{"id":"https://openalex.org/W2406273144","doi":"https://doi.org/10.21437/interspeech.2013-436","title":"Cross-entropy vs. squared error training: a theoretical and experimental comparison","display_name":"Cross-entropy vs. squared error training: a theoretical and experimental comparison","publication_year":2013,"publication_date":"2013-08-25","ids":{"openalex":"https://openalex.org/W2406273144","doi":"https://doi.org/10.21437/interspeech.2013-436","mag":"2406273144"},"language":"en","primary_location":{"id":"doi:10.21437/interspeech.2013-436","is_oa":false,"landing_page_url":"https://doi.org/10.21437/interspeech.2013-436","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Interspeech 2013","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-202806%22","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5015194760","display_name":"Pavel Golik","orcid":"https://orcid.org/0000-0002-0977-4219"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":true,"raw_author_name":"Pavel Golik","raw_affiliation_strings":["Human Language Technology and Pattern Recognition, Computer Science Department, RWTH Aachen University, 52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Human Language Technology and Pattern Recognition, Computer Science Department, RWTH Aachen University, 52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5082582385","display_name":"Patrick Doetsch","orcid":"https://orcid.org/0000-0003-0359-3027"},"institutions":[{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE"],"is_corresponding":false,"raw_author_name":"Patrick Doetsch","raw_affiliation_strings":["Human Language Technology and Pattern Recognition, Computer Science Department, RWTH Aachen University, 52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Human Language Technology and Pattern Recognition, Computer Science Department, RWTH Aachen University, 52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5112501010","display_name":"Hermann Ney","orcid":null},"institutions":[{"id":"https://openalex.org/I1294671590","display_name":"Centre National de la Recherche Scientifique","ror":"https://ror.org/02feahw73","country_code":"FR","type":"government","lineage":["https://openalex.org/I1294671590"]},{"id":"https://openalex.org/I4210115485","display_name":"Laboratoire d'Informatique pour la M\u00e9canique et les Sciences de l'Ing\u00e9nieur","ror":"https://ror.org/01raq4x89","country_code":"FR","type":"facility","lineage":["https://openalex.org/I102197404","https://openalex.org/I1294671590","https://openalex.org/I4210115485","https://openalex.org/I4210159245"]},{"id":"https://openalex.org/I887968799","display_name":"RWTH Aachen University","ror":"https://ror.org/04xfq0f34","country_code":"DE","type":"education","lineage":["https://openalex.org/I887968799"]}],"countries":["DE","FR"],"is_corresponding":false,"raw_author_name":"Hermann Ney","raw_affiliation_strings":["Spoken Language Processing Group, LIMSI CNRS, Paris, France","Human Language Technology and Pattern Recognition, Computer Science Department, RWTH Aachen University, 52056 Aachen, Germany"],"affiliations":[{"raw_affiliation_string":"Spoken Language Processing Group, LIMSI CNRS, Paris, France","institution_ids":["https://openalex.org/I4210115485","https://openalex.org/I1294671590"]},{"raw_affiliation_string":"Human Language Technology and Pattern Recognition, Computer Science Department, RWTH Aachen University, 52056 Aachen, Germany","institution_ids":["https://openalex.org/I887968799"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5015194760"],"corresponding_institution_ids":["https://openalex.org/I887968799"],"apc_list":null,"apc_paid":null,"fwci":13.8388,"has_fulltext":true,"cited_by_count":221,"citation_normalized_percentile":{"value":0.9879509,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":90,"max":100},"biblio":{"volume":null,"issue":null,"first_page":"1756","last_page":"1760"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9994999766349792,"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":0.9994999766349792,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.9973999857902527,"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/T12535","display_name":"Machine Learning and Data Classification","score":0.9952999949455261,"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/mean-squared-error","display_name":"Mean squared error","score":0.5804466009140015},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5019793510437012},{"id":"https://openalex.org/keywords/cross-entropy","display_name":"Cross entropy","score":0.49775269627571106},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.44508621096611023},{"id":"https://openalex.org/keywords/entropy","display_name":"Entropy (arrow of time)","score":0.43730974197387695},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.3927377462387085},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3831879198551178},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.34595629572868347},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3350799083709717},{"id":"https://openalex.org/keywords/speech-recognition","display_name":"Speech recognition","score":0.3280726671218872},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.3257479965686798},{"id":"https://openalex.org/keywords/pattern-recognition","display_name":"Pattern recognition (psychology)","score":0.2812774181365967},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.19481366872787476},{"id":"https://openalex.org/keywords/thermodynamics","display_name":"Thermodynamics","score":0.12164080142974854},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.07760533690452576}],"concepts":[{"id":"https://openalex.org/C139945424","wikidata":"https://www.wikidata.org/wiki/Q1940696","display_name":"Mean squared error","level":2,"score":0.5804466009140015},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5019793510437012},{"id":"https://openalex.org/C167981619","wikidata":"https://www.wikidata.org/wiki/Q1685498","display_name":"Cross entropy","level":3,"score":0.49775269627571106},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.44508621096611023},{"id":"https://openalex.org/C106301342","wikidata":"https://www.wikidata.org/wiki/Q4117933","display_name":"Entropy (arrow of time)","level":2,"score":0.43730974197387695},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.3927377462387085},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3831879198551178},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.34595629572868347},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3350799083709717},{"id":"https://openalex.org/C28490314","wikidata":"https://www.wikidata.org/wiki/Q189436","display_name":"Speech recognition","level":1,"score":0.3280726671218872},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.3257479965686798},{"id":"https://openalex.org/C153180895","wikidata":"https://www.wikidata.org/wiki/Q7148389","display_name":"Pattern recognition (psychology)","level":2,"score":0.2812774181365967},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.19481366872787476},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.12164080142974854},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.07760533690452576}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.21437/interspeech.2013-436","is_oa":false,"landing_page_url":"https://doi.org/10.21437/interspeech.2013-436","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Interspeech 2013","raw_type":"proceedings-article"},{"id":"pmh:oai:publications.rwth-aachen.de:225127","is_oa":true,"landing_page_url":"https://publications.rwth-aachen.de/record/225127","pdf_url":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-202806%22","source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Interspeech : Lyon, France ; 25-29 Aug. 2013 ; 14th Annual Conference of the International Speech Communication Association<br/>14. Annual Conference of the International Speech Communication Association, ACISCA, Lyon, France, 2013-08-25 - 2013-08-29","raw_type":"info:eu-repo/semantics/publishedVersion"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.392.8308","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.392.8308","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www-i6.informatik.rwth-aachen.de/publications/download/861/Golik--2013.pdf","raw_type":"text"}],"best_oa_location":{"id":"pmh:oai:publications.rwth-aachen.de:225127","is_oa":true,"landing_page_url":"https://publications.rwth-aachen.de/record/225127","pdf_url":"https://publications.rwth-aachen.de/search?p=id:%22RWTH-CONV-202806%22","source":{"id":"https://openalex.org/S4306401362","display_name":"RWTH Publications (RWTH Aachen)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I887968799","host_organization_name":"RWTH Aachen University","host_organization_lineage":["https://openalex.org/I887968799"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Interspeech : Lyon, France ; 25-29 Aug. 2013 ; 14th Annual Conference of the International Speech Communication Association<br/>14. Annual Conference of the International Speech Communication Association, ACISCA, Lyon, France, 2013-08-25 - 2013-08-29","raw_type":"info:eu-repo/semantics/publishedVersion"},"sustainable_development_goals":[{"display_name":"Quality Education","score":0.5099999904632568,"id":"https://metadata.un.org/sdg/4"}],"awards":[{"id":"https://openalex.org/G1541914665","display_name":null,"funder_award_id":"287755","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2531681599","display_name":null,"funder_award_id":"W911NF-12-C-0012","funder_id":"https://openalex.org/F4320338295","funder_display_name":"Army Research Laboratory"},{"id":"https://openalex.org/G3829048491","display_name":null,"funder_award_id":"FP7/2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3981126665","display_name":null,"funder_award_id":"Seventh Framework Programme","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5259331294","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338295","funder_display_name":"Army Research Laboratory"},{"id":"https://openalex.org/G5593277320","display_name":null,"funder_award_id":"2007-2013","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5702163051","display_name":null,"funder_award_id":"FP7/2007","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"}],"funders":[{"id":"https://openalex.org/F4320306078","display_name":"U.S. Department of Defense","ror":"https://ror.org/0447fe631"},{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320322263","display_name":"Conseil R\u00e9gional, \u00cele-de-France","ror":"https://ror.org/04ry1rt27"},{"id":"https://openalex.org/F4320333051","display_name":"Intelligence Advanced Research Projects Activity","ror":"https://ror.org/01v3fsc55"},{"id":"https://openalex.org/F4320338295","display_name":"Army Research Laboratory","ror":"https://ror.org/011hc8f90"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2406273144.pdf","grobid_xml":"https://content.openalex.org/works/W2406273144.grobid-xml"},"referenced_works_count":13,"referenced_works":["https://openalex.org/W1507680813","https://openalex.org/W1533861849","https://openalex.org/W1553004968","https://openalex.org/W1663973292","https://openalex.org/W2006626130","https://openalex.org/W2009086942","https://openalex.org/W2034516667","https://openalex.org/W2065554891","https://openalex.org/W2100180150","https://openalex.org/W2107878631","https://openalex.org/W2152928267","https://openalex.org/W2165712214","https://openalex.org/W2587486463"],"related_works":["https://openalex.org/W2102148524","https://openalex.org/W2314720829","https://openalex.org/W4385074335","https://openalex.org/W2626189183","https://openalex.org/W4226285110","https://openalex.org/W2973113505","https://openalex.org/W2765248831","https://openalex.org/W2621951291","https://openalex.org/W2086372684","https://openalex.org/W2994927414"],"abstract_inverted_index":{"In":[0],"this":[1],"paper":[2],"we":[3],"investigate":[4],"the":[5,12,21,24,29,34,68,88,107,117,129],"error":[6,26,70,90],"criteria":[7,32],"that":[8,63],"are":[9],"optimized":[10],"during":[11],"training":[13,136],"of":[14,23,92],"artificial":[15],"neural":[16],"networks":[17],"(ANN).":[18],"We":[19,61],"compare":[20],"bounds":[22],"squared":[25,69],"(SE)":[27],"and":[28,51,109],"crossentropy":[30],"(CE)":[31],"being":[33],"most":[35],"popular":[36],"choices":[37],"in":[38],"stateof-the":[39],"art":[40],"implementations.":[41],"The":[42],"evaluation":[43],"is":[44],"performed":[45],"on":[46,106,116],"automatic":[47,141],"speech":[48,142],"recognition":[49,53,145],"(ASR)":[50],"handwriting":[52,144],"(HWR)":[54],"tasks":[55],"using":[56],"a":[57,77,83,122],"hybrid":[58,134],"HMM-ANN":[59],"model.":[60],"find":[62],"with":[64,82,128],"randomly":[65],"initialized":[66],"weights,":[67],"based":[71],"ANN":[72,139],"does":[73],"not":[74],"converge":[75],"to":[76,104,113],"good":[78,84],"local":[79],"optimum.":[80],"However,":[81],"initialization":[85],"by":[86,120],"pre-training,":[87],"word":[89],"rate":[91],"our":[93],"best":[94],"CE":[95],"trained":[96],"system":[97],"could":[98],"be":[99],"reduced":[100],"from":[101,110],"30.9":[102],"%":[103,112,115],"30.5%":[105],"ASR,":[108],"22.7":[111],"21.9":[114],"HWR":[118],"task":[119],"performing":[121],"few":[123],"additional":[124],"\u201cfine-tuning":[125],"\u201d":[126],"iterations":[127],"SE":[130],"criterion.":[131],"Index":[132],"Terms:":[133],"approach,":[135],"criterion":[137],"for":[138],"training,":[140],"recognition,":[143]},"counts_by_year":[{"year":2026,"cited_by_count":3},{"year":2025,"cited_by_count":5},{"year":2024,"cited_by_count":8},{"year":2023,"cited_by_count":15},{"year":2022,"cited_by_count":25},{"year":2021,"cited_by_count":29},{"year":2020,"cited_by_count":34},{"year":2019,"cited_by_count":25},{"year":2018,"cited_by_count":25},{"year":2017,"cited_by_count":23},{"year":2016,"cited_by_count":13},{"year":2015,"cited_by_count":8},{"year":2014,"cited_by_count":7},{"year":2012,"cited_by_count":1}],"updated_date":"2026-04-11T08:14:18.477133","created_date":"2025-10-10T00:00:00"}
