{"id":"https://openalex.org/W4226079778","doi":"https://doi.org/10.48550/arxiv.2202.02649","title":"The Implicit Bias of Gradient Descent on Generalized Gated Linear Networks","display_name":"The Implicit Bias of Gradient Descent on Generalized Gated Linear Networks","publication_year":2022,"publication_date":"2022-02-05","ids":{"openalex":"https://openalex.org/W4226079778","doi":"https://doi.org/10.48550/arxiv.2202.02649"},"language":"en","primary_location":{"id":"pmh:oai:arXiv.org:2202.02649","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2202.02649","pdf_url":"https://arxiv.org/pdf/2202.02649","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/2202.02649","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5030803845","display_name":"Samuel Lippl","orcid":"https://orcid.org/0000-0002-8169-087X","observed_orcids":["https://orcid.org/0000-0002-8169-087X"]},"institutions":[{"id":"https://openalex.org/I4405270606","display_name":"Mortimer B. Zuckerman Mind Brain Behavior Institute","ror":"https://ror.org/0110mmp98","country_code":"US","type":"facility","lineage":["https://openalex.org/I4405270606"]},{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Lippl, Samuel","raw_affiliation_strings":["Department of Neuroscience , Zuckerman Mind Brain Behavior Institute , Columbia University , New York , NY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Neuroscience , Zuckerman Mind Brain Behavior Institute , Columbia University , New York , NY","institution_ids":["https://openalex.org/I4405270606","https://openalex.org/I78577930"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5079185098","display_name":"Larry F. Abbott","orcid":"https://orcid.org/0000-0003-1163-5688","observed_orcids":["https://orcid.org/0000-0003-1163-5688","https://orcid.org/0000-0002-5131-5200"]},"institutions":[{"id":"https://openalex.org/I4405270606","display_name":"Mortimer B. Zuckerman Mind Brain Behavior Institute","ror":"https://ror.org/0110mmp98","country_code":"US","type":"facility","lineage":["https://openalex.org/I4405270606"]},{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Abbott, L. F.","raw_affiliation_strings":["Department of Neuroscience , Zuckerman Mind Brain Behavior Institute , Columbia University , New York , NY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Neuroscience , Zuckerman Mind Brain Behavior Institute , Columbia University , New York , NY","institution_ids":["https://openalex.org/I4405270606","https://openalex.org/I78577930"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5016533438","display_name":"SueYeon Chung","orcid":"https://orcid.org/0000-0001-5726-4865","observed_orcids":["https://orcid.org/0000-0001-5726-4865"]},"institutions":[{"id":"https://openalex.org/I4387153999","display_name":"Flatiron Institute","ror":"https://ror.org/00sekdz59","country_code":"US","type":"nonprofit","lineage":["https://openalex.org/I4210107338","https://openalex.org/I4387153999"]},{"id":"https://openalex.org/I4405270606","display_name":"Mortimer B. Zuckerman Mind Brain Behavior Institute","ror":"https://ror.org/0110mmp98","country_code":"US","type":"facility","lineage":["https://openalex.org/I4405270606"]},{"id":"https://openalex.org/I78577930","display_name":"Columbia University","ror":"https://ror.org/00hj8s172","country_code":"US","type":"education","lineage":["https://openalex.org/I78577930"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Chung, SueYeon","raw_affiliation_strings":["Center for Computational Neuroscience , Flatiron Institute , New York , NY","Department of Neuroscience , Zuckerman Mind Brain Behavior Institute , Columbia University , New York , NY"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Computational Neuroscience , Flatiron Institute , New York , NY","institution_ids":["https://openalex.org/I4387153999"]},{"raw_affiliation_string":"Department of Neuroscience , Zuckerman Mind Brain Behavior Institute , Columbia University , New York , NY","institution_ids":["https://openalex.org/I4405270606","https://openalex.org/I78577930"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":null,"has_fulltext":true,"cited_by_count":0,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.7465999722480774,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.7465999722480774,"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/T10320","display_name":"Neural Networks and Applications","score":0.23999999463558197,"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/T11307","display_name":"Domain Adaptation and Few-Shot Learning","score":0.003100000089034438,"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"}}],"keywords":[{"id":"https://openalex.org/keywords/implicit-bias","display_name":"implicit bias","score":0.8960000276565552},{"id":"https://openalex.org/keywords/gradient-descent","display_name":"gradient descent","score":0.9700000286102295},{"id":"https://openalex.org/keywords/inductive-bias","display_name":"inductive bias","score":0.9380000233650208},{"id":"https://openalex.org/keywords/homogeneous-polynomials","display_name":"homogeneous polynomials","score":0.7350000143051147},{"id":"https://openalex.org/keywords/relu-neural-networks","display_name":"ReLU networks","score":0.8450000286102295},{"id":"https://openalex.org/keywords/two-layer-neural-networks","display_name":"two-layer neural networks","score":0.7979999780654907},{"id":"https://openalex.org/keywords/asymptotic-analysis","display_name":"asymptotic analysis","score":0.531000018119812},{"id":"https://openalex.org/keywords/mnist","display_name":"MNIST","score":0.5299999713897705}],"concepts":[{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.9188250303268433},{"id":"https://openalex.org/C197352929","wikidata":"https://www.wikidata.org/wiki/Q1074074","display_name":"Inductive bias","level":4,"score":0.855258584022522},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.7371726036071777},{"id":"https://openalex.org/C151201525","wikidata":"https://www.wikidata.org/wiki/Q177239","display_name":"Limit (mathematics)","level":2,"score":0.6360469460487366},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.6186670064926147},{"id":"https://openalex.org/C158622935","wikidata":"https://www.wikidata.org/wiki/Q660848","display_name":"Nonlinear system","level":2,"score":0.5878571271896362},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5837584137916565},{"id":"https://openalex.org/C66882249","wikidata":"https://www.wikidata.org/wiki/Q169336","display_name":"Homogeneous","level":2,"score":0.5491852164268494},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.5161556005477905},{"id":"https://openalex.org/C2984842247","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep neural networks","level":3,"score":0.4955679178237915},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.4742509424686432},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.38025137782096863},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3279200494289398},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.31656670570373535},{"id":"https://openalex.org/C28006648","wikidata":"https://www.wikidata.org/wiki/Q6934509","display_name":"Multi-task learning","level":3,"score":0.10871660709381104},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.09783726930618286},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.08961829543113708},{"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/C2780451532","wikidata":"https://www.wikidata.org/wiki/Q759676","display_name":"Task (project management)","level":2,"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/C187736073","wikidata":"https://www.wikidata.org/wiki/Q2920921","display_name":"Management","level":1,"score":0.0},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.0}],"mesh":[],"locations_count":2,"locations":[{"id":"pmh:oai:arXiv.org:2202.02649","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2202.02649","pdf_url":"https://arxiv.org/pdf/2202.02649","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":"doi:10.48550/arxiv.2202.02649","doi":"https://doi.org/10.48550/arxiv.2202.02649","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.2202.02649","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":false,"raw_source_name":null,"raw_type":"Preprint"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2202.02649","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/2202.02649","pdf_url":"https://arxiv.org/pdf/2202.02649","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":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G4253858762","display_name":"NeuroNex Theory Team: Columbia University Theoretical Neuroscience Center","funder_award_id":"1707398","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W4226079778.pdf","grobid_xml":"https://content.openalex.org/works/W4226079778.grobid-xml"},"referenced_works_count":0,"referenced_works":[],"related_works":["https://openalex.org/W4280596364","https://openalex.org/W3006064982","https://openalex.org/W3205384336","https://openalex.org/W7133202894","https://openalex.org/W7164549816","https://openalex.org/W7133216116","https://openalex.org/W2805926765","https://openalex.org/W7083833049","https://openalex.org/W4407186888","https://openalex.org/W3042242685"],"abstract_inverted_index":{"Understanding":[0],"the":[1,23,55,82,101,109,119],"asymptotic":[2],"behavior":[3],"of":[4,7,27,32,57,85,100,104,121],"gradient-descent":[5],"training":[6,25],"deep":[8,33],"neural":[9,35],"networks":[10,39,47],"is":[11,115],"essential":[12],"for":[13],"revealing":[14],"inductive":[15,102,110],"biases":[16],"and":[17,41,76,81,126],"improving":[18],"network":[19],"performance.":[20,89],"We":[21,53,65],"derive":[22],"infinite-time":[24],"limit":[26],"a":[28,97],"mathematically":[29],"tractable":[30],"class":[31],"nonlinear":[34],"networks,":[36],"gated":[37,46],"linear":[38],"(GLNs),":[40],"generalize":[42],"these":[43],"results":[44],"to":[45,71,117],"described":[48],"by":[49],"general":[50],"homogeneous":[51],"polynomials.":[52],"study":[54],"implications":[56],"our":[58,68,94,113],"results,":[59],"focusing":[60],"first":[61],"on":[62,74],"two-layer":[63],"GLNs.":[64],"then":[66],"apply":[67],"theoretical":[69],"predictions":[70],"GLNs":[72],"trained":[73],"MNIST":[75],"show":[77,92],"how":[78],"architectural":[79],"constraints":[80],"implicit":[83],"bias":[84,103,111],"gradient":[86],"descent":[87],"affect":[88],"Finally,":[90],"we":[91],"that":[93],"theory":[95],"captures":[96],"substantial":[98],"portion":[99],"ReLU":[105],"networks.":[106],"By":[107],"making":[108],"explicit,":[112],"framework":[114],"poised":[116],"inform":[118],"development":[120],"more":[122],"efficient,":[123],"biologically":[124],"plausible,":[125],"robust":[127],"learning":[128],"algorithms.":[129]},"counts_by_year":[],"updated_date":"2026-11-04T10:54:05.112534","created_date":"2022-05-05T00:00:00"}