{"id":"https://openalex.org/W4389665136","doi":"https://doi.org/10.1109/tnnls.2023.3339512","title":"Universality and Approximation Bounds for Echo State Networks With Random Weights","display_name":"Universality and Approximation Bounds for Echo State Networks With Random Weights","publication_year":2023,"publication_date":"2023-12-13","ids":{"openalex":"https://openalex.org/W4389665136","doi":"https://doi.org/10.1109/tnnls.2023.3339512","pmid":"https://pubmed.ncbi.nlm.nih.gov/38090874"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2023.3339512","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3339512","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 and Learning Systems","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/A5100332677","display_name":"Zhen Li","orcid":"https://orcid.org/0000-0003-3749-342X"},"institutions":[{"id":"https://openalex.org/I2250955327","display_name":"Huawei Technologies (China)","ror":"https://ror.org/00cmhce21","country_code":"CN","type":"company","lineage":["https://openalex.org/I2250955327"]}],"countries":["CN"],"is_corresponding":true,"raw_author_name":"Zhen Li","raw_affiliation_strings":["Theory Laboratory, Huawei Technologies Company Ltd., Shenzhen, China"],"affiliations":[{"raw_affiliation_string":"Theory Laboratory, Huawei Technologies Company Ltd., Shenzhen, China","institution_ids":["https://openalex.org/I2250955327"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5060388088","display_name":"Yunfei Yang","orcid":"https://orcid.org/0000-0001-7231-4816"},"institutions":[{"id":"https://openalex.org/I168719708","display_name":"City University of Hong Kong","ror":"https://ror.org/03q8dnn23","country_code":"HK","type":"education","lineage":["https://openalex.org/I168719708"]},{"id":"https://openalex.org/I200769079","display_name":"Hong Kong University of Science and Technology","ror":"https://ror.org/00q4vv597","country_code":"HK","type":"education","lineage":["https://openalex.org/I200769079"]}],"countries":["HK"],"is_corresponding":false,"raw_author_name":"Yunfei Yang","raw_affiliation_strings":["Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China","Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, Hong Kong","Department of Mathematics, City University of Hong Kong, Hong Kong, Hong Kong"],"affiliations":[{"raw_affiliation_string":"Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, China","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"Department of Mathematics, The Hong Kong University of Science and Technology, Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I200769079"]},{"raw_affiliation_string":"Department of Mathematics, City University of Hong Kong, Hong Kong, Hong Kong","institution_ids":["https://openalex.org/I168719708"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5100332677"],"corresponding_institution_ids":["https://openalex.org/I2250955327"],"apc_list":null,"apc_paid":null,"fwci":0.8625,"has_fulltext":false,"cited_by_count":5,"citation_normalized_percentile":{"value":0.79760877,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"36","issue":"2","first_page":"2720","last_page":"2732"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T12611","display_name":"Neural Networks and Reservoir Computing","score":1.0,"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/T12611","display_name":"Neural Networks and Reservoir Computing","score":1.0,"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/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9958999752998352,"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"}},{"id":"https://openalex.org/T10232","display_name":"Optical Network Technologies","score":0.991100013256073,"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/universality","display_name":"Universality (dynamical systems)","score":0.8758699297904968},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.49322956800460815},{"id":"https://openalex.org/keywords/invariant","display_name":"Invariant (physics)","score":0.4741781949996948},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3524599075317383},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.3343684673309326},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.09841260313987732},{"id":"https://openalex.org/keywords/quantum-mechanics","display_name":"Quantum mechanics","score":0.08230865001678467}],"concepts":[{"id":"https://openalex.org/C183992945","wikidata":"https://www.wikidata.org/wiki/Q2495574","display_name":"Universality (dynamical systems)","level":2,"score":0.8758699297904968},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.49322956800460815},{"id":"https://openalex.org/C190470478","wikidata":"https://www.wikidata.org/wiki/Q2370229","display_name":"Invariant (physics)","level":2,"score":0.4741781949996948},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3524599075317383},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.3343684673309326},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.09841260313987732},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.08230865001678467},{"id":"https://openalex.org/C37914503","wikidata":"https://www.wikidata.org/wiki/Q156495","display_name":"Mathematical physics","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/tnnls.2023.3339512","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2023.3339512","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"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 and Learning Systems","raw_type":"journal-article"},{"id":"pmid:38090874","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38090874","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 and learning systems","raw_type":null},{"id":"pmh:oai:repository.hkust.edu.hk:1783.1-135058","is_oa":false,"landing_page_url":"https://repository.hkust.edu.hk/ir/Record/1783.1-135058","pdf_url":null,"source":{"id":"https://openalex.org/S4306401796","display_name":"Rare & Special e-Zone (The Hong Kong University of Science and Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I200769079","host_organization_name":"Hong Kong University of Science and Technology","host_organization_lineage":["https://openalex.org/I200769079"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":40,"referenced_works":["https://openalex.org/W1582706191","https://openalex.org/W1968172088","https://openalex.org/W1988115241","https://openalex.org/W1989312953","https://openalex.org/W2026131661","https://openalex.org/W2103179919","https://openalex.org/W2103496339","https://openalex.org/W2111072639","https://openalex.org/W2118706537","https://openalex.org/W2128904261","https://openalex.org/W2141695047","https://openalex.org/W2148520247","https://openalex.org/W2158581396","https://openalex.org/W2160068178","https://openalex.org/W2166116275","https://openalex.org/W2171865010","https://openalex.org/W2479467733","https://openalex.org/W2579923771","https://openalex.org/W2803636134","https://openalex.org/W2887258823","https://openalex.org/W2963003308","https://openalex.org/W2963819248","https://openalex.org/W2982551457","https://openalex.org/W2992906545","https://openalex.org/W3006049408","https://openalex.org/W3025101483","https://openalex.org/W3099745170","https://openalex.org/W3125537303","https://openalex.org/W3128485317","https://openalex.org/W3165099133","https://openalex.org/W4226239178","https://openalex.org/W4236362309","https://openalex.org/W4245577611","https://openalex.org/W4288578125","https://openalex.org/W4298379935","https://openalex.org/W6732517885","https://openalex.org/W6746233556","https://openalex.org/W6758500826","https://openalex.org/W6763833559","https://openalex.org/W6770111215"],"related_works":["https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W4391375266","https://openalex.org/W1979597421","https://openalex.org/W2007980826","https://openalex.org/W2061531152","https://openalex.org/W3002753104","https://openalex.org/W2077600819","https://openalex.org/W1587914261","https://openalex.org/W2065095781"],"abstract_inverted_index":{"We":[0,112],"study":[1],"the":[2,20,56,73,82,87,115,119],"uniform":[3],"approximation":[4,116],"of":[5,118],"echo":[6],"state":[7],"networks":[8],"(ESNs)":[9],"with":[10,40,96],"randomly":[11],"generated":[12],"internal":[13,83],"weights.":[14],"These":[15],"models,":[16],"in":[17,31],"which":[18],"only":[19],"readout":[21],"weights":[22,84],"are":[23,43],"optimized":[24],"during":[25],"training,":[26],"have":[27],"made":[28],"empirical":[29],"success":[30],"learning":[32],"dynamical":[33],"systems.":[34],"Recent":[35],"results":[36],"showed":[37],"that":[38,55,86],"ESNs":[39,122],"ReLU":[41,102,121],"activation":[42,61,74],"universal.":[44],"In":[45,99],"this":[46],"article,":[47],"we":[48,104],"give":[49,105],"an":[50],"alternative":[51],"construction":[52,107],"and":[53],"prove":[54],"universality":[57],"holds":[58],"for":[59,81,101,108,123],"general":[60],"functions.":[62],"Specifically,":[63],"our":[64],"main":[65],"result":[66],"shows":[67],"that,":[68],"under":[69],"certain":[70],"condition":[71],"on":[72],"function,":[75],"there":[76],"exists":[77],"a":[78],"sampling":[79,110],"procedure":[80],"so":[85],"ESN":[88],"can":[89],"approximate":[90],"any":[91],"continuous":[92],"casual":[93],"time-invariant":[94],"operators":[95],"high":[97],"probability.":[98],"particular,":[100],"activation,":[103],"explicit":[106],"these":[109],"procedures.":[111],"also":[113],"quantify":[114],"error":[117],"constructed":[120],"sufficiently":[124],"regular":[125],"operators.":[126]},"counts_by_year":[{"year":2025,"cited_by_count":4},{"year":2023,"cited_by_count":1}],"updated_date":"2026-04-13T07:58:08.660418","created_date":"2025-10-10T00:00:00"}
