn","orcid":null},"institutions":[{"id":"https://openalex.org/I138285227","display_name":"Agilent Technologies (United States)","ror":"https://ror.org/02tryst02","country_code":"US","type":"company","lineage":["https://openalex.org/I138285227"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"J. Horn","raw_affiliation_strings":["Agilent Technologies High Frequency Technology Center, Santa Clara, CA 95051 USA. jason@jasonhorn.com","High Frequency Technology Center, Agilent Technologies, Inc., Santa Clara, CA, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Agilent Technologies High Frequency Technology Center, Santa Clara, CA 95051 USA. jason@jasonhorn.com","institution_ids":["https://openalex.org/I138285227"]},{"raw_affiliation_string":"High Frequency Technology Center, Agilent Technologies, Inc., Santa Clara, CA, USA","institution_ids":["https://openalex.org/I138285227"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5077309119","display_name":"Orlando De Jes\u00fas","orcid":"https://orcid.org/0000-0001-8078-3882"},"institutions":[{"id":"https://openalex.org/I4210137549","display_name":"Halliburton (United States)","ror":"https://ror.org/03s918289","country_code":"US","type":"company","lineage":["https://openalex.org/I4210137549"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"O. De Jesus","raw_affiliation_strings":["Research Department, Halliburton Energy Services, Dallas, TX, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Research Department, Halliburton Energy Services, Dallas, TX, USA","institution_ids":["https://openalex.org/I4210137549"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5084013215","display_name":"Martin Hagan","orcid":"https://orcid.org/0000-0003-1624-5558"},"institutions":[{"id":"https://openalex.org/I115475287","display_name":"Oklahoma State University","ror":"https://ror.org/01g9vbr38","country_code":"US","type":"education","lineage":["https://openalex.org/I115475287"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"M.T. Hagan","raw_affiliation_strings":["School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, OK, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"School of Electrical and Computer Engineering, Oklahoma State University, Stillwater, OK, USA","institution_ids":["https://openalex.org/I115475287"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":2.2207,"has_fulltext":false,"cited_by_count":32,"citation_normalized_percentile":{"value":0.89987406,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":98},"biblio":{"volume":"20","issue":"4","first_page":"686","last_page":"700"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9994000196456909,"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":0.9994000196456909,"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9871000051498413,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T11689","display_name":"Adversarial Robustness in Machine Learning","score":0.9829999804496765,"subfield":{"id":"https://openalex.org/subfields/1702","display_name":"Artificial Intelligence"},"field":{"id":"https://openalex.org/fields/17","display_name":"Computer Science"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}}],"keywords":[{"id":"https://openalex.org/keywords/spurious-relationship","display_name":"Spurious relationship","score":0.9622824192047119},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6526927351951599},{"id":"https://openalex.org/keywords/reliability","display_name":"Reliability (semiconductor)","score":0.5844699144363403},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.5118757486343384},{"id":"https://openalex.org/keywords/error-detection-and-correction","display_name":"Error detection and correction","score":0.4569661021232605},{"id":"https://openalex.org/keywords/mechanism","display_name":"Mechanism (biology)","score":0.43246757984161377},{"id":"https://openalex.org/keywords/random-error","display_name":"Random error","score":0.42572855949401855},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4190223813056946},{"id":"https://openalex.org/keywords/mean-squared-prediction-error","display_name":"Mean squared prediction error","score":0.4163423776626587},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.40945276618003845},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3235558271408081},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.2587912678718567},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.1760622262954712},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.13947400450706482}],"concepts":[{"id":"https://openalex.org/C97256817","wikidata":"https://www.wikidata.org/wiki/Q1462316","display_name":"Spurious relationship","level":2,"score":0.9622824192047119},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6526927351951599},{"id":"https://openalex.org/C43214815","wikidata":"https://www.wikidata.org/wiki/Q7310987","display_name":"Reliability (semiconductor)","level":3,"score":0.5844699144363403},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.5118757486343384},{"id":"https://openalex.org/C103088060","wikidata":"https://www.wikidata.org/wiki/Q1062839","display_name":"Error detection and correction","level":2,"score":0.4569661021232605},{"id":"https://openalex.org/C89611455","wikidata":"https://www.wikidata.org/wiki/Q6804646","display_name":"Mechanism (biology)","level":2,"score":0.43246757984161377},{"id":"https://openalex.org/C73782692","wikidata":"https://www.wikidata.org/wiki/Q196372","display_name":"Random error","level":2,"score":0.42572855949401855},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4190223813056946},{"id":"https://openalex.org/C167085575","wikidata":"https://www.wikidata.org/wiki/Q6803654","display_name":"Mean squared prediction error","level":2,"score":0.4163423776626587},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.40945276618003845},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3235558271408081},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.2587912678718567},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.1760622262954712},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.13947400450706482},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C163258240","wikidata":"https://www.wikidata.org/wiki/Q25342","display_name":"Power (physics)","level":2,"score":0.0},{"id":"https://openalex.org/C138885662","wikidata":"https://www.wikidata.org/wiki/Q5891","display_name":"Philosophy","level":0,"score":0.0},{"id":"https://openalex.org/C111472728","wikidata":"https://www.wikidata.org/wiki/Q9471","display_name":"Epistemology","level":1,"score":0.0}],"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":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D001185","descriptor_name":"Artificial Intelligence","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":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false},{"descriptor_ui":"D017711","descriptor_name":"Nonlinear Dynamics","qualifier_ui":null,"qualifier_name":null,"is_major_topic":false}],"locations_count":2,"locations":[{"id":"doi:10.1109/tnn.2008.2012257","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnn.2008.2012257","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks","raw_type":"journal-article"},{"id":"pmid:19273043","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/19273043","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE transactions on neural networks","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[{"score":0.6299999952316284,"display_name":"Sustainable cities and communities","id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":42,"referenced_works":["https://openalex.org/W103128726","https://openalex.org/W194249466","https://openalex.org/W1526990717","https://openalex.org/W1665200104","https://openalex.org/W1998916693","https://openalex.org/W2001114491","https://openalex.org/W2016589492","https://openalex.org/W2038997435","https://openalex.org/W2064675550","https://openalex.org/W2066564032","https://openalex.org/W2099716683","https://openalex.org/W2105613941","https://openalex.org/W2107878631","https://openalex.org/W2109519791","https://openalex.org/W2110871230","https://openalex.org/W2110975419","https://openalex.org/W2113634576","https://openalex.org/W2121235888","https://openalex.org/W2121492054","https://openalex.org/W2127141656","https://openalex.org/W2127150270","https://openalex.org/W2132423763","https://openalex.org/W2143545157","https://openalex.org/W2143956139","https://openalex.org/W2144308638","https://openalex.org/W2149223397","https://openalex.org/W2156798505","https://openalex.org/W2158773148","https://openalex.org/W2163919741","https://openalex.org/W2166662865","https://openalex.org/W2167898728","https://openalex.org/W2169762136","https://openalex.org/W2330216979","https://openalex.org/W2342043828","https://openalex.org/W2480466982","https://openalex.org/W2481916066","https://openalex.org/W2490030495","https://openalex.org/W2911546748","https://openalex.org/W4231173317","https://openalex.org/W6604146980","https://openalex.org/W6684575925","https://openalex.org/W7064788384"],"related_works":["https://openalex.org/W2386520220","https://openalex.org/W2380243770","https://openalex.org/W2392422136","https://openalex.org/W2377495875","https://openalex.org/W2080389153","https://openalex.org/W2390973415","https://openalex.org/W2389075589","https://openalex.org/W2379687917","https://openalex.org/W2137019427","https://openalex.org/W2076217607"],"abstract_inverted_index":{"This":[0,62],"paper":[1,63],"gives":[2],"a":[3],"detailed":[4],"analysis":[5,55],"of":[6,10,56,59],"the":[7,36,40,47,54,57,77],"error":[8,27],"surfaces":[9,28],"certain":[11],"recurrent":[12,21],"networks":[13],"and":[14,33,87],"explains":[15],"some":[16],"difficulties":[17,78],"encountered":[18],"in":[19,69],"training":[20,71,85],"networks.":[22],"We":[23,44],"show":[24],"that":[25,38,46,73],"these":[26],"contain":[29],"many":[30],"spurious":[31,81],"valleys,":[32,82],"we":[34],"analyze":[35],"mechanisms":[37],"cause":[39],"valleys":[41],"to":[42],"appear.":[43],"demonstrate":[45],"principle":[48],"mechanism":[49],"can":[50,74],"be":[51],"understood":[52],"through":[53],"roots":[58],"random":[60],"polynomials.":[61],"also":[64],"provides":[65],"suggestions":[66],"for":[67],"improvements":[68],"batch":[70],"procedures":[72],"help":[75],"avoid":[76],"caused":[79],"by":[80],"thereby":[83],"improving":[84],"speed":[86],"reliability.":[88]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2023,"cited_by_count":2},{"year":2021,"cited_by_count":2},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":3},{"year":2018,"cited_by_count":5},{"year":2016,"cited_by_count":3},{"year":2015,"cited_by_count":5},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":2},{"year":2012,"cited_by_count":2}],"updated_date":"2026-01-13T01:12:25.745995","created_date":"2025-10-10T00:00:00"}
