{"id":"https://openalex.org/W4210756901","doi":"https://doi.org/10.1109/cdc45484.2021.9683271","title":"Deep MinMax Networks","display_name":"Deep MinMax Networks","publication_year":2021,"publication_date":"2021-12-14","ids":{"openalex":"https://openalex.org/W4210756901","doi":"https://doi.org/10.1109/cdc45484.2021.9683271"},"language":"en","primary_location":{"id":"doi:10.1109/cdc45484.2021.9683271","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc45484.2021.9683271","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE Conference on Decision and Control (CDC)","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 60th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://dspace.mit.edu/bitstream/1721.1/155758/2/2306.09253v1.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5071209920","display_name":"Winfried Lohmiller","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Winfried Lohmiller","raw_affiliation_strings":["Massachusetts Institute of Technology,Nonlinear Systems Laboratory,Cambridge,Massachusetts,USA,02139"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology,Nonlinear Systems Laboratory,Cambridge,Massachusetts,USA,02139","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5027119544","display_name":"Philipp Gassert","orcid":null},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Philipp Gassert","raw_affiliation_strings":["Massachusetts Institute of Technology,Nonlinear Systems Laboratory,Cambridge,Massachusetts,USA,02139"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology,Nonlinear Systems Laboratory,Cambridge,Massachusetts,USA,02139","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5044026747","display_name":"Jean-Jacques Slotine","orcid":"https://orcid.org/0000-0002-7161-7812"},"institutions":[{"id":"https://openalex.org/I63966007","display_name":"Massachusetts Institute of Technology","ror":"https://ror.org/042nb2s44","country_code":"US","type":"education","lineage":["https://openalex.org/I63966007"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jean-Jacques Slotine","raw_affiliation_strings":["Massachusetts Institute of Technology,Nonlinear Systems Laboratory,Cambridge,Massachusetts,USA,02139"],"affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology,Nonlinear Systems Laboratory,Cambridge,Massachusetts,USA,02139","institution_ids":["https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5071209920"],"corresponding_institution_ids":["https://openalex.org/I63966007"],"apc_list":null,"apc_paid":null,"fwci":0.0,"has_fulltext":true,"cited_by_count":0,"citation_normalized_percentile":{"value":0.22453319,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":"2929","last_page":"2934"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9991999864578247,"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":0.9991999864578247,"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/T12772","display_name":"Control and Stability of Dynamical Systems","score":0.9990000128746033,"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"}},{"id":"https://openalex.org/T11206","display_name":"Model Reduction and Neural Networks","score":0.9988999962806702,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/minimax","display_name":"Minimax","score":0.6918802857398987},{"id":"https://openalex.org/keywords/observability","display_name":"Observability","score":0.5423056483268738},{"id":"https://openalex.org/keywords/contraction","display_name":"Contraction (grammar)","score":0.5071189403533936},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5009324550628662},{"id":"https://openalex.org/keywords/lyapunov-function","display_name":"Lyapunov function","score":0.4981839656829834},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.47448328137397766},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.4722435176372528},{"id":"https://openalex.org/keywords/stability","display_name":"Stability (learning theory)","score":0.45931509137153625},{"id":"https://openalex.org/keywords/maxima-and-minima","display_name":"Maxima and minima","score":0.43736323714256287},{"id":"https://openalex.org/keywords/function","display_name":"Function (biology)","score":0.4264538586139679},{"id":"https://openalex.org/keywords/saddle-point","display_name":"Saddle point","score":0.4209798574447632},{"id":"https://openalex.org/keywords/exponential-stability","display_name":"Exponential stability","score":0.41926708817481995},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.4110032916069031},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.4093932509422302},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3788676857948303},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.28425052762031555},{"id":"https://openalex.org/keywords/machine-learning","display_name":"Machine learning","score":0.1542169451713562},{"id":"https://openalex.org/keywords/nonlinear-system","display_name":"Nonlinear system","score":0.12811020016670227},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.09324139356613159}],"concepts":[{"id":"https://openalex.org/C149728462","wikidata":"https://www.wikidata.org/wiki/Q751319","display_name":"Minimax","level":2,"score":0.6918802857398987},{"id":"https://openalex.org/C36299963","wikidata":"https://www.wikidata.org/wiki/Q1369844","display_name":"Observability","level":2,"score":0.5423056483268738},{"id":"https://openalex.org/C163415756","wikidata":"https://www.wikidata.org/wiki/Q126473","display_name":"Contraction (grammar)","level":2,"score":0.5071189403533936},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5009324550628662},{"id":"https://openalex.org/C60640748","wikidata":"https://www.wikidata.org/wiki/Q2337858","display_name":"Lyapunov function","level":3,"score":0.4981839656829834},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.47448328137397766},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.4722435176372528},{"id":"https://openalex.org/C112972136","wikidata":"https://www.wikidata.org/wiki/Q7595718","display_name":"Stability (learning theory)","level":2,"score":0.45931509137153625},{"id":"https://openalex.org/C186633575","wikidata":"https://www.wikidata.org/wiki/Q845060","display_name":"Maxima and minima","level":2,"score":0.43736323714256287},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.4264538586139679},{"id":"https://openalex.org/C2681867","wikidata":"https://www.wikidata.org/wiki/Q690935","display_name":"Saddle point","level":2,"score":0.4209798574447632},{"id":"https://openalex.org/C167964875","wikidata":"https://www.wikidata.org/wiki/Q17011487","display_name":"Exponential stability","level":3,"score":0.41926708817481995},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.4110032916069031},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.4093932509422302},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3788676857948303},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.28425052762031555},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","level":1,"score":0.1542169451713562},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.12811020016670227},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09324139356613159},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0},{"id":"https://openalex.org/C126322002","wikidata":"https://www.wikidata.org/wiki/Q11180","display_name":"Internal medicine","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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"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/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C71924100","wikidata":"https://www.wikidata.org/wiki/Q11190","display_name":"Medicine","level":0,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/cdc45484.2021.9683271","is_oa":false,"landing_page_url":"https://doi.org/10.1109/cdc45484.2021.9683271","pdf_url":null,"source":{"id":"https://openalex.org/S4363607724","display_name":"2021 60th IEEE Conference on Decision and Control (CDC)","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":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2021 60th IEEE Conference on Decision and Control (CDC)","raw_type":"proceedings-article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/155758","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/155758","pdf_url":"https://dspace.mit.edu/bitstream/1721.1/155758/2/2306.09253v1.pdf","source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Author","raw_type":"http://purl.org/eprint/type/ConferencePaper"}],"best_oa_location":{"id":"pmh:oai:dspace.mit.edu:1721.1/155758","is_oa":true,"landing_page_url":"https://hdl.handle.net/1721.1/155758","pdf_url":"https://dspace.mit.edu/bitstream/1721.1/155758/2/2306.09253v1.pdf","source":{"id":"https://openalex.org/S4306400425","display_name":"DSpace@MIT (Massachusetts Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I63966007","host_organization_name":"Massachusetts Institute of Technology","host_organization_lineage":["https://openalex.org/I63966007"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by-nc-sa","license_id":"https://openalex.org/licenses/cc-by-nc-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Author","raw_type":"http://purl.org/eprint/type/ConferencePaper"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4210756901.pdf","grobid_xml":"https://content.openalex.org/works/W4210756901.grobid-xml"},"referenced_works_count":5,"referenced_works":["https://openalex.org/W2134889984","https://openalex.org/W2497832900","https://openalex.org/W2623127191","https://openalex.org/W2919115771","https://openalex.org/W4298362508"],"related_works":["https://openalex.org/W1557737441","https://openalex.org/W131971937","https://openalex.org/W1996762907","https://openalex.org/W2095858157","https://openalex.org/W2752635268","https://openalex.org/W2324860879","https://openalex.org/W2021599769","https://openalex.org/W3114201969","https://openalex.org/W2056823902","https://openalex.org/W4234513027"],"abstract_inverted_index":{"While":[0],"much":[1],"progress":[2],"has":[3],"been":[4],"achieved":[5],"over":[6],"the":[7,29,42,77,154,161,175,233],"last":[8],"decades":[9],"in":[10,19,47,227],"neuro-inspired":[11],"machine":[12],"learning,":[13],"there":[14,119],"are":[15,97,102,131,217,225],"still":[16],"fundamental":[17],"problems":[18],"gradient-based":[20],"learning":[21,88,142],"using":[22,165],"combinations":[23],"of":[24,41,53,58,71,79,124,146,160,181,205,232,245],"neurons,":[25,148],"especially":[26],"away":[27],"from":[28],"infinite":[30],"width":[31],"limit.These":[32],"problems,":[33],"such":[34],"as":[35,210],"saddle":[36],"points":[37],"and":[38,49,129,168,247],"suboptimal":[39],"plateaus":[40],"cost":[43],"function,":[44],"can":[45],"lead":[46],"theory":[48],"practice":[50],"to":[51,107,153,178],"failures":[52],"learning.":[54],"In":[55],"addition,":[56],"because":[57],"their":[59],"global":[60,74],"geometry,":[61],"Rectified":[62],"Linear":[63],"Units":[64],"(ReLUs)":[65],"do":[66],"not":[67,98],"allow":[68],"local":[69,87],"adjustment":[70,204],"a":[72,136,143,179,206],"pre-learned":[73],"network,":[75],"making":[76],"incorporation":[78],"new":[80,137,211,223],"data":[81,212],"inefficient.This":[82],"paper":[83],"describes":[84],"an":[85],"alternative":[86],"approach":[89,134],"for":[90,242],"arbitrary":[91],"piece-wise":[92],"linear":[93,147,185],"continuous":[94],"functions.":[95],"Neurons":[96],"superimposed,":[99],"but":[100,127],"rather":[101],"spatially":[103],"separated.":[104],"Also,":[105],"contrary":[106],"classical":[108],"approximations":[109],"based":[110,140],"e.g.":[111],"on":[112,141],"radial":[113],"basis":[114,125],"functions":[115],"or":[116,191],"finite":[117],"elements,":[118],"is":[120,150,163,172,189,197,236,240],"no":[121],"pre-fixed":[122],"set":[123,180],"functions,":[126],"location":[128],"support":[130],"all":[132],"adaptable.The":[133],"yields":[135],"multi-layer":[138],"algorithm":[139,162,176],"MinMax":[144],"combination":[145,188,244],"which":[149,200],"applicable":[151],"directly":[152],"high-dimensional":[155],"case.":[156],"Global":[157],"exponential":[158],"convergence":[159],"established":[164],"Lyapunov":[166,190],"analysis":[167],"contraction":[169,192],"theory.":[170],"It":[171],"shown":[173,241],"that":[174],"corresponds":[177],"separate":[182],"exponentially":[183],"stable":[184,193],"regressions,":[186],"whose":[187],"under":[194],"observability":[195],"conditions.Learning":[196],"fundamentally":[198],"local,":[199],"allows":[201],"simple":[202],"progressive":[203],"previously":[207],"learned":[208],"network":[209],"becomes":[213],"available.":[214],"Unused":[215],"neurons":[216,224],"pruned,":[218],"avoiding":[219],"unnecessary":[220],"over-parameterization.":[221],"Conversely,":[222],"created":[226],"areas":[228],"where":[229],"better":[230],"approximation":[231],"true":[234],"function":[235],"needed.":[237],"Overall":[238],"stability":[239],"this":[243],"pruning":[246],"creation":[248],"mechanisms.":[249]},"counts_by_year":[],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}