{"id":"https://openalex.org/W3062959591","doi":"https://doi.org/10.1109/access.2020.3017436","title":"Effective Activation Functions for Homomorphic Evaluation of Deep Neural Networks","display_name":"Effective Activation Functions for Homomorphic Evaluation of Deep Neural Networks","publication_year":2020,"publication_date":"2020-01-01","ids":{"openalex":"https://openalex.org/W3062959591","doi":"https://doi.org/10.1109/access.2020.3017436","mag":"3062959591"},"language":"en","primary_location":{"id":"doi:10.1109/access.2020.3017436","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3017436","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09169889.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"type":"article","indexed_in":["crossref","doaj"],"open_access":{"is_oa":true,"oa_status":"gold","oa_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09169889.pdf","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5050800490","display_name":"Srinath Obla","orcid":"https://orcid.org/0000-0002-3864-7892"},"institutions":[{"id":"https://openalex.org/I155173764","display_name":"Rochester Institute of Technology","ror":"https://ror.org/00v4yb702","country_code":"US","type":"education","lineage":["https://openalex.org/I155173764"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Srinath Obla","raw_affiliation_strings":["Department of Computer Science, Rochester Institute of Technology, Rochester, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Rochester Institute of Technology, Rochester, USA","institution_ids":["https://openalex.org/I155173764"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5042793721","display_name":"Xinghan Gong","orcid":null},"institutions":[{"id":"https://openalex.org/I155173764","display_name":"Rochester Institute of Technology","ror":"https://ror.org/00v4yb702","country_code":"US","type":"education","lineage":["https://openalex.org/I155173764"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Xinghan Gong","raw_affiliation_strings":["Department of Computer Science, Rochester Institute of Technology, Rochester, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Rochester Institute of Technology, Rochester, USA","institution_ids":["https://openalex.org/I155173764"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5039640157","display_name":"Asma Aloufi","orcid":"https://orcid.org/0000-0002-8362-2432"},"institutions":[{"id":"https://openalex.org/I155173764","display_name":"Rochester Institute of Technology","ror":"https://ror.org/00v4yb702","country_code":"US","type":"education","lineage":["https://openalex.org/I155173764"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Asma Aloufi","raw_affiliation_strings":["Department of Computer Science, Rochester Institute of Technology, Rochester, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Rochester Institute of Technology, Rochester, USA","institution_ids":["https://openalex.org/I155173764"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5090846864","display_name":"Peizhao Hu","orcid":"https://orcid.org/0000-0001-7260-6325"},"institutions":[{"id":"https://openalex.org/I155173764","display_name":"Rochester Institute of Technology","ror":"https://ror.org/00v4yb702","country_code":"US","type":"education","lineage":["https://openalex.org/I155173764"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Peizhao Hu","raw_affiliation_strings":["Department of Computer Science, Rochester Institute of Technology, Rochester, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Rochester Institute of Technology, Rochester, USA","institution_ids":["https://openalex.org/I155173764"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5002423453","display_name":"Daniel Takabi","orcid":"https://orcid.org/0000-0003-0447-3641"},"institutions":[{"id":"https://openalex.org/I181565077","display_name":"Georgia State University","ror":"https://ror.org/03qt6ba18","country_code":"US","type":"education","lineage":["https://openalex.org/I181565077"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Takabi","raw_affiliation_strings":["Department of Computer Science, Georgia State University, Atlanta, USA"],"affiliations":[{"raw_affiliation_string":"Department of Computer Science, Georgia State University, Atlanta, USA","institution_ids":["https://openalex.org/I181565077"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":5,"corresponding_author_ids":["https://openalex.org/A5050800490"],"corresponding_institution_ids":["https://openalex.org/I155173764"],"apc_list":{"value":1850,"currency":"USD","value_usd":1850},"apc_paid":{"value":1850,"currency":"USD","value_usd":1850},"fwci":4.465,"has_fulltext":true,"cited_by_count":51,"citation_normalized_percentile":{"value":0.95493505,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":89,"max":100},"biblio":{"volume":"8","issue":null,"first_page":"153098","last_page":"153112"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10237","display_name":"Cryptography and Data Security","score":0.9994999766349792,"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/T10237","display_name":"Cryptography and Data Security","score":0.9994999766349792,"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/T11693","display_name":"Cryptography and Residue Arithmetic","score":0.9937999844551086,"subfield":{"id":"https://openalex.org/subfields/1710","display_name":"Information Systems"},"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/T10720","display_name":"Complexity and Algorithms in Graphs","score":0.9868999719619751,"subfield":{"id":"https://openalex.org/subfields/1703","display_name":"Computational Theory and Mathematics"},"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/sigmoid-function","display_name":"Sigmoid function","score":0.822214663028717},{"id":"https://openalex.org/keywords/mnist-database","display_name":"MNIST database","score":0.8190715909004211},{"id":"https://openalex.org/keywords/activation-function","display_name":"Activation function","score":0.7794212102890015},{"id":"https://openalex.org/keywords/normalization","display_name":"Normalization (sociology)","score":0.6308484077453613},{"id":"https://openalex.org/keywords/convolutional-neural-network","display_name":"Convolutional neural network","score":0.6210537552833557},{"id":"https://openalex.org/keywords/polynomial","display_name":"Polynomial","score":0.5734686851501465},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.5392943620681763},{"id":"https://openalex.org/keywords/computation","display_name":"Computation","score":0.5284585356712341},{"id":"https://openalex.org/keywords/convolution","display_name":"Convolution (computer science)","score":0.5189968347549438},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.49575337767601013},{"id":"https://openalex.org/keywords/homomorphic-encryption","display_name":"Homomorphic encryption","score":0.4853273928165436},{"id":"https://openalex.org/keywords/algorithm","display_name":"Algorithm","score":0.4567509889602661},{"id":"https://openalex.org/keywords/smoothness","display_name":"Smoothness","score":0.4428061544895172},{"id":"https://openalex.org/keywords/norm","display_name":"Norm (philosophy)","score":0.4346056580543518},{"id":"https://openalex.org/keywords/approximation-theory","display_name":"Approximation theory","score":0.41332292556762695},{"id":"https://openalex.org/keywords/mathematics","display_name":"Mathematics","score":0.35945791006088257},{"id":"https://openalex.org/keywords/artificial-intelligence","display_name":"Artificial intelligence","score":0.2579793334007263},{"id":"https://openalex.org/keywords/encryption","display_name":"Encryption","score":0.1859114170074463}],"concepts":[{"id":"https://openalex.org/C81388566","wikidata":"https://www.wikidata.org/wiki/Q526668","display_name":"Sigmoid function","level":3,"score":0.822214663028717},{"id":"https://openalex.org/C190502265","wikidata":"https://www.wikidata.org/wiki/Q17069496","display_name":"MNIST database","level":3,"score":0.8190715909004211},{"id":"https://openalex.org/C38365724","wikidata":"https://www.wikidata.org/wiki/Q4677469","display_name":"Activation function","level":3,"score":0.7794212102890015},{"id":"https://openalex.org/C136886441","wikidata":"https://www.wikidata.org/wiki/Q926129","display_name":"Normalization (sociology)","level":2,"score":0.6308484077453613},{"id":"https://openalex.org/C81363708","wikidata":"https://www.wikidata.org/wiki/Q17084460","display_name":"Convolutional neural network","level":2,"score":0.6210537552833557},{"id":"https://openalex.org/C90119067","wikidata":"https://www.wikidata.org/wiki/Q43260","display_name":"Polynomial","level":2,"score":0.5734686851501465},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.5392943620681763},{"id":"https://openalex.org/C45374587","wikidata":"https://www.wikidata.org/wiki/Q12525525","display_name":"Computation","level":2,"score":0.5284585356712341},{"id":"https://openalex.org/C45347329","wikidata":"https://www.wikidata.org/wiki/Q5166604","display_name":"Convolution (computer science)","level":3,"score":0.5189968347549438},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.49575337767601013},{"id":"https://openalex.org/C158338273","wikidata":"https://www.wikidata.org/wiki/Q2154943","display_name":"Homomorphic encryption","level":3,"score":0.4853273928165436},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.4567509889602661},{"id":"https://openalex.org/C102634674","wikidata":"https://www.wikidata.org/wiki/Q868473","display_name":"Smoothness","level":2,"score":0.4428061544895172},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.4346056580543518},{"id":"https://openalex.org/C145242015","wikidata":"https://www.wikidata.org/wiki/Q774123","display_name":"Approximation theory","level":2,"score":0.41332292556762695},{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.35945791006088257},{"id":"https://openalex.org/C154945302","wikidata":"https://www.wikidata.org/wiki/Q11660","display_name":"Artificial intelligence","level":1,"score":0.2579793334007263},{"id":"https://openalex.org/C148730421","wikidata":"https://www.wikidata.org/wiki/Q141090","display_name":"Encryption","level":2,"score":0.1859114170074463},{"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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C17744445","wikidata":"https://www.wikidata.org/wiki/Q36442","display_name":"Political science","level":0,"score":0.0},{"id":"https://openalex.org/C144024400","wikidata":"https://www.wikidata.org/wiki/Q21201","display_name":"Sociology","level":0,"score":0.0},{"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":4,"locations":[{"id":"doi:10.1109/access.2020.3017436","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3017436","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09169889.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},{"id":"pmh:oai:scholarworks.rit.edu:theses-11739","is_oa":false,"landing_page_url":"https://scholarworks.rit.edu/theses/10593","pdf_url":null,"source":{"id":"https://openalex.org/S4306402456","display_name":"RIT Scholar Works (Rochester Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I155173764","host_organization_name":"Rochester Institute of Technology","host_organization_lineage":["https://openalex.org/I155173764"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Theses","raw_type":"text"},{"id":"pmh:oai:doaj.org/article:8ce0914ab08a4af0b56de9071044e20f","is_oa":true,"landing_page_url":"https://doaj.org/article/8ce0914ab08a4af0b56de9071044e20f","pdf_url":null,"source":{"id":"https://openalex.org/S112646816","display_name":"SHILAP Revista de lepidopterolog\u00eda","issn_l":"0300-5267","issn":["0300-5267","2340-4078"],"is_oa":true,"is_in_doaj":true,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"journal"},"license":"cc-by-sa","license_id":"https://openalex.org/licenses/cc-by-sa","version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Access, Vol 8, Pp 153098-153112 (2020)","raw_type":"article"},{"id":"pmh:oai:repository.rit.edu:theses-11739","is_oa":false,"landing_page_url":"https://repository.rit.edu/theses/10593","pdf_url":null,"source":{"id":"https://openalex.org/S4306402456","display_name":"RIT Scholar Works (Rochester Institute of Technology)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":"https://openalex.org/I155173764","host_organization_name":"Rochester Institute of Technology","host_organization_lineage":["https://openalex.org/I155173764"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"Theses","raw_type":"text"}],"best_oa_location":{"id":"doi:10.1109/access.2020.3017436","is_oa":true,"landing_page_url":"https://doi.org/10.1109/access.2020.3017436","pdf_url":"https://ieeexplore.ieee.org/ielx7/6287639/8948470/09169889.pdf","source":{"id":"https://openalex.org/S2485537415","display_name":"IEEE Access","issn_l":"2169-3536","issn":["2169-3536"],"is_oa":true,"is_in_doaj":true,"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":"cc-by","license_id":"https://openalex.org/licenses/cc-by","version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"IEEE Access","raw_type":"journal-article"},"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"pdf":true,"grobid_xml":true},"content_urls":{"pdf":"https://content.openalex.org/works/W3062959591.pdf","grobid_xml":"https://content.openalex.org/works/W3062959591.grobid-xml"},"referenced_works_count":65,"referenced_works":["https://openalex.org/W162878246","https://openalex.org/W948663339","https://openalex.org/W1572063013","https://openalex.org/W1836465849","https://openalex.org/W1971119909","https://openalex.org/W1971991172","https://openalex.org/W1973079148","https://openalex.org/W1988115241","https://openalex.org/W1992493944","https://openalex.org/W1992774725","https://openalex.org/W2012276148","https://openalex.org/W2043841621","https://openalex.org/W2068143382","https://openalex.org/W2075273870","https://openalex.org/W2103496339","https://openalex.org/W2108834246","https://openalex.org/W2123045220","https://openalex.org/W2132172731","https://openalex.org/W2152926062","https://openalex.org/W2160397751","https://openalex.org/W2226167778","https://openalex.org/W2333542206","https://openalex.org/W2435473771","https://openalex.org/W2502390809","https://openalex.org/W2504108613","https://openalex.org/W2557738935","https://openalex.org/W2585580772","https://openalex.org/W2606882085","https://openalex.org/W2620369751","https://openalex.org/W2750384547","https://openalex.org/W2752840253","https://openalex.org/W2766736793","https://openalex.org/W2767286248","https://openalex.org/W2768174108","https://openalex.org/W2768347741","https://openalex.org/W2773773675","https://openalex.org/W2811248283","https://openalex.org/W2884552531","https://openalex.org/W2900763147","https://openalex.org/W2901469102","https://openalex.org/W2949117887","https://openalex.org/W2963009098","https://openalex.org/W2963399222","https://openalex.org/W2963857746","https://openalex.org/W3028867652","https://openalex.org/W3118608800","https://openalex.org/W3125537303","https://openalex.org/W4210300416","https://openalex.org/W4244779605","https://openalex.org/W4287714351","https://openalex.org/W4297779039","https://openalex.org/W4298350284","https://openalex.org/W4320930577","https://openalex.org/W6638667902","https://openalex.org/W6667374887","https://openalex.org/W6732586565","https://openalex.org/W6743688258","https://openalex.org/W6743881906","https://openalex.org/W6746023985","https://openalex.org/W6746138031","https://openalex.org/W6749036959","https://openalex.org/W6755310813","https://openalex.org/W6756592279","https://openalex.org/W6776626371","https://openalex.org/W6787972765"],"related_works":["https://openalex.org/W3082263874","https://openalex.org/W3024979424","https://openalex.org/W4283785902","https://openalex.org/W2895192346","https://openalex.org/W2041004593","https://openalex.org/W3134817226","https://openalex.org/W3032499992","https://openalex.org/W3110577345","https://openalex.org/W3116943156","https://openalex.org/W3173926637"],"abstract_inverted_index":{"CryptoNets":[0],"and":[1,135,143],"subsequent":[2],"work":[3],"have":[4,87],"demonstrated":[5],"the":[6,13,32,46,62,77,152,166,177],"capability":[7],"of":[8,15,52,61,149,169,179],"homomorphic":[9],"encryption":[10],"(HE)":[11],"in":[12,93,116],"applications":[14],"private":[16],"artificial":[17],"intelligence":[18],"(AI).":[19],"In":[20,96],"convolutional":[21],"neural":[22],"networks":[23],"(CNNs),":[24],"many":[25],"computations":[26],"are":[27,42],"linear":[28],"functions":[29,54,71,82,108,128],"such":[30,44,129,185],"as":[31,45,80,130,186],"convolution":[33],"layer":[34,48],"which":[35,49,85],"can":[36],"be":[37,57],"homomorphically":[38,58],"evaluated.":[39,59],"However,":[40,75],"there":[41],"layers":[43],"activation":[47,81,107,119],"is":[50,67],"comprised":[51],"non-linear":[53,70],"that":[55],"cannot":[56],"One":[60],"most":[63],"commonly":[64,126],"used":[65,127],"methods":[66,142],"approximating":[68],"these":[69],"using":[72,76,182],"low-degree":[73],"polynomials.":[74],"approximated":[78],"polynomials":[79],"introduces":[83],"errors":[84],"could":[86],"a":[88,101,117,158,170],"significant":[89],"impact":[90],"on":[91],"accuracy":[92],"classification":[94],"tasks.":[95],"this":[97],"paper,":[98],"we":[99,138,175],"present":[100],"systematic":[102],"method":[103,163,181],"to":[104,122,165],"construct":[105],"HE-friendly":[106],"for":[109,145,151],"CNNs.":[110],"We":[111,155],"first":[112],"determine":[113],"what":[114],"properties":[115],"good":[118],"function":[120],"contribute":[121],"performance":[123],"by":[124],"analyzing":[125],"Rectified":[131],"Linear":[132],"Units":[133],"(ReLU)":[134],"Sigmoid.":[136],"Then,":[137],"compare":[139],"polynomial":[140,153,161],"approximation":[141,150,162],"search":[144],"an":[146],"optimal":[147],"range":[148],"activation.":[154],"also":[156],"propose":[157],"novel":[159],"weighted":[160],"tailored":[164],"output":[167],"distribution":[168],"batch":[171],"normalization":[172],"layer.":[173],"Finally,":[174],"demonstrate":[176],"effectiveness":[178],"our":[180],"several":[183],"datasets":[184],"MNIST,":[187],"FMNIST,":[188],"CIFAR-10.":[189]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":6},{"year":2024,"cited_by_count":10},{"year":2023,"cited_by_count":16},{"year":2022,"cited_by_count":8},{"year":2021,"cited_by_count":8},{"year":2020,"cited_by_count":1}],"updated_date":"2026-04-04T16:13:02.066488","created_date":"2025-10-10T00:00:00"}