{"id":"https://openalex.org/W4411203146","doi":"https://doi.org/10.1109/access.2025.3578826","title":"Quasi-Analytical Least-Squares Generative Adversarial Networks: Further 1-D Results and Extension to Two Data Dimensions","display_name":"Quasi-Analytical Least-Squares Generative Adversarial Networks: Further 1-D Results and Extension to Two Data Dimensions","publication_year":2025,"publication_date":"2025-01-01","ids":{"openalex":"https://openalex.org/W4411203146","doi":"https://doi.org/10.1109/access.2025.3578826"},"language":"en","primary_location":{"id":"doi:10.1109/access.2025.3578826","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3578826","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://doi.org/10.1109/access.2025.3578826","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5057210859","display_name":"G.W. Pulford","orcid":"https://orcid.org/0000-0002-5241-2301"},"institutions":[],"countries":[],"is_corresponding":true,"raw_author_name":"Graham W. Pulford","raw_affiliation_strings":["Independent Consultant, Toulouse, France","Independent consultant, Toulouse, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Independent Consultant, Toulouse, France","institution_ids":[]},{"raw_affiliation_string":"Independent consultant, Toulouse, France","institution_ids":[]}]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5057210859"],"corresponding_institution_ids":[],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":0.0,"has_fulltext":false,"cited_by_count":0,"citation_normalized_percentile":{"value":0.10375867,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":"13","issue":null,"first_page":"107872","last_page":"107889"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10057","display_name":"Face and Expression Recognition","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T10057","display_name":"Face and Expression Recognition","score":0.9904999732971191,"subfield":{"id":"https://openalex.org/subfields/1707","display_name":"Computer Vision and Pattern Recognition"},"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/T11512","display_name":"Anomaly Detection Techniques and Applications","score":0.9848999977111816,"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/T10876","display_name":"Fault Detection and Control Systems","score":0.9786999821662903,"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/extension","display_name":"Extension (predicate logic)","score":0.7743690013885498},{"id":"https://openalex.org/keywords/adversarial-system","display_name":"Adversarial system","score":0.7243331670761108},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.6300716400146484},{"id":"https://openalex.org/keywords/generative-grammar","display_name":"Generative grammar","score":0.5154012441635132},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4487532377243042},{"id":"https://openalex.org/keywords/least-squares-function-approximation","display_name":"Least-squares function approximation","score":0.44421321153640747},{"id":"https://openalex.org/keywords/theoretical-computer-science","display_name":"Theoretical computer science","score":0.3302205801010132},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3248692750930786},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3133643865585327},{"id":"https://openalex.org/keywords/statistics","display_name":"Statistics","score":0.16586819291114807},{"id":"https://openalex.org/keywords/programming-language","display_name":"Programming language","score":0.06500115990638733}],"concepts":[{"id":"https://openalex.org/C2778029271","wikidata":"https://www.wikidata.org/wiki/Q5421931","display_name":"Extension (predicate logic)","level":2,"score":0.7743690013885498},{"id":"https://openalex.org/C37736160","wikidata":"https://www.wikidata.org/wiki/Q1801315","display_name":"Adversarial system","level":2,"score":0.7243331670761108},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6300716400146484},{"id":"https://openalex.org/C39890363","wikidata":"https://www.wikidata.org/wiki/Q36108","display_name":"Generative grammar","level":2,"score":0.5154012441635132},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4487532377243042},{"id":"https://openalex.org/C9936470","wikidata":"https://www.wikidata.org/wiki/Q6510405","display_name":"Least-squares function approximation","level":3,"score":0.44421321153640747},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3302205801010132},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3248692750930786},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3133643865585327},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.16586819291114807},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.06500115990638733},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/access.2025.3578826","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3578826","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},{"id":"pmh:oai:doaj.org/article:3404ac3df93a4b9c80ea3ca7c199d319","is_oa":true,"landing_page_url":"https://doaj.org/article/3404ac3df93a4b9c80ea3ca7c199d319","pdf_url":null,"source":{"id":"https://openalex.org/S4306401280","display_name":"DOAJ (DOAJ: Directory of Open Access Journals)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 13, Pp 107872-107889 (2025)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.1109/access.2025.3578826","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2025.3578826","pdf_url":null,"source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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 Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":36,"referenced_works":["https://openalex.org/W2035141480","https://openalex.org/W2785678896","https://openalex.org/W2904843110","https://openalex.org/W2921353139","https://openalex.org/W2962765321","https://openalex.org/W2964038363","https://openalex.org/W3011847380","https://openalex.org/W3031135612","https://openalex.org/W3114930201","https://openalex.org/W3166639454","https://openalex.org/W3216759837","https://openalex.org/W4206810559","https://openalex.org/W4230959423","https://openalex.org/W4308449531","https://openalex.org/W4324135233","https://openalex.org/W4387562857","https://openalex.org/W4390645393","https://openalex.org/W4402834117","https://openalex.org/W4406610520","https://openalex.org/W6718379498","https://openalex.org/W6739448629","https://openalex.org/W6748356020","https://openalex.org/W6749927861","https://openalex.org/W6751726386","https://openalex.org/W6753312401","https://openalex.org/W6753580626","https://openalex.org/W6764029338","https://openalex.org/W6765779288","https://openalex.org/W6770715010","https://openalex.org/W6785016324","https://openalex.org/W6785092453","https://openalex.org/W6794264631","https://openalex.org/W6798351829","https://openalex.org/W6800538763","https://openalex.org/W6847177113","https://openalex.org/W6875897452"],"related_works":["https://openalex.org/W2502115930","https://openalex.org/W2482350142","https://openalex.org/W4246396837","https://openalex.org/W3126451824","https://openalex.org/W1561927205","https://openalex.org/W3191453585","https://openalex.org/W4297672492","https://openalex.org/W4310988119","https://openalex.org/W4285226279","https://openalex.org/W4288019534"],"abstract_inverted_index":{"Generative":[0],"adversarial":[1],"networks":[2],"(GANs)":[3],"are":[4,99,111,206,331,338],"notoriously":[5],"difficult":[6],"to":[7,32,76,101,176,209,217,266,283,341],"analyse,":[8],"necessitating":[9],"empirical":[10],"studies":[11],"in":[12,28,38,185,274,311],"high":[13,102],"dimensional":[14],"spaces":[15],"that":[16,139,161,236],"suffer":[17],"from":[18],"stochastic":[19,130],"sampling":[20],"noise.":[21],"Quasi-analytical,":[22],"low-dimensional":[23],"GANs":[24],"can":[25,47,214],"be":[26,48,242],"developed":[27,53],"various":[29],"special":[30],"cases":[31],"elucidate":[33],"aspects":[34],"of":[35,45,79,193,246,260,269,278,307,327],"GAN":[36,59,180],"training":[37],"a":[39,243,251,275],"manageable,":[40],"precise":[41,134],"setting":[42,240],"where":[43],"variables":[44],"interest":[46],"easily":[49],"visualised.":[50],"A":[51,291],"previously":[52],"1-D":[54,62,69,106,187,253],"Rayleigh/Square/Exponential/Erf":[55],"(R/S/E/E)":[56],"least":[57],"squares":[58],"(LSGAN),":[60],"with":[61,127,296],"latent":[63],"variable":[64],"<italic":[65,71],"xmlns:mml=\"http://www.w3.org/1998/Math/MathML\"":[66,72,147,149,153,155],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">z</i>":[67],"and":[68,91,118,172,213,314,324],"data":[70,170,287,329],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x</i>,":[73],"is":[74,125,137,162,173,201,234,289,301,305],"extended":[75],"the":[77,114,128,140,169,186,190,194,210,218,237,247,258,267,270,281,312,319,325,328,336],"case":[78],"2-D":[80,85,141,292],"exponentially":[81],"distributed":[82],"data.":[83],"The":[84],"R/S/E/E":[86,142,294],"LSGAN":[87,295],"has":[88,157],"8":[89],"parameters":[90,205,313],"its":[92,204],"dynamics":[93],"under":[94],"gradient":[95],"descent":[96],"ascent":[97],"(GDA)":[98],"analysable":[100],"accuracy":[103],"via":[104],"two":[105],"numerical":[107,183],"integrals.":[108],"Visualisation":[109],"strategies":[110],"given":[112,276],"for":[113,225,263],"cost":[115,315],"(loss)":[116],"function":[117,316],"parameter":[119,299],"trajectories":[120,300],"during":[121],"training.":[122],"Numerical":[123],"performance":[124],"compared":[126],"equivalent":[129],"GDA":[131,248],"algorithm,":[132],"obtaining":[133],"agreement.":[135],"It":[136,233],"shown":[138],"LSGAN,":[143],"which":[144,264],"satisfies":[145],"d<italic":[146,152],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">im</i>(<italic":[148,154],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">z</i>)":[150],"<":[151],"xmlns:xlink=\"http://www.w3.org/1999/xlink\">x</i>),":[156],"an":[158,284],"optimal":[159,195,211,219,238,271],"discriminator":[160,196],"not":[163,166,207,222,339],"differentiable,":[164],"does":[165,221],"depend":[167],"on":[168],"PDF":[171,288],"nowhere":[174],"equal":[175],"1/2,":[177],"contradicting":[178],"conventional":[179],"theory.":[181],"For":[182,250],"simulations":[184],"case,":[188,254],"when":[189,317],"functional":[191],"form":[192],"(a":[197],"scaled":[198],"logistic":[199],"function)":[200],"fixed":[202],"but":[203],"matched":[208],"generator":[212,239,272],"vary,":[215],"convergence":[216,265],"settings":[220],"occur,":[223],"and,":[224],"certain":[226],"initial":[227,261],"settings,":[228],"severe":[229],"error":[230],"propagation":[231],"results.":[232],"proven":[235],"cannot":[241],"stable":[244],"point":[245],"recursion.":[249],"specific":[252],"we":[255],"also":[256],"characterise":[257],"range":[259],"conditions":[262],"neighbourhood":[268],"occurs":[273],"number":[277],"steps.":[279],"Finally,":[280],"extension":[282],"exponential":[285],"mixture":[286,293],"considered.":[290],"bifurcating":[297],"(chaotic)":[298],"exhibited.":[302],"Empirical":[303],"evidence":[304],"provided":[306],"long-term":[308],"oscillatory":[309],"behaviour":[310],"both":[318],"step":[320],"size":[321],"(learning":[322],"rate)":[323],"support":[326],"distribution":[330],"large.":[332],"In":[333],"this":[334],"instance,":[335],"oscillations":[337],"due":[340],"mode":[342],"collapse.":[343]},"counts_by_year":[],"updated_date":"2026-05-06T08:25:59.206177","created_date":"2025-10-10T00:00:00"}