{"id":"https://openalex.org/W4407585209","doi":"https://doi.org/10.3390/a18020104","title":"A Training Algorithm for Locally Recurrent Neural Networks Based on the Explicit Gradient of the Loss Function","display_name":"A Training Algorithm for Locally Recurrent Neural Networks Based on the Explicit Gradient of the Loss Function","publication_year":2025,"publication_date":"2025-02-14","ids":{"openalex":"https://openalex.org/W4407585209","doi":"https://doi.org/10.3390/a18020104"},"language":"en","primary_location":{"id":"doi:10.3390/a18020104","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18020104","pdf_url":"https://www.mdpi.com/1999-4893/18/2/104/pdf?version=1739523074","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://www.mdpi.com/1999-4893/18/2/104/pdf?version=1739523074","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5040365981","display_name":"Sara Carcangiu","orcid":"https://orcid.org/0000-0002-0270-6432"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":false,"raw_author_name":"Sara Carcangiu","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Cagliari, 09124 Cagliari, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Cagliari, 09124 Cagliari, Italy","institution_ids":["https://openalex.org/I172446870"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5078463546","display_name":"Augusto Montisci","orcid":"https://orcid.org/0000-0003-0008-2985"},"institutions":[{"id":"https://openalex.org/I172446870","display_name":"University of Cagliari","ror":"https://ror.org/003109y17","country_code":"IT","type":"education","lineage":["https://openalex.org/I172446870"]}],"countries":["IT"],"is_corresponding":true,"raw_author_name":"Augusto Montisci","raw_affiliation_strings":["Department of Electrical and Electronic Engineering, University of Cagliari, 09124 Cagliari, Italy"],"affiliations":[{"raw_affiliation_string":"Department of Electrical and Electronic Engineering, University of Cagliari, 09124 Cagliari, Italy","institution_ids":["https://openalex.org/I172446870"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5078463546"],"corresponding_institution_ids":["https://openalex.org/I172446870"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.01017528,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"18","issue":"2","first_page":"104","last_page":"104"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9990000128746033,"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":0.9990000128746033,"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/T12676","display_name":"Machine Learning and ELM","score":0.9925000071525574,"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/T13717","display_name":"Advanced Algorithms and Applications","score":0.9891999959945679,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems 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/computer-science","display_name":"Computer science","score":0.6143171787261963},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5946450233459473},{"id":"https://openalex.org/keywords/training","display_name":"Training (meteorology)","score":0.5943990349769592},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.5869249701499939},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5402888655662537},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3666214346885681},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.0935559868812561}],"concepts":[{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6143171787261963},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5946450233459473},{"id":"https://openalex.org/C2777211547","wikidata":"https://www.wikidata.org/wiki/Q17141490","display_name":"Training (meteorology)","level":2,"score":0.5943990349769592},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.5869249701499939},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5402888655662537},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3666214346885681},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0935559868812561},{"id":"https://openalex.org/C153294291","wikidata":"https://www.wikidata.org/wiki/Q25261","display_name":"Meteorology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.3390/a18020104","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18020104","pdf_url":"https://www.mdpi.com/1999-4893/18/2/104/pdf?version=1739523074","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},{"id":"pmh:oai:iris.unica.it:11584/447845","is_oa":true,"landing_page_url":"https://www.mdpi.com/1999-4893/18/2/104","pdf_url":"https://www.mdpi.com/1999-4893/18/2/104/pdf","source":{"id":"https://openalex.org/S4377196293","display_name":"UNICA IRIS Institutional Research Information System (University of Cagliari)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I172446870","host_organization_name":"University of Cagliari","host_organization_lineage":["https://openalex.org/I172446870"],"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":"info:eu-repo/semantics/article"},{"id":"pmh:oai:doaj.org/article:e1ea637efcfe425b9346c533ec2ab1b2","is_oa":true,"landing_page_url":"https://doaj.org/article/e1ea637efcfe425b9346c533ec2ab1b2","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Algorithms, Vol 18, Iss 2, p 104 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a18020104","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a18020104","pdf_url":"https://www.mdpi.com/1999-4893/18/2/104/pdf?version=1739523074","source":{"id":"https://openalex.org/S190629608","display_name":"Algorithms","issn_l":"1999-4893","issn":["1999-4893"],"is_oa":true,"is_in_doaj":true,"is_core":true,"host_organization":"https://openalex.org/P4310310987","host_organization_name":"Multidisciplinary Digital Publishing Institute","host_organization_lineage":["https://openalex.org/P4310310987"],"host_organization_lineage_names":["Multidisciplinary Digital Publishing Institute"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Algorithms","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1857088242","display_name":null,"funder_award_id":"Mission 4","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G2974696270","display_name":null,"funder_award_id":"Component 2","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3111988204","display_name":null,"funder_award_id":"11.10.2022","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G3146550615","display_name":null,"funder_award_id":"PE000002","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G3587303335","display_name":null,"funder_award_id":"Resilience Plan (NRRP)","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G3843967785","display_name":null,"funder_award_id":"Mission 4","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G4447653093","display_name":null,"funder_award_id":"Network","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4740527787","display_name":null,"funder_award_id":"CUP F53C22000770007","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G4807752964","display_name":null,"funder_award_id":"PE0000021","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G5753995467","display_name":null,"funder_award_id":"PE0000021","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G6761578532","display_name":null,"funder_award_id":"CUP F53C22000770007","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G7701723471","display_name":null,"funder_award_id":"Component 2","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"},{"id":"https://openalex.org/G8386731437","display_name":null,"funder_award_id":"Resilience Plan (NRRP)","funder_id":"https://openalex.org/F4320320300","funder_display_name":"European Commission"},{"id":"https://openalex.org/G887653052","display_name":null,"funder_award_id":"F53C22000770007","funder_id":"https://openalex.org/F4320331528","funder_display_name":"Ministero dell'Universit\u00e0 e della Ricerca"}],"funders":[{"id":"https://openalex.org/F4320320300","display_name":"European Commission","ror":"https://ror.org/00k4n6c32"},{"id":"https://openalex.org/F4320331528","display_name":"Ministero dell'Universit\u00e0 e della Ricerca","ror":null}],"has_content":{"pdf":true,"grobid_xml":false},"content_urls":{"pdf":"https://content.openalex.org/works/W4407585209.pdf"},"referenced_works_count":25,"referenced_works":["https://openalex.org/W1485981043","https://openalex.org/W1982470977","https://openalex.org/W1996773027","https://openalex.org/W1997449813","https://openalex.org/W2006544565","https://openalex.org/W2025333006","https://openalex.org/W2039053838","https://openalex.org/W2105861781","https://openalex.org/W2108517517","https://openalex.org/W2110075977","https://openalex.org/W2110485445","https://openalex.org/W2115072676","https://openalex.org/W2116241688","https://openalex.org/W2124889695","https://openalex.org/W2126434873","https://openalex.org/W2127589108","https://openalex.org/W2132394702","https://openalex.org/W2139842256","https://openalex.org/W2150355110","https://openalex.org/W2500385585","https://openalex.org/W2598251739","https://openalex.org/W3007307343","https://openalex.org/W3204647170","https://openalex.org/W4377012581","https://openalex.org/W4393382892"],"related_works":["https://openalex.org/W2051487156","https://openalex.org/W230091440","https://openalex.org/W2073681303","https://openalex.org/W2233261550","https://openalex.org/W2810751659","https://openalex.org/W258997015","https://openalex.org/W2997094352","https://openalex.org/W3216976533","https://openalex.org/W100620283","https://openalex.org/W2495260952"],"abstract_inverted_index":{"In":[0],"this":[1,97],"paper,":[2],"a":[3],"new":[4],"algorithm":[5,43,59],"for":[6],"the":[7,25,29,32,35,41,45,49,52,62,68,85,89,99,102,106,120,124,127],"training":[8,107],"of":[9,31,40,51,64,70,88,101,119,126],"Locally":[10],"Recurrent":[11],"Neural":[12],"Networks":[13],"(LRNNs)":[14],"is":[15,44],"presented,":[16],"which":[17,75,122],"aims":[18],"to":[19,47,79,91,96],"reduce":[20],"computational":[21],"complexity":[22],"and":[23,112],"at":[24],"same":[26],"time":[27],"guarantee":[28],"stability":[30,125],"network":[33],"during":[34,105],"training.":[36],"The":[37,58],"main":[38],"feature":[39],"proposed":[42],"capability":[46],"represent":[48],"gradient":[50,100],"error":[53],"in":[54,117],"an":[55,71],"explicit":[56],"form.":[57],"builds":[60],"on":[61],"interpretation":[63],"Fibonacci\u2019s":[65],"sequence":[66,90],"as":[67],"output":[69],"IIR":[72],"second-order":[73],"filter,":[74],"makes":[76],"it":[77,113],"possible":[78],"use":[80],"Binet\u2019s":[81],"formula":[82],"that":[83],"allows":[84],"generic":[86],"terms":[87,118],"be":[92,109,115],"calculated":[93],"directly.":[94],"Thanks":[95],"approach,":[98],"loss":[103],"function":[104],"can":[108,114],"explicitly":[110],"calculated,":[111],"expressed":[116],"parameters,":[121],"control":[123],"neural":[128],"network.":[129]},"counts_by_year":[],"updated_date":"2026-04-19T08:26:33.389920","created_date":"2025-02-15T00:00:00"}