{"id":"https://openalex.org/W4315472029","doi":"https://doi.org/10.1109/cdc51059.2022.9992535","title":"A Sequential Greedy Approach for Training Implicit Deep Models","display_name":"A Sequential Greedy Approach for Training Implicit Deep Models","publication_year":2022,"publication_date":"2022-12-06","ids":{"openalex":"https://openalex.org/W4315472029","doi":"https://doi.org/10.1109/cdc51059.2022.9992535"},"language":"en","primary_location":{"id":"doi:10.1109/cdc51059.2022.9992535","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc51059.2022.9992535","pdf_url":null,"source":{"id":"https://openalex.org/S4363607710","display_name":"2022 IEEE 61st 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":"2022 IEEE 61st Conference on Decision and Control (CDC)","raw_type":"proceedings-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/A5086755692","display_name":"Tanmay Gautam","orcid":null},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Tanmay Gautam","raw_affiliation_strings":["Berkeley and VinUniversity,University of California","University of California, Berkeley and VinUniversity"],"affiliations":[{"raw_affiliation_string":"Berkeley and VinUniversity,University of California","institution_ids":[]},{"raw_affiliation_string":"University of California, Berkeley and VinUniversity","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5062099905","display_name":"Brendon G. Anderson","orcid":"https://orcid.org/0000-0001-7239-158X"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Brendon G. Anderson","raw_affiliation_strings":["Berkeley and VinUniversity,University of California","University of California, Berkeley and VinUniversity"],"affiliations":[{"raw_affiliation_string":"Berkeley and VinUniversity,University of California","institution_ids":[]},{"raw_affiliation_string":"University of California, Berkeley and VinUniversity","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5072786751","display_name":"Somayeh Sojoudi","orcid":"https://orcid.org/0000-0001-7177-7712"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Somayeh Sojoudi","raw_affiliation_strings":["Berkeley and VinUniversity,University of California","University of California, Berkeley and VinUniversity"],"affiliations":[{"raw_affiliation_string":"Berkeley and VinUniversity,University of California","institution_ids":[]},{"raw_affiliation_string":"University of California, Berkeley and VinUniversity","institution_ids":["https://openalex.org/I95457486"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5069598493","display_name":"Laurent El Ghaoui","orcid":"https://orcid.org/0000-0002-0499-5610"},"institutions":[{"id":"https://openalex.org/I95457486","display_name":"University of California, Berkeley","ror":"https://ror.org/01an7q238","country_code":"US","type":"education","lineage":["https://openalex.org/I95457486"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Laurent El Ghaoui","raw_affiliation_strings":["Berkeley and VinUniversity,University of California","University of California, Berkeley and VinUniversity"],"affiliations":[{"raw_affiliation_string":"Berkeley and VinUniversity,University of California","institution_ids":[]},{"raw_affiliation_string":"University of California, Berkeley and VinUniversity","institution_ids":["https://openalex.org/I95457486"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5086755692"],"corresponding_institution_ids":["https://openalex.org/I95457486"],"apc_list":null,"apc_paid":null,"fwci":0.06,"has_fulltext":false,"cited_by_count":1,"citation_normalized_percentile":{"value":0.342079,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":"33","issue":null,"first_page":"2751","last_page":"2758"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9980000257492065,"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/T10775","display_name":"Generative Adversarial Networks and Image Synthesis","score":0.9980000257492065,"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/T10812","display_name":"Human Pose and Action Recognition","score":0.9976000189781189,"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/T10036","display_name":"Advanced Neural Network Applications","score":0.9973000288009644,"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/mnist-database","display_name":"MNIST database","score":0.7500569224357605},{"id":"https://openalex.org/keywords/deep-learning","display_name":"Deep learning","score":0.5896337628364563},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5272625684738159},{"id":"https://openalex.org/keywords/block","display_name":"Block (permutation group theory)","score":0.4734618067741394},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4693300127983093},{"id":"https://openalex.org/keywords/differentiable-function","display_name":"Differentiable function","score":0.4471585154533386},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.4464944899082184},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.4429108500480652},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.3853170871734619},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.3602149486541748}],"concepts":[{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.7500569224357605},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5896337628364563},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5272625684738159},{"id":"https://openalex.org/C2777210771","wikidata":"https://www.wikidata.org/wiki/Q4927124","display_name":"Block (permutation group theory)","level":2,"score":0.4734618067741394},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4693300127983093},{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.4471585154533386},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.4464944899082184},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4429108500480652},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.3853170871734619},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3602149486541748},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/cdc51059.2022.9992535","is_oa":false,"landing_page_url":"http://dx.doi.org/10.1109/cdc51059.2022.9992535","pdf_url":null,"source":{"id":"https://openalex.org/S4363607710","display_name":"2022 IEEE 61st 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":"2022 IEEE 61st Conference on Decision and Control (CDC)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[{"display_name":"Sustainable cities and communities","score":0.41999998688697815,"id":"https://metadata.un.org/sdg/11"}],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":39,"referenced_works":["https://openalex.org/W1522301498","https://openalex.org/W1686810756","https://openalex.org/W2110798204","https://openalex.org/W2155007355","https://openalex.org/W2194775991","https://openalex.org/W2331143823","https://openalex.org/W2342840547","https://openalex.org/W2559655401","https://openalex.org/W2750384547","https://openalex.org/W2754252319","https://openalex.org/W2777662428","https://openalex.org/W2963047948","https://openalex.org/W2963446712","https://openalex.org/W2963623651","https://openalex.org/W2963755523","https://openalex.org/W2970900903","https://openalex.org/W2992146231","https://openalex.org/W3034634365","https://openalex.org/W3085131702","https://openalex.org/W3125537303","https://openalex.org/W3201167453","https://openalex.org/W4247541366","https://openalex.org/W4315472029","https://openalex.org/W6626481562","https://openalex.org/W6631190155","https://openalex.org/W6637373629","https://openalex.org/W6676481782","https://openalex.org/W6682849425","https://openalex.org/W6684191040","https://openalex.org/W6704559304","https://openalex.org/W6734728544","https://openalex.org/W6743688258","https://openalex.org/W6747381837","https://openalex.org/W6757376125","https://openalex.org/W6767563556","https://openalex.org/W6779806301","https://openalex.org/W6782808188","https://openalex.org/W6789572788","https://openalex.org/W6848797913"],"related_works":["https://openalex.org/W2950475743","https://openalex.org/W4386603768","https://openalex.org/W2886711096","https://openalex.org/W4380078352","https://openalex.org/W3046591097","https://openalex.org/W2590796488","https://openalex.org/W4389249638","https://openalex.org/W2733410219","https://openalex.org/W2734358244","https://openalex.org/W4388700941"],"abstract_inverted_index":{"Recent":[0],"works":[1],"in":[2,90],"deep":[3,11,44,92,102],"learning":[4],"have":[5],"demonstrated":[6],"impressive":[7],"performance":[8,89],"using":[9],"\"implicit":[10],"models,\"":[12],"wherein":[13],"conventional":[14,91],"architectures":[15],"composed":[16,28],"of":[17,29,79,125,158,197],"forward-propagating,":[18],"differentiable":[19],"parametric":[20],"layers":[21],"are":[22,46],"replaced":[23],"by":[24],"more":[25,202],"expressive":[26],"models":[27,45,103,116,139,226],"an":[30,65,83,147],"implicitly":[31],"defined":[32],"fixed-point":[33,58],"equation":[34,59],"together":[35],"with":[36,104,141],"a":[37,56,95,105,176,187],"prediction":[38],"equation.":[39],"Methods":[40],"for":[41,100,151,194],"training":[42,98,168,175,186],"implicit":[43,101,115,181,231],"currently":[47],"restricted":[48],"to":[49,60,86,94,185,200,225],"end-to-end":[50,230],"optimization,":[51],"which":[52,156],"relies":[53],"on":[54,206,213],"solving":[55],"matrix-variable":[57],"compute":[61],"the":[62,77,133,142,195],"gradient":[63],"and":[64,130,165,208,212,215],"expensive":[66],"projection":[67],"step":[68],"at":[69],"every":[70],"iteration.":[71],"In":[72],"this":[73],"work,":[74],"we":[75,145,171],"extend":[76],"idea":[78],"greedy":[80,97],"layer-wise":[81],"training,":[82],"approach":[84],"found":[85],"yield":[87],"state-of-the-art":[88,229],"learning,":[93],"sequential":[96,153],"algorithm":[99,199,222],"strictly":[106,188],"upper":[107,178,189],"block":[108,123,190],"triangular":[109,179,191],"structure.":[110],"We":[111],"show":[112,219],"that":[113,174,220,227],"such":[114],"can":[117],"be":[118],"regarded":[119],"as":[120],"generalized":[121],"dense":[122],"modules":[124],"Dense":[126],"Convolutional":[127],"Networks":[128],"(DenseNets),":[129],"thus":[131],"inherit":[132],"underlying":[134],"parameter":[135],"efficiency":[136],"property.":[137],"For":[138],"trained":[140],"Euclidean":[143],"loss,":[144],"develop":[146],"alternating":[148,159],"minimization":[149],"subroutine":[150],"our":[152,198,221],"optimization":[154],"algorithm,":[155],"consists":[157],"between":[160],"efficiently-solvable":[161],"least":[162],"squares":[163],"problems":[164],"single":[166],"hidden-layer":[167],"problems.":[169],"Furthermore,":[170],"theoretically":[172],"prove":[173],"non-strictly":[177],"ReLU":[180],"model":[182],"is":[183],"equivalent":[184],"one,":[192],"allowing":[193],"application":[196],"even":[201],"general":[203],"models.":[204],"Experiments":[205],"smooth":[207],"nonsmooth":[209],"function":[210],"interpolation,":[211],"MNIST":[214],"Fashion-MNIST":[216],"classification":[217],"tasks,":[218],"consistently":[223],"converges":[224],"outperform":[228],"learning.":[232]},"counts_by_year":[{"year":2022,"cited_by_count":1}],"updated_date":"2025-12-23T23:11:35.936235","created_date":"2025-10-10T00:00:00"}