{"id":"https://openalex.org/W4386996974","doi":"https://doi.org/10.3390/a16100453","title":"Separable Gaussian Neural Networks: Structure, Analysis, and Function Approximations","display_name":"Separable Gaussian Neural Networks: Structure, Analysis, and Function Approximations","publication_year":2023,"publication_date":"2023-09-22","ids":{"openalex":"https://openalex.org/W4386996974","doi":"https://doi.org/10.3390/a16100453"},"language":"en","primary_location":{"id":"doi:10.3390/a16100453","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16100453","pdf_url":"https://www.mdpi.com/1999-4893/16/10/453/pdf?version=1695606614","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/1999-4893/16/10/453/pdf?version=1695606614","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5003255279","display_name":"Siyuan Xing","orcid":"https://orcid.org/0000-0001-6916-719X"},"institutions":[{"id":"https://openalex.org/I149919469","display_name":"California Polytechnic State University","ror":"https://ror.org/001gpfp45","country_code":"US","type":"education","lineage":["https://openalex.org/I149919469"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Siyuan Xing","raw_affiliation_strings":["Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, California Polytechnic State University, San Luis Obispo, CA 93407, USA","institution_ids":["https://openalex.org/I149919469"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5017350937","display_name":"Jian\u2010Qiao Sun","orcid":"https://orcid.org/0000-0002-5441-7982"},"institutions":[{"id":"https://openalex.org/I156087764","display_name":"University of California, Merced","ror":"https://ror.org/00d9ah105","country_code":"US","type":"education","lineage":["https://openalex.org/I156087764"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jian-Qiao Sun","raw_affiliation_strings":["Department of Mechanical Engineering, School of Engineering, University of California Merced, Merced, CA 95343, USA"],"affiliations":[{"raw_affiliation_string":"Department of Mechanical Engineering, School of Engineering, University of California Merced, Merced, CA 95343, USA","institution_ids":["https://openalex.org/I156087764"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":["https://openalex.org/A5017350937"],"corresponding_institution_ids":["https://openalex.org/I156087764"],"apc_list":{"value":1400,"currency":"CHF","value_usd":1515},"apc_paid":{"value":1400,"currency":"CHF","value_usd":1515},"fwci":1.5657,"has_fulltext":true,"cited_by_count":9,"citation_normalized_percentile":{"value":0.86563363,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":98},"biblio":{"volume":"16","issue":"10","first_page":"453","last_page":"453"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.994700014591217,"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":0.994700014591217,"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":0.9890999794006348,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.9648000001907349,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/hessian-matrix","display_name":"Hessian matrix","score":0.7639224529266357},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.6522712707519531},{"id":"https://openalex.org/keywords/dimension","display_name":"Dimension (graph theory)","score":0.6242586374282837},{"id":"https://openalex.org/keywords/sigmoid-function","display_name":"Sigmoid function","score":0.6112396717071533},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.5591158270835876},{"id":"https://openalex.org/keywords/separable-space","display_name":"Separable space","score":0.5551584959030151},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5245097875595093},{"id":"https://openalex.org/keywords/gaussian-function","display_name":"Gaussian function","score":0.49049443006515503},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.48786163330078125},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4704272747039795},{"id":"https://openalex.org/keywords/radial-basis-function","display_name":"Radial basis function","score":0.4483566880226135},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.44428762793540955},{"id":"https://openalex.org/keywords/basis-function","display_name":"Basis function","score":0.44339683651924133},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"Gradient descent","score":0.4405038058757782},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.3917897045612335},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.38711750507354736},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.23993393778800964},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.23682567477226257},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.11345914006233215}],"concepts":[{"id":"https://openalex.org/C203616005","wikidata":"https://www.wikidata.org/wiki/Q620495","display_name":"Hessian matrix","level":2,"score":0.7639224529266357},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.6522712707519531},{"id":"https://openalex.org/C33676613","wikidata":"https://www.wikidata.org/wiki/Q13415176","display_name":"Dimension (graph theory)","level":2,"score":0.6242586374282837},{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.6112396717071533},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.5591158270835876},{"id":"https://openalex.org/C70710897","wikidata":"https://www.wikidata.org/wiki/Q680081","display_name":"Separable space","level":2,"score":0.5551584959030151},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5245097875595093},{"id":"https://openalex.org/C7218915","wikidata":"https://www.wikidata.org/wiki/Q1054475","display_name":"Gaussian function","level":3,"score":0.49049443006515503},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.48786163330078125},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4704272747039795},{"id":"https://openalex.org/C98856871","wikidata":"https://www.wikidata.org/wiki/Q1588488","display_name":"Radial basis function","level":3,"score":0.4483566880226135},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.44428762793540955},{"id":"https://openalex.org/C5917680","wikidata":"https://www.wikidata.org/wiki/Q2621825","display_name":"Basis function","level":2,"score":0.44339683651924133},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.4405038058757782},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.3917897045612335},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.38711750507354736},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.23993393778800964},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.23682567477226257},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.11345914006233215},{"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},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C62520636","wikidata":"https://www.wikidata.org/wiki/Q944","display_name":"Quantum mechanics","level":1,"score":0.0},{"id":"https://openalex.org/C104114177","wikidata":"https://www.wikidata.org/wiki/Q79782","display_name":"Motion (physics)","level":2,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.3390/a16100453","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16100453","pdf_url":"https://www.mdpi.com/1999-4893/16/10/453/pdf?version=1695606614","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:doaj.org/article:28877750e22a4d9d98440e64712d9c7f","is_oa":true,"landing_page_url":"https://doaj.org/article/28877750e22a4d9d98440e64712d9c7f","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 16, Iss 10, p 453 (2023)","raw_type":"article"}],"best_oa_location":{"id":"doi:10.3390/a16100453","is_oa":true,"landing_page_url":"https://doi.org/10.3390/a16100453","pdf_url":"https://www.mdpi.com/1999-4893/16/10/453/pdf?version=1695606614","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":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4386996974.pdf"},"referenced_works_count":32,"referenced_works":["https://openalex.org/W1594640477","https://openalex.org/W1999433604","https://openalex.org/W2002358485","https://openalex.org/W2034374737","https://openalex.org/W2073713860","https://openalex.org/W2093022009","https://openalex.org/W2110916332","https://openalex.org/W2113442785","https://openalex.org/W2114865067","https://openalex.org/W2116119284","https://openalex.org/W2135894089","https://openalex.org/W2137983211","https://openalex.org/W2143956139","https://openalex.org/W2151205149","https://openalex.org/W2155399784","https://openalex.org/W2158426375","https://openalex.org/W2171277043","https://openalex.org/W2497532187","https://openalex.org/W2582881728","https://openalex.org/W2917723212","https://openalex.org/W2962727772","https://openalex.org/W2968460293","https://openalex.org/W2970971581","https://openalex.org/W3035024835","https://openalex.org/W3125537303","https://openalex.org/W4211093736","https://openalex.org/W4362509393","https://openalex.org/W6638908295","https://openalex.org/W6676656513","https://openalex.org/W6682039458","https://openalex.org/W6713134421","https://openalex.org/W6851205445"],"related_works":["https://openalex.org/W4385957115","https://openalex.org/W2611031068","https://openalex.org/W2061372042","https://openalex.org/W1704347466","https://openalex.org/W3047779762","https://openalex.org/W1996936972","https://openalex.org/W2146794907","https://openalex.org/W2441614350","https://openalex.org/W603561220","https://openalex.org/W3013195559"],"abstract_inverted_index":{"The":[0,155],"Gaussian-radial-basis":[1,51],"function":[2,153],"neural":[3,40],"network":[4,41],"(GRBFNN)":[5],"has":[6,158],"been":[7],"a":[8,35,123,144,176,195],"popular":[9],"choice":[10],"for":[11],"interpolation":[12],"and":[13,60,93,161,169,203],"classification.":[14],"However,":[15],"it":[16,95],"is":[17,27,131,162],"computationally":[18],"intensive":[19],"when":[20],"the":[21,24,47,75,88,99,108,112,199,204],"dimension":[22,101],"of":[23,46,50,77,81,91,111,115,126,140,147,188,194,201,206],"input":[25,55,100],"vector":[26],"high.":[28],"To":[29],"address":[30],"this":[31],"issue,":[32],"we":[33],"propose":[34],"new":[36],"feedforward":[37],"network-separable":[38],"Gaussian":[39,70],"(SGNN)":[42],"by":[43,68],"taking":[44],"advantage":[45],"separable":[48],"property":[49],"functions,":[52],"which":[53,85],"splits":[54],"data":[56],"into":[57,64],"multiple":[58],"columns":[59],"sequentially":[61],"feeds":[62],"them":[63],"parallel":[65],"layers":[66,202],"formed":[67],"uni-variate":[69],"functions.":[71,171],"This":[72],"structure":[73],"reduces":[74],"number":[76,200,205],"neurons":[78,207],"from":[79],"O(Nd)":[80],"GRBFNN":[82,116,150],"to":[83,122,128,182],"O(dN),":[84],"exponentially":[86],"improves":[87],"computational":[89],"speed":[90],"SGNN":[92,105,135,156,179],"makes":[94],"scale":[96],"linearly":[97],"as":[98],"increases.":[102],"In":[103],"addition,":[104],"can":[106,136,180],"preserve":[107],"dominant":[109],"subspace":[110],"Hessian":[113],"matrix":[114],"in":[117],"gradient":[118],"descent":[119],"training,":[120],"leading":[121],"similar":[124,145],"level":[125,146],"accuracy":[127,148],"GRBFNN.":[129],"It":[130],"experimentally":[132],"demonstrated":[133],"that":[134,184],"achieve":[137],"an":[138],"acceleration":[139],"100":[141],"times":[142],"with":[143,167,175,197],"over":[149],"on":[151],"tri-variate":[152],"approximations.":[154],"also":[157],"better":[159],"trainability":[160],"more":[163,190],"tuning-friendly":[164],"than":[165,192],"DNNs":[166],"RuLU":[168],"Sigmoid":[170],"For":[172],"approximating":[173],"functions":[174],"complex":[177],"geometry,":[178],"lead":[181],"results":[183],"are":[185],"three":[186],"orders":[187],"magnitude":[189],"accurate":[191],"those":[193],"RuLU-DNN":[196],"twice":[198],"per":[208],"layer.":[209]},"counts_by_year":[{"year":2025,"cited_by_count":2},{"year":2024,"cited_by_count":6},{"year":2023,"cited_by_count":1}],"updated_date":"2026-03-27T05:58:40.876381","created_date":"2025-10-10T00:00:00"}
