{"id":"https://openalex.org/W4220655231","doi":"https://doi.org/10.1162/neco_a_01494","title":"On Neural Network Kernels and the Storage Capacity Problem","display_name":"On Neural Network Kernels and the Storage Capacity Problem","publication_year":2022,"publication_date":"2022-03-28","ids":{"openalex":"https://openalex.org/W4220655231","doi":"https://doi.org/10.1162/neco_a_01494","pmid":"https://pubmed.ncbi.nlm.nih.gov/35344992"},"language":"en","primary_location":{"id":"doi:10.1162/neco_a_01494","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_01494","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},"type":"article","indexed_in":["arxiv","crossref","pubmed"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/2201.04669","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5063822685","display_name":"Jacob A. Zavatone-Veth","orcid":"https://orcid.org/0000-0002-4060-1738"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Jacob A. Zavatone-Veth","raw_affiliation_strings":["Department of Physics and Center for Brain Science, Harvard University, Cambridge, MA 02138, U.S.A. jzavatoneveth@g.harvard.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Department of Physics and Center for Brain Science, Harvard University, Cambridge, MA 02138, U.S.A. jzavatoneveth@g.harvard.edu","institution_ids":["https://openalex.org/I136199984"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5023195984","display_name":"Cengiz Pehlevan","orcid":"https://orcid.org/0000-0001-9767-6063"},"institutions":[{"id":"https://openalex.org/I136199984","display_name":"Harvard University","ror":"https://ror.org/03vek6s52","country_code":"US","type":"education","lineage":["https://openalex.org/I136199984"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Cengiz Pehlevan","raw_affiliation_strings":["Center for Brain Science and John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, U.S.A. cpehlevan@seas.harvard.edu"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Center for Brain Science and John A. Paulson School of Engineering and Applied Sciences, Harvard University, Cambridge, MA 02138, U.S.A. cpehlevan@seas.harvard.edu","institution_ids":["https://openalex.org/I136199984"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":1,"corresponding_author_ids":["https://openalex.org/A5023195984","https://openalex.org/A5063822685"],"corresponding_institution_ids":["https://openalex.org/I136199984"],"apc_list":null,"apc_paid":null,"fwci":0.7873,"has_fulltext":false,"cited_by_count":7,"citation_normalized_percentile":{"value":0.75487779,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":97},"biblio":{"volume":"34","issue":"5","first_page":"1136","last_page":"1142"},"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/T11206","display_name":"Model Reduction and Neural Networks","score":0.9905999898910522,"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"}},{"id":"https://openalex.org/T12261","display_name":"Statistical Mechanics and Entropy","score":0.984000027179718,"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/artificial-neural-network","display_name":"Artificial neural network","score":0.7461583018302917},{"id":"https://openalex.org/keywords/connection","display_name":"Connection (principal bundle)","score":0.5479273796081543},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.4961622655391693},{"id":"https://openalex.org/keywords/kernel","display_name":"Kernel (algebra)","score":0.49163419008255005},{"id":"https://openalex.org/keywords/gaussian","display_name":"Gaussian","score":0.482927531003952},{"id":"https://openalex.org/keywords/process","display_name":"Process (computing)","score":0.45131823420524597},{"id":"https://openalex.org/keywords/gaussian-process","display_name":"Gaussian process","score":0.43433430790901184},{"id":"https://openalex.org/keywords/stochastic-neural-network","display_name":"Stochastic neural network","score":0.41021743416786194},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.39157772064208984},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.3822810649871826},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33928507566452026},{"id":"https://openalex.org/keywords/topology","display_name":"Topology (electrical circuits)","score":0.32559216022491455},{"id":"https://openalex.org/keywords/recurrent-neural-network","display_name":"Recurrent neural network","score":0.3215126395225525},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.21114793419837952},{"id":"https://openalex.org/keywords/combinatorics","display_name":"Combinatorics","score":0.16042575240135193},{"id":"https://openalex.org/keywords/physics","display_name":"Physics","score":0.1590140461921692},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.09774979948997498}],"concepts":[{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.7461583018302917},{"id":"https://openalex.org/C13355873","wikidata":"https://www.wikidata.org/wiki/Q2920850","display_name":"Connection (principal bundle)","level":2,"score":0.5479273796081543},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.4961622655391693},{"id":"https://openalex.org/C74193536","wikidata":"https://www.wikidata.org/wiki/Q574844","display_name":"Kernel (algebra)","level":2,"score":0.49163419008255005},{"id":"https://openalex.org/C163716315","wikidata":"https://www.wikidata.org/wiki/Q901177","display_name":"Gaussian","level":2,"score":0.482927531003952},{"id":"https://openalex.org/C98045186","wikidata":"https://www.wikidata.org/wiki/Q205663","display_name":"Process (computing)","level":2,"score":0.45131823420524597},{"id":"https://openalex.org/C61326573","wikidata":"https://www.wikidata.org/wiki/Q1496376","display_name":"Gaussian process","level":3,"score":0.43433430790901184},{"id":"https://openalex.org/C86582703","wikidata":"https://www.wikidata.org/wiki/Q7617824","display_name":"Stochastic neural network","level":4,"score":0.41021743416786194},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.39157772064208984},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.3822810649871826},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33928507566452026},{"id":"https://openalex.org/C184720557","wikidata":"https://www.wikidata.org/wiki/Q7825049","display_name":"Topology (electrical circuits)","level":2,"score":0.32559216022491455},{"id":"https://openalex.org/C147168706","wikidata":"https://www.wikidata.org/wiki/Q1457734","display_name":"Recurrent neural network","level":3,"score":0.3215126395225525},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.21114793419837952},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.16042575240135193},{"id":"https://openalex.org/C121332964","wikidata":"https://www.wikidata.org/wiki/Q413","display_name":"Physics","level":0,"score":0.1590140461921692},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.09774979948997498},{"id":"https://openalex.org/C111919701","wikidata":"https://www.wikidata.org/wiki/Q9135","display_name":"Operating system","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}],"mesh":[{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D000465","descriptor_name":"Algorithms","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true},{"descriptor_ui":"D016571","descriptor_name":"Neural Networks, Computer","qualifier_ui":null,"qualifier_name":null,"is_major_topic":true}],"locations_count":3,"locations":[{"id":"doi:10.1162/neco_a_01494","is_oa":false,"landing_page_url":"https://doi.org/10.1162/neco_a_01494","pdf_url":null,"source":{"id":"https://openalex.org/S207023548","display_name":"Neural Computation","issn_l":"0899-7667","issn":["0899-7667","1530-888X"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310315718","host_organization_name":"The MIT Press","host_organization_lineage":["https://openalex.org/P4310315718"],"host_organization_lineage_names":["The MIT Press"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural Computation","raw_type":"journal-article"},{"id":"pmid:35344992","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/35344992","pdf_url":null,"source":{"id":"https://openalex.org/S4306525036","display_name":"PubMed","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I1299303238","host_organization_name":"National Institutes of Health","host_organization_lineage":["https://openalex.org/I1299303238"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"Neural computation","raw_type":null},{"id":"pmh:oai:arXiv.org:2201.04669","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2201.04669","pdf_url":"https://arxiv.org/pdf/2201.04669","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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"}],"best_oa_location":{"id":"pmh:oai:arXiv.org:2201.04669","is_oa":true,"landing_page_url":"http://arxiv.org/abs/2201.04669","pdf_url":"https://arxiv.org/pdf/2201.04669","source":{"id":"https://openalex.org/S4306400194","display_name":"arXiv (Cornell University)","issn_l":null,"issn":null,"is_oa":true,"is_in_doaj":false,"is_core":false,"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":[],"awards":[],"funders":[],"has_content":{"pdf":false,"grobid_xml":false},"content_urls":null,"referenced_works_count":32,"referenced_works":["https://openalex.org/W1544131626","https://openalex.org/W2001570872","https://openalex.org/W2030450972","https://openalex.org/W2056517685","https://openalex.org/W2070784404","https://openalex.org/W2154087390","https://openalex.org/W2167608136","https://openalex.org/W2276387674","https://openalex.org/W2423689290","https://openalex.org/W2559655401","https://openalex.org/W2597289420","https://openalex.org/W2766678531","https://openalex.org/W2809090039","https://openalex.org/W2968729399","https://openalex.org/W2973471489","https://openalex.org/W3044599724","https://openalex.org/W3111154923","https://openalex.org/W3172130470","https://openalex.org/W4206333827","https://openalex.org/W4212774754","https://openalex.org/W4229706427","https://openalex.org/W4287755499","https://openalex.org/W4294205985","https://openalex.org/W6650809868","https://openalex.org/W6657839258","https://openalex.org/W6682631133","https://openalex.org/W6684918892","https://openalex.org/W6695029320","https://openalex.org/W6717556742","https://openalex.org/W6745256532","https://openalex.org/W6752495264","https://openalex.org/W6842469858"],"related_works":["https://openalex.org/W4298287631","https://openalex.org/W2953061907","https://openalex.org/W587735977","https://openalex.org/W1847088711","https://openalex.org/W4225394202","https://openalex.org/W3036642985","https://openalex.org/W3032952384","https://openalex.org/W1538606284","https://openalex.org/W2373874059","https://openalex.org/W1538193578"],"abstract_inverted_index":{"In":[0],"this":[1],"short":[2],"note,":[3],"we":[4,36],"reify":[5],"the":[6,11,22,39,45,53,63],"connection":[7],"between":[8],"work":[9],"on":[10,28],"storage":[12],"capacity":[13],"problem":[14],"in":[15,44],"wide":[16,32,68],"two-layer":[17,69],"treelike":[18],"neural":[19,33,55,70],"networks":[20],"and":[21,65],"rapidly":[23],"growing":[24],"body":[25],"of":[26,31,67],"literature":[27,48],"kernel":[29],"limits":[30],"networks.":[34,71],"Concretely,":[35],"observe":[37],"that":[38],"\"effective":[40],"order":[41],"parameter\"":[42],"studied":[43],"statistical":[46],"mechanics":[47],"is":[49],"exactly":[50],"equivalent":[51],"to":[52],"infinite-width":[54],"network":[56],"gaussian":[57],"process":[58],"kernel.":[59],"This":[60],"correspondence":[61],"connects":[62],"expressivity":[64],"trainability":[66]},"counts_by_year":[{"year":2026,"cited_by_count":1},{"year":2025,"cited_by_count":3},{"year":2024,"cited_by_count":1},{"year":2023,"cited_by_count":2}],"updated_date":"2026-05-21T06:26:12.895304","created_date":"2025-10-10T00:00:00"}
