{"id":"https://openalex.org/W4410772205","doi":"https://doi.org/10.1109/tac.2025.3574364","title":"Automatic Implementation of Neural Networks Through Reaction Networks\u2014Part II: Error Analysis","display_name":"Automatic Implementation of Neural Networks Through Reaction Networks\u2014Part II: Error Analysis","publication_year":2025,"publication_date":"2025-05-27","ids":{"openalex":"https://openalex.org/W4410772205","doi":"https://doi.org/10.1109/tac.2025.3574364"},"language":"en","primary_location":{"id":"doi:10.1109/tac.2025.3574364","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3574364","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"},"type":"article","indexed_in":["crossref"],"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/A5110161005","display_name":"Yuzhen Fan","orcid":null},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Yuzhen Fan","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0009-0009-6922-0304","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"middle","author":{"id":null,"display_name":"Xiaoyu Zhang","orcid":"https://orcid.org/0000-0003-1580-2586"},"institutions":[{"id":"https://openalex.org/I76569877","display_name":"Southeast University","ror":"https://ror.org/04ct4d772","country_code":"CN","type":"education","lineage":["https://openalex.org/I76569877"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Xiaoyu Zhang","raw_affiliation_strings":["School of Mathematics, Southeast University, Nanjing, China"],"raw_orcid":"https://orcid.org/0000-0003-1580-2586","affiliations":[{"raw_affiliation_string":"School of Mathematics, Southeast University, Nanjing, China","institution_ids":["https://openalex.org/I76569877"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5067163066","display_name":"Chuanhou Gao","orcid":"https://orcid.org/0000-0001-9030-2042"},"institutions":[{"id":"https://openalex.org/I76130692","display_name":"Zhejiang University","ror":"https://ror.org/00a2xv884","country_code":"CN","type":"education","lineage":["https://openalex.org/I76130692"]}],"countries":["CN"],"is_corresponding":false,"raw_author_name":"Chuanhou Gao","raw_affiliation_strings":["School of Mathematical Sciences, Zhejiang University, Hangzhou, China"],"raw_orcid":"https://orcid.org/0000-0001-9030-2042","affiliations":[{"raw_affiliation_string":"School of Mathematical Sciences, Zhejiang University, Hangzhou, China","institution_ids":["https://openalex.org/I76130692"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5024190334","display_name":"Denis Dochain","orcid":"https://orcid.org/0000-0001-5206-7352"},"institutions":[{"id":"https://openalex.org/I95674353","display_name":"UCLouvain","ror":"https://ror.org/02495e989","country_code":"BE","type":"education","lineage":["https://openalex.org/I95674353"]}],"countries":["BE"],"is_corresponding":false,"raw_author_name":"Denis Dochain","raw_affiliation_strings":["ICTEAM, UCLouvain, B&#x00E2;timent Euler, avenue Georges Lema&#x00EE;tre 4-6, Louvain-la-Neuve, Belgium","ICTEAM, UCLouvain, B&#x02C6;atiment Euler, avenue Georges Lema&#x02C6;&imath;tre 4-6, Louvain-la-Neuve, Belgium"],"raw_orcid":"https://orcid.org/0000-0001-5206-7352","affiliations":[{"raw_affiliation_string":"ICTEAM, UCLouvain, B&#x00E2;timent Euler, avenue Georges Lema&#x00EE;tre 4-6, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]},{"raw_affiliation_string":"ICTEAM, UCLouvain, B&#x02C6;atiment Euler, avenue Georges Lema&#x02C6;&imath;tre 4-6, Louvain-la-Neuve, Belgium","institution_ids":["https://openalex.org/I95674353"]}]}],"institutions":[],"countries_distinct_count":2,"institutions_distinct_count":4,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.04866842,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"70","issue":"10","first_page":"6372","last_page":"6387"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.8737000226974487,"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":0.8737000226974487,"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/artificial-neural-network","display_name":"Artificial neural network","score":0.6592937707901001},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6251826882362366},{"id":"https://openalex.org/keywords/error-analysis","display_name":"Error analysis","score":0.44625362753868103},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.37064820528030396},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.18174874782562256},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.1116996705532074}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6592937707901001},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6251826882362366},{"id":"https://openalex.org/C3018824978","wikidata":"https://www.wikidata.org/wiki/Q2894891","display_name":"Error analysis","level":2,"score":0.44625362753868103},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.37064820528030396},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.18174874782562256},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.1116996705532074}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/tac.2025.3574364","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tac.2025.3574364","pdf_url":null,"source":{"id":"https://openalex.org/S184954342","display_name":"IEEE Transactions on Automatic Control","issn_l":"0018-9286","issn":["0018-9286","1558-2523","2334-3303"],"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 Automatic Control","raw_type":"journal-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[{"id":"https://openalex.org/G1104770628","display_name":null,"funder_award_id":"62303409","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"},{"id":"https://openalex.org/G1173065548","display_name":null,"funder_award_id":"12320101001","funder_id":"https://openalex.org/F4320321001","funder_display_name":"National Natural Science Foundation of China"}],"funders":[{"id":"https://openalex.org/F4320321001","display_name":"National Natural Science Foundation of China","ror":"https://ror.org/01h0zpd94"}],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":24,"referenced_works":["https://openalex.org/W1512198009","https://openalex.org/W1986292487","https://openalex.org/W2000804241","https://openalex.org/W2019582172","https://openalex.org/W2036546758","https://openalex.org/W2247294682","https://openalex.org/W2737153105","https://openalex.org/W2743947100","https://openalex.org/W2775574730","https://openalex.org/W2810268565","https://openalex.org/W2951169596","https://openalex.org/W2952738056","https://openalex.org/W3027256974","https://openalex.org/W3155509232","https://openalex.org/W3160831379","https://openalex.org/W3185748912","https://openalex.org/W3199106546","https://openalex.org/W4210934279","https://openalex.org/W4223610891","https://openalex.org/W4238640588","https://openalex.org/W4281768956","https://openalex.org/W4362671348","https://openalex.org/W4368341979","https://openalex.org/W4408780424"],"related_works":["https://openalex.org/W4391375266","https://openalex.org/W2899084033","https://openalex.org/W2748952813","https://openalex.org/W2390279801","https://openalex.org/W4391913857","https://openalex.org/W2358668433","https://openalex.org/W4396701345","https://openalex.org/W2376932109","https://openalex.org/W2001405890","https://openalex.org/W4396696052"],"abstract_inverted_index":{"Neural":[0],"network":[1,39,89,100],"related":[2],"machine":[3],"learning":[4],"algorithms,":[5],"inspired":[6],"by":[7,152],"biological":[8],"neuron":[9],"interaction":[10],"mechanisms,":[11],"are":[12,223],"advancing":[13],"rapidly":[14],"in":[15,25,53,58,71,102],"the":[16,93,120,137,154,163,178,188,191,197,216,227,235],"field":[17],"of":[18,122,136,210,230],"computing.":[19],"This":[20],"development":[21],"may":[22],"be":[23],"leveraged":[24],"reverse":[26],"to":[27,36,82,95,111,182,225],"advance":[28],"synthetic":[29],"biology":[30],"progress.":[31],"A":[32],"challenging":[33],"exploration":[34],"is":[35,49,108],"implement":[37],"neural":[38,72,88,99],"functionalities":[40],"through":[41],"biochemical":[42,85],"reaction":[43],"networks":[44],"(BCRNs),":[45],"a":[46,84,98,130],"language":[47],"that":[48,63,91],"inherently":[50],"compatible":[51],"with":[52,55,115],"vivo,":[54],"difficulties":[56],"specifically":[57],"constructing":[59],"an":[60,148,211],"appropriate":[61],"BCRN":[62],"respects":[64],"computation":[65],"and":[66,159,162,176,200,239],"information":[67],"processing":[68],"steps":[69],"involved":[70],"networks.":[73],"By":[74],"addressing":[75],"these":[76],"difficulties,":[77],"this":[78,126],"paired":[79],"article":[80],"manages":[81],"develop":[83],"fully":[86],"connected":[87,172],"(BFCNN)":[90],"has":[92],"potential":[94],"behave":[96],"like":[97],"independently":[101],"vivo.":[103],"In":[104,125],"Part":[105],"I,":[106],"BFCNN":[107],"designed":[109,138],"according":[110],"five":[112],"different":[113,170],"modules":[114,171,180],"concrete":[116],"theoretical":[117],"support":[118],"on":[119,219],"stability":[121],"every":[123],"module.":[124],"article,":[127],"we":[128],"establish":[129],"systematic":[131],"framework":[132],"for":[133,190],"error":[134,143,145,165,167,193,232],"analysis":[135],"BFCNN.":[139],"We":[140,185],"introduce":[141],"current":[142],"evaluating":[144],"generation":[146],"within":[147,177],"individual":[149],"computational":[150],"module":[151],"measuring":[153],"deviation":[155],"between":[156],"finite-time":[157],"concentration":[158],"steady-state":[160],"concentration,":[161],"accumulative":[164],"characterizing":[166],"propagation":[168],"across":[169],"via":[173],"oscillatory":[174,212],"signals":[175],"repeated":[179],"due":[181],"multiple":[183],"iterations.":[184],"further":[186],"derive":[187],"formula":[189],"total":[192,231],"upper":[194],"bound":[195],"about":[196,206,234],"iteration":[198,240],"number":[199],"illustrate":[201],"its":[202],"exponential":[203],"convergence":[204],"order":[205],"non-zero":[207,236],"duration":[208,237],"time":[209,238],"signal":[213],"concentration.":[214],"Ultimately,":[215],"numerical":[217],"experiments":[218],"two":[220],"classification":[221],"examples":[222],"made":[224],"exhibit":[226],"change":[228],"tendency":[229],"bounds":[233],"number.":[241]},"counts_by_year":[],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
