{"id":"https://openalex.org/W2107389842","doi":"https://doi.org/10.1109/72.809096","title":"The \"weight smoothing\" regularization of MLP for Jacobian stabilization","display_name":"The \"weight smoothing\" regularization of MLP for Jacobian stabilization","publication_year":1999,"publication_date":"1999-01-01","ids":{"openalex":"https://openalex.org/W2107389842","doi":"https://doi.org/10.1109/72.809096","mag":"2107389842","pmid":"https://pubmed.ncbi.nlm.nih.gov/18252652"},"language":"en","primary_location":{"id":"doi:10.1109/72.809096","is_oa":false,"landing_page_url":"https://doi.org/10.1109/72.809096","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"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","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/A5055929239","display_name":"Filipe Aires","orcid":"https://orcid.org/0000-0002-9426-866X"},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210087306","display_name":"Laboratoire de M\u00e9t\u00e9orologie Dynamique","ror":"https://ror.org/000ehr937","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I142631665","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I39804081","https://openalex.org/I4210087306","https://openalex.org/I4210145102","https://openalex.org/I4210145102","https://openalex.org/I4210148025"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"F. Aires","raw_affiliation_strings":["Laboratoire de Meteorologie Dynamique du C.N.R.S., Ecole Polytechnique, Palaiseau, France","Laboratoire de M\u00e9t\u00e9orologie Dynamique du C.N.R.S., Ecole Polytechnique, Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de Meteorologie Dynamique du C.N.R.S., Ecole Polytechnique, Palaiseau, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210087306"]},{"raw_affiliation_string":"Laboratoire de M\u00e9t\u00e9orologie Dynamique du C.N.R.S., Ecole Polytechnique, Palaiseau, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210087306"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079034254","display_name":"Michel Schmitt","orcid":"https://orcid.org/0000-0002-5003-1062"},"institutions":[{"id":"https://openalex.org/I70768539","display_name":"\u00c9cole Nationale Sup\u00e9rieure des Mines de Paris","ror":"https://ror.org/04y8cs423","country_code":"FR","type":"education","lineage":["https://openalex.org/I190752583","https://openalex.org/I2746051580","https://openalex.org/I70768539"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"M. Schmitt","raw_affiliation_strings":["L'Ecole Nationale Sup\u00e9rieure des Mines de Paris, Centre de G\u00e9ostatistique, Fontainebleau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"L'Ecole Nationale Sup\u00e9rieure des Mines de Paris, Centre de G\u00e9ostatistique, Fontainebleau, France","institution_ids":["https://openalex.org/I70768539"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5050128429","display_name":"A. Ch\u00e9din","orcid":"https://orcid.org/0000-0003-2010-7561"},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210087306","display_name":"Laboratoire de M\u00e9t\u00e9orologie Dynamique","ror":"https://ror.org/000ehr937","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I142631665","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I39804081","https://openalex.org/I4210087306","https://openalex.org/I4210145102","https://openalex.org/I4210145102","https://openalex.org/I4210148025"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"A. Chedin","raw_affiliation_strings":["Laboratoire de M\u00e9t\u00e9orologie Dynamique du C.N.R.S., Ecole Polytechnique, Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de M\u00e9t\u00e9orologie Dynamique du C.N.R.S., Ecole Polytechnique, Palaiseau, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210087306"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5077103281","display_name":"N. A. Scott","orcid":"https://orcid.org/0000-0002-1583-6965"},"institutions":[{"id":"https://openalex.org/I142476485","display_name":"\u00c9cole Polytechnique","ror":"https://ror.org/05hy3tk52","country_code":"FR","type":"education","lineage":["https://openalex.org/I142476485","https://openalex.org/I4210145102"]},{"id":"https://openalex.org/I4210087306","display_name":"Laboratoire de M\u00e9t\u00e9orologie Dynamique","ror":"https://ror.org/000ehr937","country_code":"FR","type":"facility","lineage":["https://openalex.org/I1294671590","https://openalex.org/I1294671590","https://openalex.org/I142476485","https://openalex.org/I142631665","https://openalex.org/I2746051580","https://openalex.org/I29607241","https://openalex.org/I39804081","https://openalex.org/I4210087306","https://openalex.org/I4210145102","https://openalex.org/I4210145102","https://openalex.org/I4210148025"]}],"countries":["FR"],"is_corresponding":false,"raw_author_name":"N. Scott","raw_affiliation_strings":["Laboratoire de M\u00e9t\u00e9orologie Dynamique du C.N.R.S., Ecole Polytechnique, Palaiseau, France"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Laboratoire de M\u00e9t\u00e9orologie Dynamique du C.N.R.S., Ecole Polytechnique, Palaiseau, France","institution_ids":["https://openalex.org/I142476485","https://openalex.org/I4210087306"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":1.4381,"has_fulltext":false,"cited_by_count":48,"citation_normalized_percentile":{"value":0.82574124,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":99},"biblio":{"volume":"10","issue":"6","first_page":"1502","last_page":"1510"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9944000244140625,"subfield":{"id":"https://openalex.org/subfields/3109","display_name":"Statistical and Nonlinear Physics"},"field":{"id":"https://openalex.org/fields/31","display_name":"Physics and Astronomy"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10466","display_name":"Meteorological Phenomena and Simulations","score":0.9897000193595886,"subfield":{"id":"https://openalex.org/subfields/1902","display_name":"Atmospheric Science"},"field":{"id":"https://openalex.org/fields/19","display_name":"Earth and Planetary Sciences"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T10688","display_name":"Image and Signal Denoising Methods","score":0.9884999990463257,"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/smoothing","display_name":"Smoothing","score":0.7074735760688782},{"id":"https://openalex.org/keywords/jacobian-matrix-and-determinant","display_name":"Jacobian matrix and determinant","score":0.5999837517738342},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.544032633304596},{"id":"https://openalex.org/keywords/discretization","display_name":"Discretization","score":0.5332118272781372},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.48425790667533875},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.470251202583313},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4348737597465515},{"id":"https://openalex.org/keywords/regularization","display_name":"Regularization (linguistics)","score":0.4213537275791168},{"id":"https://openalex.org/keywords/robustness","display_name":"Robustness (evolution)","score":0.4213183522224426},{"id":"https://openalex.org/keywords/scalar","display_name":"Scalar (mathematics)","score":0.41783928871154785},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4059329926967621},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33761054277420044},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.1799599528312683},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.16658321022987366}],"concepts":[{"id":"https://openalex.org/C3770464","wikidata":"https://www.wikidata.org/wiki/Q775963","display_name":"Smoothing","level":2,"score":0.7074735760688782},{"id":"https://openalex.org/C200331156","wikidata":"https://www.wikidata.org/wiki/Q506041","display_name":"Jacobian matrix and determinant","level":2,"score":0.5999837517738342},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.544032633304596},{"id":"https://openalex.org/C73000952","wikidata":"https://www.wikidata.org/wiki/Q17007827","display_name":"Discretization","level":2,"score":0.5332118272781372},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.48425790667533875},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.470251202583313},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4348737597465515},{"id":"https://openalex.org/C2776135515","wikidata":"https://www.wikidata.org/wiki/Q17143721","display_name":"Regularization (linguistics)","level":2,"score":0.4213537275791168},{"id":"https://openalex.org/C63479239","wikidata":"https://www.wikidata.org/wiki/Q7353546","display_name":"Robustness (evolution)","level":3,"score":0.4213183522224426},{"id":"https://openalex.org/C57691317","wikidata":"https://www.wikidata.org/wiki/Q1289248","display_name":"Scalar (mathematics)","level":2,"score":0.41783928871154785},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4059329926967621},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33761054277420044},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.1799599528312683},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.16658321022987366},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"doi:10.1109/72.809096","is_oa":false,"landing_page_url":"https://doi.org/10.1109/72.809096","pdf_url":null,"source":{"id":"https://openalex.org/S42080949","display_name":"IEEE Transactions on Neural Networks","issn_l":"1045-9227","issn":["1045-9227","1941-0093"],"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","raw_type":"journal-article"},{"id":"pmid:18252652","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/18252652","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","raw_type":"Journal Article"},{"id":"pmh:oai:CiteSeerX.psu:10.1.1.419.1207","is_oa":false,"landing_page_url":"http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.419.1207","pdf_url":null,"source":null,"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"http://www.lmd.jussieu.fr/~falmd/articles/1999_AiresSchmitt.pdf","raw_type":"text"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":20,"referenced_works":["https://openalex.org/W1968178976","https://openalex.org/W1981025032","https://openalex.org/W2005140191","https://openalex.org/W2043968544","https://openalex.org/W2076118331","https://openalex.org/W2077437848","https://openalex.org/W2080278412","https://openalex.org/W2091344992","https://openalex.org/W2111406701","https://openalex.org/W2112594540","https://openalex.org/W2143956139","https://openalex.org/W2147874666","https://openalex.org/W2148603752","https://openalex.org/W2149846618","https://openalex.org/W2163577891","https://openalex.org/W2175384239","https://openalex.org/W2286699414","https://openalex.org/W2316478175","https://openalex.org/W4254721730","https://openalex.org/W4285719527"],"related_works":["https://openalex.org/W1974670814","https://openalex.org/W1976727549","https://openalex.org/W2397650592","https://openalex.org/W2075929579","https://openalex.org/W2087715118","https://openalex.org/W2015590640","https://openalex.org/W2957740688","https://openalex.org/W425311387","https://openalex.org/W3088316828","https://openalex.org/W3202260829"],"abstract_inverted_index":{"In":[0,21,84,112],"an":[1,32,38,137,160,224],"approximation":[2,42,67,88,133,202],"problem":[3,139,196],"with":[4,35,91],"a":[5,8,18,50,72,81,95,105,161,165,170,192],"neural":[6,123,201],"network,":[7],"low-output":[9],"root":[10],"mean":[11],"square":[12],"(rms)":[13],"error":[14],"is":[15,89],"not":[16],"always":[17],"universal":[19],"criterion.":[20],"this":[22,85,113,218],"paper,":[23],"we":[24,62],"investigate":[25],"problems":[26],"where":[27],"the":[28,41,57,66,87,92,119,132,147,154,181,184,200,204,212,229,232],"Jacobians--first":[29],"derivative":[30],"of":[31,68,74,98,108,122,129,134,156,183,203,207,217,231],"output":[33],"value":[34],"respect":[36,117],"to":[37,48,80,118,152,227],"input":[39,100,120],"value--of":[40],"model":[43,206,219],"are":[44,125,220],"needed":[45],"and":[46,168,172,194],"propose":[47,151],"add":[49],"quality":[51],"criterion":[52],"on":[53,65,191],"these":[54],"Jacobians":[55,124,216,233],"during":[56],"learning":[58,148,174],"step.":[59],"More":[60],"specifically,":[61],"focus":[63],"here":[64],"functionals":[69],"A;":[70],"from":[71,198],"space":[73],"continuous":[75],"functions":[76],"(discretized":[77],"in":[78,211,223],"pratice)":[79],"scalar":[82],"space.":[83],"case,":[86,114],"confronted":[90],"compensation":[93],"phenomenon:":[94],"lower":[96],"contribution":[97],"one":[99,107],"can":[101,143],"be":[102,144],"compensated":[103],"by":[104,146,188],"larger":[106],"its":[109],"neighboring":[110],"inputs.":[111],"profiles":[115,158],"(with":[116],"index)":[121],"very":[126],"irregular":[127],"instead":[128],"smooth.":[130],"Then,":[131],"A":[135],"becomes":[136],"ill-posed":[138],"because":[140],"many":[141],"solutions":[142],"chosen":[145],"process.":[149],"We":[150,179],"introduce":[153],"smoothness":[155],"Jacobian":[157],"as":[159],"priori":[162],"information":[163],"via":[164],"regularization":[166],"technique":[167],"develop":[169],"new":[171],"efficient":[173],"algorithm,":[175],"called":[176],"\"weight":[177],"smoothing.\"":[178],"assess":[180],"robustness":[182],"weight":[185,235],"smoothing":[186],"algorithm":[187],"testing":[189],"it":[190],"real":[193],"complex":[195],"stemming":[197],"meteorology:":[199],"forward":[205],"radiative":[208],"transfer":[209],"equation":[210],"atmosphere.":[213],"The":[214],"stabilized":[215],"then":[221],"used":[222],"inversion":[225],"process":[226],"illustrate":[228],"improvement":[230],"after":[234],"smoothing.":[236]},"counts_by_year":[{"year":2026,"cited_by_count":4},{"year":2024,"cited_by_count":4},{"year":2023,"cited_by_count":1},{"year":2022,"cited_by_count":2},{"year":2021,"cited_by_count":3},{"year":2020,"cited_by_count":3},{"year":2019,"cited_by_count":2},{"year":2018,"cited_by_count":1},{"year":2014,"cited_by_count":1},{"year":2013,"cited_by_count":3}],"updated_date":"2026-08-26T07:47:46.906454","created_date":"2025-10-10T00:00:00"}
