{"id":"https://openalex.org/W4394994853","doi":"https://doi.org/10.1109/tnnls.2024.3387878","title":"Size and Depth of Monotone Neural Networks: Interpolation and Approximation","display_name":"Size and Depth of Monotone Neural Networks: Interpolation and Approximation","publication_year":2024,"publication_date":"2024-04-22","ids":{"openalex":"https://openalex.org/W4394994853","doi":"https://doi.org/10.1109/tnnls.2024.3387878","pmid":"https://pubmed.ncbi.nlm.nih.gov/38648127"},"language":"en","primary_location":{"id":"doi:10.1109/tnnls.2024.3387878","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2024.3387878","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","pubmed"],"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/A5086897744","display_name":"Dan Mikulincer","orcid":"https://orcid.org/0000-0003-3597-3550"},"institutions":[{"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":"Dan Mikulincer","raw_affiliation_strings":["Massachusetts Institute of Technology, Cambridge, MA, USA"],"raw_orcid":"https://orcid.org/0000-0003-3597-3550","affiliations":[{"raw_affiliation_string":"Massachusetts Institute of Technology, Cambridge, MA, USA","institution_ids":["https://openalex.org/I63966007"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5081855980","display_name":"Daniel Reichman","orcid":"https://orcid.org/0000-0003-0566-7528"},"institutions":[{"id":"https://openalex.org/I107077323","display_name":"Worcester Polytechnic Institute","ror":"https://ror.org/05ejpqr48","country_code":"US","type":"education","lineage":["https://openalex.org/I107077323"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Reichman","raw_affiliation_strings":["Worcester Polytechnic Institute, Worcester, MA, USA"],"raw_orcid":"https://orcid.org/0000-0003-0566-7528","affiliations":[{"raw_affiliation_string":"Worcester Polytechnic Institute, Worcester, MA, USA","institution_ids":["https://openalex.org/I107077323"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":2,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":null,"apc_paid":null,"fwci":0.6109,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.71495933,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":90,"max":95},"biblio":{"volume":"36","issue":"4","first_page":"6314","last_page":"6325"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10320","display_name":"Neural Networks and Applications","score":0.9451000094413757,"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":0.9451000094413757,"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/monotone-polygon","display_name":"Monotone polygon","score":0.7140527963638306},{"id":"https://openalex.org/keywords/interpolation","display_name":"Interpolation (computer graphics)","score":0.6958131790161133},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5654634833335876},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.5647183656692505},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.4512190520763397},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.382450670003891},{"id":"https://openalex.org/keywords/mathematical-optimization","display_name":"Mathematical optimization","score":0.36469733715057373},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.33862006664276123},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.32572412490844727},{"id":"https://openalex.org/keywords/geometry","display_name":"Geometry","score":0.2052888572216034},{"id":"https://openalex.org/keywords/image","display_name":"Image (mathematics)","score":0.0658872127532959}],"concepts":[{"id":"https://openalex.org/C2834757","wikidata":"https://www.wikidata.org/wiki/Q4925424","display_name":"Monotone polygon","level":2,"score":0.7140527963638306},{"id":"https://openalex.org/C137800194","wikidata":"https://www.wikidata.org/wiki/Q11713455","display_name":"Interpolation (computer graphics)","level":3,"score":0.6958131790161133},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5654634833335876},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.5647183656692505},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.4512190520763397},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.382450670003891},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.36469733715057373},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.33862006664276123},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.32572412490844727},{"id":"https://openalex.org/C2524010","wikidata":"https://www.wikidata.org/wiki/Q8087","display_name":"Geometry","level":1,"score":0.2052888572216034},{"id":"https://openalex.org/C115961682","wikidata":"https://www.wikidata.org/wiki/Q860623","display_name":"Image (mathematics)","level":2,"score":0.0658872127532959}],"mesh":[],"locations_count":2,"locations":[{"id":"doi:10.1109/tnnls.2024.3387878","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tnnls.2024.3387878","pdf_url":null,"source":{"id":"https://openalex.org/S4210175523","display_name":"IEEE Transactions on Neural Networks and Learning Systems","issn_l":"2162-237X","issn":["2162-237X","2162-2388"],"is_oa":false,"is_in_doaj":false,"is_core":true,"host_organization":"https://openalex.org/P4310319808","host_organization_name":"Institute of Electrical and Electronics Engineers","host_organization_lineage":["https://openalex.org/P4310319808"],"host_organization_lineage_names":["Institute of Electrical and Electronics Engineers"],"type":"journal"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Transactions on Neural Networks and Learning Systems","raw_type":"journal-article"},{"id":"pmid:38648127","is_oa":false,"landing_page_url":"https://pubmed.ncbi.nlm.nih.gov/38648127","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":"IEEE transactions on neural networks and learning systems","raw_type":null}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":46,"referenced_works":["https://openalex.org/W1536484404","https://openalex.org/W1990284858","https://openalex.org/W1994584977","https://openalex.org/W2009546904","https://openalex.org/W2012476164","https://openalex.org/W2012903341","https://openalex.org/W2014640260","https://openalex.org/W2021082954","https://openalex.org/W2044095368","https://openalex.org/W2046898063","https://openalex.org/W2071951166","https://openalex.org/W2080210666","https://openalex.org/W2101587888","https://openalex.org/W2103496339","https://openalex.org/W2113692909","https://openalex.org/W2125406789","https://openalex.org/W2137983211","https://openalex.org/W2152772468","https://openalex.org/W2166116275","https://openalex.org/W2528305538","https://openalex.org/W2566079294","https://openalex.org/W2768379587","https://openalex.org/W2809677183","https://openalex.org/W2951593186","https://openalex.org/W2963276484","https://openalex.org/W3093643472","https://openalex.org/W3170515206","https://openalex.org/W4224209627","https://openalex.org/W4230719014","https://openalex.org/W4236362309","https://openalex.org/W4238187298","https://openalex.org/W4245577611","https://openalex.org/W4394994853","https://openalex.org/W6607280820","https://openalex.org/W6661705076","https://openalex.org/W6684813833","https://openalex.org/W6690771958","https://openalex.org/W6691187937","https://openalex.org/W6697097869","https://openalex.org/W6729598720","https://openalex.org/W6770436524","https://openalex.org/W6779736682","https://openalex.org/W6784710326","https://openalex.org/W6786243064","https://openalex.org/W6790606811","https://openalex.org/W6796103900"],"related_works":["https://openalex.org/W2963936214","https://openalex.org/W4301895170","https://openalex.org/W2610026222","https://openalex.org/W2784024314","https://openalex.org/W1970485118","https://openalex.org/W4249252985","https://openalex.org/W4297415344","https://openalex.org/W3093949365","https://openalex.org/W1481475550","https://openalex.org/W3122495059"],"abstract_inverted_index":{"We":[0,18,110],"study":[1],"monotone":[2,38,53,80,84,89,102,115,132],"neural":[3,105],"networks":[4,106,124,133],"with":[5,107,125],"threshold":[6,90,108],"gates":[7],"where":[8],"all":[9],"the":[10,14,21,27,63,79,129,141],"weights":[11],"(other":[12],"than":[13],"biases)":[15],"are":[16,114],"nonnegative.":[17],"focus":[19],"on":[20,128],"expressive":[22],"power":[23],"and":[24,103],"efficiency":[25],"of":[26,29,71],"representation":[28],"such":[30],"networks.":[31],"Our":[32,74],"first":[33],"result":[34],"establishes":[35],"that":[36,112,118],"every":[37],"function":[39],"over":[40],"$[{0,1}]^{d}$":[41],"can":[42,119],"be":[43,120],"approximated":[44],"within":[45],"arbitrarily":[46],"small":[47],"additive":[48],"error":[49],"by":[50,77,123],"a":[51,69,87],"depth-4":[52,88],"network.":[54,91],"When":[55],"$d":[56],">":[57],"3$":[58],",":[59],"we":[60,97],"improve":[61],"upon":[62],"previous":[64],"best-known":[65],"construction,":[66],"which":[67],"has":[68],"depth":[70],"$d+1$":[72],".":[73],"proof":[75],"goes":[76],"solving":[78],"interpolation":[81],"problem":[82],"for":[83],"datasets":[85],"using":[86],"In":[92],"our":[93],"second":[94],"main":[95],"result,":[96],"compare":[98],"size":[99,139],"bounds":[100],"between":[101],"arbitrary":[104],"gates.":[109],"find":[111],"there":[113],"real":[116],"functions":[117,136],"computed":[121],"efficiently":[122],"no":[126],"restriction":[127],"gates,":[130],"whereas":[131],"approximating":[134],"these":[135],"need":[137],"exponential":[138],"in":[140],"dimension.":[142]},"counts_by_year":[{"year":2025,"cited_by_count":1},{"year":2024,"cited_by_count":1}],"updated_date":"2026-06-11T09:08:48.828518","created_date":"2025-10-10T00:00:00"}
