{"id":"https://openalex.org/W3128200149","doi":"https://doi.org/10.48550/arxiv.2102.03869","title":"Structured Sparsity Inducing Adaptive Optimizers for Deep Learning","display_name":"Structured Sparsity Inducing Adaptive Optimizers for Deep Learning","publication_year":2021,"publication_date":"2021-02-07","ids":{"openalex":"https://openalex.org/W3128200149","doi":"https://doi.org/10.48550/arxiv.2102.03869","mag":"3128200149"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2102.03869","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.03869","pdf_url":"https://arxiv.org/pdf/2102.03869","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"volume":null,"type":"preprint","indexed_in":["arxiv","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2102.03869","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5074204532","display_name":"Tristan Deleu","orcid":"https://orcid.org/0009-0005-1943-3484","observed_orcids":["https://orcid.org/0009-0005-1943-3484"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Deleu, Tristan","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]},{"author_position":"last","author":{"id":"https://openalex.org/A5086198262","display_name":"Yoshua Bengio","orcid":"https://orcid.org/0000-0002-9322-3515","observed_orcids":["https://orcid.org/0000-0002-9322-3515"]},"institutions":[],"countries":[],"is_corresponding":false,"raw_author_name":"Bengio, Yoshua","raw_affiliation_strings":[],"raw_orcid":null,"affiliations":[]}],"institutions":[],"countries_distinct_count":0,"institutions_distinct_count":0,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":5,"citation_normalized_percentile":null,"cited_by_percentile_year":null,"biblio":{"volume":null,"issue":null,"first_page":null,"last_page":null},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.4975999891757965,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10500","display_name":"Sparse and Compressive Sensing Techniques","score":0.4975999891757965,"subfield":{"id":"https://openalex.org/subfields/2206","display_name":"Computational Mechanics"},"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.30880001187324524,"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":0.11110000312328339,"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/structured-sparsity","display_name":"structured sparsity","score":0.9959999918937683},{"id":"https://openalex.org/keywords/neural-network-pruning","display_name":"neural network pruning","score":0.8450000286102295},{"id":"https://openalex.org/keywords/adaptive-optimization","display_name":"adaptive optimization","score":0.6010000109672546},{"id":"https://openalex.org/keywords/proximal-gradient-method","display_name":"proximal gradient method","score":0.9229999780654907},{"id":"https://openalex.org/keywords/convergence-guarantees","display_name":"convergence guarantees","score":0.9010000228881836},{"id":"https://openalex.org/keywords/sparsity-inducing-penalties","display_name":"sparsity-inducing penalties","score":0.6370000243186951},{"id":"https://openalex.org/keywords/deep-learning","display_name":"deep learning","score":0.5230000019073486}],"concepts":[{"id":"https://openalex.org/C202615002","wikidata":"https://www.wikidata.org/wiki/Q783507","display_name":"Differentiable function","level":2,"score":0.746990442276001},{"id":"https://openalex.org/C2778770139","wikidata":"https://www.wikidata.org/wiki/Q1966904","display_name":"Solver","level":2,"score":0.7432180643081665},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.6617175340652466},{"id":"https://openalex.org/C2777303404","wikidata":"https://www.wikidata.org/wiki/Q759757","display_name":"Convergence (economics)","level":2,"score":0.6506582498550415},{"id":"https://openalex.org/C17020691","wikidata":"https://www.wikidata.org/wiki/Q139677","display_name":"Operator (biology)","level":5,"score":0.6338386535644531},{"id":"https://openalex.org/C10494615","wikidata":"https://www.wikidata.org/wiki/Q17086765","display_name":"Proximal Gradient Methods","level":4,"score":0.5505311489105225},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5311924815177917},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.4868621230125427},{"id":"https://openalex.org/C168167062","wikidata":"https://www.wikidata.org/wiki/Q1117970","display_name":"Component (thermodynamics)","level":2,"score":0.484235018491745},{"id":"https://openalex.org/C14036430","wikidata":"https://www.wikidata.org/wiki/Q3736076","display_name":"Function (biology)","level":2,"score":0.48167431354522705},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.42658936977386475},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4247535467147827},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.25388017296791077},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.20612740516662598},{"id":"https://openalex.org/C104317684","wikidata":"https://www.wikidata.org/wiki/Q7187","display_name":"Gene","level":2,"score":0.0},{"id":"https://openalex.org/C86339819","wikidata":"https://www.wikidata.org/wiki/Q407384","display_name":"Transcription factor","level":3,"score":0.0},{"id":"https://openalex.org/C162324750","wikidata":"https://www.wikidata.org/wiki/Q8134","display_name":"Economics","level":0,"score":0.0},{"id":"https://openalex.org/C158448853","wikidata":"https://www.wikidata.org/wiki/Q425218","display_name":"Repressor","level":4,"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/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.0},{"id":"https://openalex.org/C97355855","wikidata":"https://www.wikidata.org/wiki/Q11473","display_name":"Thermodynamics","level":1,"score":0.0},{"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/C78458016","wikidata":"https://www.wikidata.org/wiki/Q840400","display_name":"Evolutionary biology","level":1,"score":0.0},{"id":"https://openalex.org/C50522688","wikidata":"https://www.wikidata.org/wiki/Q189833","display_name":"Economic growth","level":1,"score":0.0},{"id":"https://openalex.org/C185592680","wikidata":"https://www.wikidata.org/wiki/Q2329","display_name":"Chemistry","level":0,"score":0.0},{"id":"https://openalex.org/C55493867","wikidata":"https://www.wikidata.org/wiki/Q7094","display_name":"Biochemistry","level":1,"score":0.0}],"mesh":[],"locations_count":3,"locations":[{"id":"pmh:oai:arXiv.org:2102.03869","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.03869","pdf_url":"https://arxiv.org/pdf/2102.03869","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},{"id":"mag:3128200149","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/2102.03869.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"arXiv (Cornell University)","raw_type":null},{"id":"doi:10.48550/arxiv.2102.03869","doi":"https://doi.org/10.48550/arxiv.2102.03869","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2102.03869","pdf_url":null,"source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":null,"is_accepted":false,"is_published":null,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2102.03869","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2102.03869","pdf_url":"https://arxiv.org/pdf/2102.03869","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":"2331-8422","issn":["2331-8422"],"is_oa":true,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I205783295","host_organization_name":"Cornell University","host_organization_lineage":["https://openalex.org/I205783295"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"text"},"sustainable_development_goals":[],"sustainable_development_goals_aurora":[{"id":"https://metadata.un.org/sdg/16","score":0.550000011920929,"display_name":"Peace, justice, and strong institutions"}],"study_designs":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":38,"referenced_works":["https://openalex.org/W48332454","https://openalex.org/W1037812049","https://openalex.org/W1498436455","https://openalex.org/W1503398984","https://openalex.org/W1686810756","https://openalex.org/W1866230956","https://openalex.org/W1965125844","https://openalex.org/W2006262045","https://openalex.org/W2008634296","https://openalex.org/W2038497950","https://openalex.org/W2093545205","https://openalex.org/W2120160881","https://openalex.org/W2122825543","https://openalex.org/W2138019504","https://openalex.org/W2138265962","https://openalex.org/W2146502635","https://openalex.org/W2163605009","https://openalex.org/W2400429454","https://openalex.org/W2513419314","https://openalex.org/W2515385951","https://openalex.org/W2520760693","https://openalex.org/W2765202580","https://openalex.org/W2784930045","https://openalex.org/W2942475188","https://openalex.org/W2948607799","https://openalex.org/W2952975724","https://openalex.org/W2963208657","https://openalex.org/W2963223345","https://openalex.org/W2963341956","https://openalex.org/W2963748441","https://openalex.org/W2964121744","https://openalex.org/W2970421292","https://openalex.org/W2976833415","https://openalex.org/W2979174981","https://openalex.org/W2995869484","https://openalex.org/W3038246103","https://openalex.org/W3042271683","https://openalex.org/W3099715410"],"related_works":["https://openalex.org/W1037812049","https://openalex.org/W2951036040","https://openalex.org/W2950035978","https://openalex.org/W2952139899","https://openalex.org/W2943860135","https://openalex.org/W2948802143","https://openalex.org/W2996176259","https://openalex.org/W2963195695","https://openalex.org/W2096291962","https://openalex.org/W3115341478","https://openalex.org/W1989087436","https://openalex.org/W2082319640","https://openalex.org/W3085500338","https://openalex.org/W17855072","https://openalex.org/W78749393","https://openalex.org/W2963828549","https://openalex.org/W2963239776","https://openalex.org/W2891595829","https://openalex.org/W2306311493","https://openalex.org/W3194256511"],"abstract_inverted_index":{"The":[0],"parameters":[1],"of":[2,12,26,59,63,98,122],"a":[3,56,76,99],"neural":[4],"network":[5],"are":[6,89,94],"naturally":[7],"organized":[8],"in":[9,127],"groups,":[10],"some":[11,31],"which":[13,54],"might":[14],"not":[15],"contribute":[16],"to":[17,34],"its":[18],"overall":[19],"performance.":[20],"To":[21],"prune":[22],"out":[23],"unimportant":[24],"groups":[25],"parameters,":[27],"we":[28,48,83,105],"can":[29,71],"include":[30],"non-differentiable":[32],"penalty":[33],"the":[35,50,113],"objective":[36],"function,":[37],"and":[38,79,137],"minimize":[39],"it":[40],"using":[41],"proximal":[42,52,61,102,115],"gradient":[43],"methods.":[44],"In":[45],"this":[46,81,108],"paper,":[47],"derive":[49],"weighted":[51,114],"operator,":[53],"is":[55,119],"necessary":[57],"component":[58],"these":[60,92],"methods,":[62],"two":[64],"structured":[65],"sparsity":[66,129],"inducing":[67],"penalties.":[68],"Moreover,":[69],"they":[70],"be":[72],"approximated":[73],"efficiently":[74],"with":[75,112,125],"numerical":[77],"solver,":[78],"despite":[80],"approximation,":[82],"prove":[84],"that":[85,107],"existing":[86],"convergence":[87],"guarantees":[88],"preserved":[90],"when":[91],"operators":[93,116],"integrated":[95],"as":[96],"part":[97],"generic":[100],"adaptive":[101,109],"method.":[103],"Finally,":[104],"show":[106],"method,":[110],"together":[111],"derived":[117],"here,":[118],"indeed":[120],"capable":[121],"finding":[123],"solutions":[124],"structure":[126],"their":[128],"patterns,":[130],"on":[131],"representative":[132],"examples":[133],"from":[134],"computer":[135],"vision":[136],"natural":[138],"language":[139],"processing.":[140]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1},{"year":2021,"cited_by_count":2}],"updated_date":"2026-10-16T09:59:22.235173","created_date":"2025-10-10T00:00:00"}
