{"id":"https://openalex.org/W2550848904","doi":"https://doi.org/10.1007/s11633-017-1054-2","title":"Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review","display_name":"Why and when can deep-but not shallow-networks avoid the curse of dimensionality: A review","publication_year":2017,"publication_date":"2017-03-14","ids":{"openalex":"https://openalex.org/W2550848904","doi":"https://doi.org/10.1007/s11633-017-1054-2","mag":"2550848904"},"language":"en","primary_location":{"id":"doi:10.1007/s11633-017-1054-2","doi":"https://doi.org/10.1007/s11633-017-1054-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11633-017-1054-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11633-017-1054-2.pdf","source":{"id":"https://openalex.org/S28082686","display_name":"Machine Intelligence Research","issn_l":"1476-8186","issn":["1476-8186","1751-8520","2731-538X","2731-5398"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Automation and Computing","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"hybrid","oa_url":"https://link.springer.com/content/pdf/10.1007/s11633-017-1054-2.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5001833084","display_name":"Tomaso Poggio","orcid":"https://orcid.org/0000-0002-3944-0455","observed_orcids":["https://orcid.org/0000-0002-3944-0455"]},"institutions":[{"id":"https://openalex.org/I144112489","display_name":"McGovern Institute for Brain Research","ror":"https://ror.org/05ymca674","country_code":"US","type":"facility","lineage":["https://openalex.org/I144112489","https://openalex.org/I63966007"]},{"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":"Tomaso Poggio","raw_affiliation_strings":["Center for Brains, Minds, and Machines, McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA"],"raw_orcid":"https://orcid.org/0000-0002-3944-0455","affiliations":[{"raw_affiliation_string":"Center for Brains, Minds, and Machines, McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA","institution_ids":["https://openalex.org/I144112489","https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5056481363","display_name":"Hrushikesh  N. Mhaskar","orcid":"https://orcid.org/0000-0001-8793-4321","observed_orcids":["https://orcid.org/0000-0001-8793-4321"]},"institutions":[{"id":"https://openalex.org/I122411786","display_name":"California Institute of Technology","ror":"https://ror.org/05dxps055","country_code":"US","type":"education","lineage":["https://openalex.org/I122411786"]},{"id":"https://openalex.org/I136722135","display_name":"Claremont Graduate University","ror":"https://ror.org/0157pnt69","country_code":"US","type":"education","lineage":["https://openalex.org/I136722135"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Hrushikesh Mhaskar","raw_affiliation_strings":["Department of Mathematics, California Institute of Technology, Pasadena, CA, 91125, USA","Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, 91711, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Mathematics, California Institute of Technology, Pasadena, CA, 91125, USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Institute of Mathematical Sciences, Claremont Graduate University, Claremont, CA, 91711, USA","institution_ids":["https://openalex.org/I136722135"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5061220999","display_name":"Lorenzo Rosasco","orcid":"https://orcid.org/0000-0003-3098-383X","observed_orcids":["https://orcid.org/0000-0003-3098-383X"]},"institutions":[{"id":"https://openalex.org/I144112489","display_name":"McGovern Institute for Brain Research","ror":"https://ror.org/05ymca674","country_code":"US","type":"facility","lineage":["https://openalex.org/I144112489","https://openalex.org/I63966007"]},{"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":"Lorenzo Rosasco","raw_affiliation_strings":["Center for Brains, Minds, and Machines, McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Brains, Minds, and Machines, McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA","institution_ids":["https://openalex.org/I144112489","https://openalex.org/I63966007"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5007251379","display_name":"Brando Miranda","orcid":"https://orcid.org/0009-0008-5031-0126","observed_orcids":["https://orcid.org/0009-0008-5031-0126"]},"institutions":[{"id":"https://openalex.org/I144112489","display_name":"McGovern Institute for Brain Research","ror":"https://ror.org/05ymca674","country_code":"US","type":"facility","lineage":["https://openalex.org/I144112489","https://openalex.org/I63966007"]},{"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":"Brando Miranda","raw_affiliation_strings":["Center for Brains, Minds, and Machines, McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Brains, Minds, and Machines, McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA","institution_ids":["https://openalex.org/I144112489","https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5089682862","display_name":"Qianli Liao","orcid":"https://orcid.org/0000-0003-0076-621X","observed_orcids":["https://orcid.org/0000-0003-0076-621X"]},"institutions":[{"id":"https://openalex.org/I144112489","display_name":"McGovern Institute for Brain Research","ror":"https://ror.org/05ymca674","country_code":"US","type":"facility","lineage":["https://openalex.org/I144112489","https://openalex.org/I63966007"]},{"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":"Qianli Liao","raw_affiliation_strings":["Center for Brains, Minds, and Machines, McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Brains, Minds, and Machines, McGovern Institute for Brain Research, Massachusetts Institute of Technology, Cambridge, MA, 02139, USA","institution_ids":["https://openalex.org/I144112489","https://openalex.org/I63966007"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":4,"corresponding_author_ids":["https://openalex.org/A5001833084"],"corresponding_institution_ids":["https://openalex.org/I144112489","https://openalex.org/I63966007"],"apc_list":{"value":3190,"currency":"USD","value_usd":3190},"apc_paid":{"value":3190,"currency":"USD","value_usd":3190},"fwci":29.4297,"has_fulltext":true,"cited_by_count":611,"citation_normalized_percentile":{"value":0.99771335,"is_in_top_1_percent":true,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":97,"max":100},"biblio":{"volume":"14","issue":"5","first_page":"503","last_page":"519"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.6826000213623047,"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":0.6826000213623047,"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/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.21850000321865082,"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/T12072","display_name":"Machine Learning and Algorithms","score":0.028999999165534973,"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/curse-of-dimensionality","display_name":"curse of dimensionality","score":0.9340000152587891},{"id":"https://openalex.org/keywords/deep-learning","display_name":"deep learning","score":0.6389999985694885},{"id":"https://openalex.org/keywords/shallow-learning","display_name":"shallow learning","score":0.8259999752044678},{"id":"https://openalex.org/keywords/deep-convolutional-neural-networks","display_name":"deep convolutional neural networks","score":0.7170000076293945},{"id":"https://openalex.org/keywords/weight-sharing","display_name":"parameter sharing","score":0.7089999914169312},{"id":"https://openalex.org/keywords/neural-network-approximation","display_name":"neural network approximation","score":0.382999986410141}],"concepts":[{"id":"https://openalex.org/C111030470","wikidata":"https://www.wikidata.org/wiki/Q1430460","display_name":"Curse of dimensionality","level":2,"score":0.7555364370346069},{"id":"https://openalex.org/C26517878","wikidata":"https://www.wikidata.org/wiki/Q228039","display_name":"Key (lock)","level":2,"score":0.6219116449356079},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5554085969924927},{"id":"https://openalex.org/C2780273121","wikidata":"https://www.wikidata.org/wiki/Q109411","display_name":"Curse","level":2,"score":0.5266131162643433},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.5253714323043823},{"id":"https://openalex.org/C108583219","wikidata":"https://www.wikidata.org/wiki/Q197536","display_name":"Deep learning","level":2,"score":0.5126509070396423},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.47138601541519165},{"id":"https://openalex.org/C2777212361","wikidata":"https://www.wikidata.org/wiki/Q5127848","display_name":"Class (philosophy)","level":2,"score":0.46201008558273315},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.4599027633666992},{"id":"https://openalex.org/C75235859","wikidata":"https://www.wikidata.org/wiki/Q582659","display_name":"Exponential growth","level":2,"score":0.41686922311782837},{"id":"https://openalex.org/C2522767166","wikidata":"https://www.wikidata.org/wiki/Q2374463","display_name":"Data science","level":1,"score":0.371528685092926},{"id":"https://openalex.org/C13736549","wikidata":"https://www.wikidata.org/wiki/Q4489420","display_name":"Industrial engineering","level":1,"score":0.3293240964412689},{"id":"https://openalex.org/C80444323","wikidata":"https://www.wikidata.org/wiki/Q2878974","display_name":"Theoretical computer science","level":1,"score":0.3262307643890381},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.24531465768814087},{"id":"https://openalex.org/C127413603","wikidata":"https://www.wikidata.org/wiki/Q11023","display_name":"Engineering","level":0,"score":0.21820178627967834},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.1490815281867981},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.13964715600013733},{"id":"https://openalex.org/C38652104","wikidata":"https://www.wikidata.org/wiki/Q3510521","display_name":"Computer security","level":1,"score":0.12204405665397644},{"id":"https://openalex.org/C19165224","wikidata":"https://www.wikidata.org/wiki/Q23404","display_name":"Anthropology","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}],"mesh":[],"locations_count":9,"locations":[{"id":"doi:10.1007/s11633-017-1054-2","doi":"https://doi.org/10.1007/s11633-017-1054-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11633-017-1054-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11633-017-1054-2.pdf","source":{"id":"https://openalex.org/S28082686","display_name":"Machine Intelligence Research","issn_l":"1476-8186","issn":["1476-8186","1751-8520","2731-538X","2731-5398"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Automation and Computing","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1611.00740","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1611.00740","pdf_url":"https://arxiv.org/pdf/1611.00740","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":"pmh:oai:iris.unige.it:11567/888539","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11567/888539","pdf_url":"http://hdl.handle.net/11567/888539","source":{"id":"https://openalex.org/S4377196291","display_name":"CINECA IRIS Institutial Research Information System (University of Genoa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I83816512","host_organization_name":"University of Genoa","host_organization_lineage":["https://openalex.org/I83816512"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"mag:2546686227","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/abs/1611.00740v1","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":"pmh:oai:authors.library.caltech.edu:77987","doi":null,"is_oa":true,"landing_page_url":"https://resolver.caltech.edu/CaltechAUTHORS:20170607-072954485","pdf_url":null,"source":{"id":"https://openalex.org/S4306402161","display_name":"CaltechAUTHORS (California Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I122411786","host_organization_name":"California Institute of Technology","host_organization_lineage":["https://openalex.org/I122411786"],"host_organization_lineage_names":[],"type":"repository"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"Article"},{"id":"pmh:oai:dspace.mit.edu:1721.1/107679","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/1721.1/107679","pdf_url":null,"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,"listed_in":[],"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":"Springer","raw_type":"Article"},{"id":"pmh:oai:iris.unige.it:11567/888631","doi":null,"is_oa":true,"landing_page_url":"http://hdl.handle.net/11567/888631","pdf_url":null,"source":{"id":"https://openalex.org/S4377196291","display_name":"CINECA IRIS Institutial Research Information System (University of Genoa)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I83816512","host_organization_name":"University of Genoa","host_organization_lineage":["https://openalex.org/I83816512"],"host_organization_lineage_names":[],"type":"repository"},"license":"other-oa","license_id":"https://openalex.org/licenses/other-oa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"","raw_type":"info:eu-repo/semantics/article"},{"id":"doi:10.48550/arxiv.1611.00740","doi":"https://doi.org/10.48550/arxiv.1611.00740","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1611.00740","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":null,"is_accepted":false,"is_published":false,"raw_source_name":null,"raw_type":"Preprint"},{"id":"mag:2608372357","doi":null,"is_oa":false,"landing_page_url":"https://dspace.mit.edu/openaccess-disseminate/1721.1/107679","pdf_url":null,"source":{"id":"https://openalex.org/S2764986464","display_name":"Springer US","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core"],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"Springer US","raw_type":null}],"best_oa_location":{"id":"doi:10.1007/s11633-017-1054-2","doi":"https://doi.org/10.1007/s11633-017-1054-2","is_oa":true,"landing_page_url":"https://doi.org/10.1007/s11633-017-1054-2","pdf_url":"https://link.springer.com/content/pdf/10.1007/s11633-017-1054-2.pdf","source":{"id":"https://openalex.org/S28082686","display_name":"Machine Intelligence Research","issn_l":"1476-8186","issn":["1476-8186","1751-8520","2731-538X","2731-5398"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["cwts-core","dongbi-b","jufo-1","norway-1","poland-20","russia-white-list-4"],"host_organization":"https://openalex.org/P4310319900","host_organization_name":"Springer Science+Business Media","host_organization_lineage":["https://openalex.org/P4310319900","https://openalex.org/P4310319965"],"host_organization_lineage_names":["Springer Science+Business Media","Springer Nature"],"type":"journal"},"license":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"International Journal of Automation and Computing","raw_type":"journal-article"},"sustainable_development_goals":[],"study_designs":[],"awards":[{"id":"https://openalex.org/G2208512154","display_name":null,"funder_award_id":"W911NF-15-1-0385","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G5385673730","display_name":null,"funder_award_id":"W911NF-15-1-","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G7201050375","display_name":"A Center for Brains, Minds and Machines: the Science and the Technology of Intelligence","funder_award_id":"1231216","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G7452299184","display_name":null,"funder_award_id":"W911NF","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"},{"id":"https://openalex.org/G8257659198","display_name":null,"funder_award_id":"W911NF-15","funder_id":"https://openalex.org/F4320338281","funder_display_name":"Army Research Office"}],"funders":[{"id":"https://openalex.org/F4320306076","display_name":"National Science Foundation","ror":"https://ror.org/021nxhr62"},{"id":"https://openalex.org/F4320324608","display_name":"Companhia Brasileira de Metalurgia e Minera\u00e7\u00e3o","ror":"https://ror.org/03k8d9631"},{"id":"https://openalex.org/F4320338281","display_name":"Army Research Office","ror":"https://ror.org/05epdh915"}],"has_content":{"grobid_xml":true,"pdf":true},"content_urls":{"pdf":"https://content.openalex.org/works/W2550848904.pdf","grobid_xml":"https://content.openalex.org/works/W2550848904.grobid-xml"},"referenced_works_count":63,"referenced_works":["https://openalex.org/W78812187","https://openalex.org/W613766092","https://openalex.org/W937846259","https://openalex.org/W1522301498","https://openalex.org/W1526741802","https://openalex.org/W1530733563","https://openalex.org/W1542886316","https://openalex.org/W1548502347","https://openalex.org/W1809225062","https://openalex.org/W1852909287","https://openalex.org/W1865894638","https://openalex.org/W1899006432","https://openalex.org/W1981025032","https://openalex.org/W1990261069","https://openalex.org/W2006240266","https://openalex.org/W2007700211","https://openalex.org/W2017290750","https://openalex.org/W2038198231","https://openalex.org/W2042194938","https://openalex.org/W2048024397","https://openalex.org/W2065861083","https://openalex.org/W2077597269","https://openalex.org/W2077887717","https://openalex.org/W2079224763","https://openalex.org/W2085481869","https://openalex.org/W2086789740","https://openalex.org/W2089498782","https://openalex.org/W2097998348","https://openalex.org/W2107822587","https://openalex.org/W2108671543","https://openalex.org/W2123507038","https://openalex.org/W2141473882","https://openalex.org/W2149194912","https://openalex.org/W2156267734","https://openalex.org/W2158581396","https://openalex.org/W2161388792","https://openalex.org/W2162836072","https://openalex.org/W2194321275","https://openalex.org/W2206396100","https://openalex.org/W2208555118","https://openalex.org/W2253400648","https://openalex.org/W2271840356","https://openalex.org/W2286501826","https://openalex.org/W2288433034","https://openalex.org/W2337199865","https://openalex.org/W2395092015","https://openalex.org/W2511261638","https://openalex.org/W2513671774","https://openalex.org/W2521270750","https://openalex.org/W2535756153","https://openalex.org/W2548024026","https://openalex.org/W2595713799","https://openalex.org/W2613634265","https://openalex.org/W2738212823","https://openalex.org/W2919115771","https://openalex.org/W2962742960","https://openalex.org/W2964121744","https://openalex.org/W3105432754","https://openalex.org/W4235178139","https://openalex.org/W4236362309","https://openalex.org/W4242686374","https://openalex.org/W4244723818","https://openalex.org/W6814457508"],"related_works":["https://openalex.org/W2546686227","https://openalex.org/W2782623608","https://openalex.org/W2953130038","https://openalex.org/W2969946283","https://openalex.org/W2410678056","https://openalex.org/W2513671774","https://openalex.org/W2995896684","https://openalex.org/W2906267027","https://openalex.org/W2604268533","https://openalex.org/W2963482148"],"abstract_inverted_index":{"The":[0],"paper":[1],"reviews":[2],"and":[3,67],"extends":[4],"an":[5,34],"emerging":[6],"body":[7],"of":[8,29,38,54],"theoretical":[9],"results":[10],"on":[11],"deep":[12,30],"learning":[13],"including":[14],"the":[15,46],"conditions":[16],"under":[17],"which":[18],"it":[19],"can":[20],"be":[21],"exponentially":[22],"better":[23],"than":[24],"shallow":[25],"learning.":[26],"A":[27],"class":[28],"convolutional":[31],"networks":[32],"represent":[33],"important":[35],"special":[36],"case":[37],"these":[39],"conditions,":[40],"though":[41],"weight":[42],"sharing":[43],"is":[44],"not":[45],"main":[47],"reason":[48],"for":[49],"their":[50],"exponential":[51],"advantage.":[52],"Implications":[53],"a":[55],"few":[56],"key":[57],"theorems":[58],"are":[59],"discussed,":[60],"together":[61],"with":[62],"new":[63],"results,":[64],"open":[65],"problems":[66],"conjectures.":[68]},"counts_by_year":[{"year":2026,"cited_by_count":47},{"year":2025,"cited_by_count":52},{"year":2024,"cited_by_count":58},{"year":2023,"cited_by_count":80},{"year":2022,"cited_by_count":78},{"year":2021,"cited_by_count":88},{"year":2020,"cited_by_count":83},{"year":2019,"cited_by_count":59},{"year":2018,"cited_by_count":45},{"year":2017,"cited_by_count":17},{"year":2016,"cited_by_count":4}],"updated_date":"2026-11-08T12:12:28.789561","created_date":"2016-11-30T00:00:00"}
