{"id":"https://openalex.org/W2989787172","doi":"https://doi.org/10.1109/tit.2022.3161620","title":"vqSGD: Vector Quantized Stochastic Gradient Descent","display_name":"vqSGD: Vector Quantized Stochastic Gradient Descent","publication_year":2022,"publication_date":"2022-03-23","ids":{"openalex":"https://openalex.org/W2989787172","doi":"https://doi.org/10.1109/tit.2022.3161620","mag":"2989787172"},"language":"en","primary_location":{"id":"doi:10.1109/tit.2022.3161620","doi":"https://doi.org/10.1109/tit.2022.3161620","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3161620","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","ccf-a","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"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 Information Theory","raw_type":"journal-article"},"volume":null,"type":"article","is_traditional":true,"indexed_in":["arxiv","crossref","datacite"],"open_access":{"is_oa":true,"oa_status":"green","oa_url":"https://arxiv.org/pdf/1911.07971","any_repository_has_fulltext":true},"authorships":[{"author_position":"first","author":{"id":"https://openalex.org/A5089321118","display_name":"Venkata Gandikota","orcid":"https://orcid.org/0000-0003-2381-7788","observed_orcids":["https://orcid.org/0000-0003-2381-7788"]},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]},{"id":"https://openalex.org/I70983195","display_name":"Syracuse University","ror":"https://ror.org/025r5qe02","country_code":"US","type":"education","lineage":["https://openalex.org/I70983195"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Venkata Gandikota","raw_affiliation_strings":["Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY, USA","University of Massachusetts Amherst, Amherst Center, United States"],"raw_orcid":"https://orcid.org/0000-0003-2381-7788","affiliations":[{"raw_affiliation_string":"Department of Electrical Engineering and Computer Science, Syracuse University, Syracuse, NY, USA","institution_ids":["https://openalex.org/I70983195"]},{"raw_affiliation_string":"University of Massachusetts Amherst, Amherst Center, United States","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5035962853","display_name":"Daniel M. Kane","orcid":"https://orcid.org/0009-0007-9647-2609","observed_orcids":["https://orcid.org/0009-0007-9647-2609","https://orcid.org/0000-0002-0220-9962","https://orcid.org/0000-0002-5884-3487"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Daniel Kane","raw_affiliation_strings":["Departments of Computer Science and Mathematics, UC San Diego, La Jolla, CA, USA","University of California, San Diego, San Diego, United States"],"raw_orcid":null,"affiliations":[{"raw_affiliation_string":"Departments of Computer Science and Mathematics, UC San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"University of California, San Diego, San Diego, United States","institution_ids":["https://openalex.org/I36258959"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5083450236","display_name":"Raj Kumar Maity","orcid":"https://orcid.org/0000-0002-4759-696X","observed_orcids":["https://orcid.org/0000-0002-4759-696X"]},"institutions":[{"id":"https://openalex.org/I24603500","display_name":"University of Massachusetts Amherst","ror":"https://ror.org/0072zz521","country_code":"US","type":"education","lineage":["https://openalex.org/I24603500"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Raj Kumar Maity","raw_affiliation_strings":["College of Information and Computer Sciences, UMass Amherst, Amherst, MA, USA","University of Massachusetts Amherst, Amherst Center, United States"],"raw_orcid":"https://orcid.org/0000-0002-4759-696X","affiliations":[{"raw_affiliation_string":"College of Information and Computer Sciences, UMass Amherst, Amherst, MA, USA","institution_ids":["https://openalex.org/I24603500"]},{"raw_affiliation_string":"University of Massachusetts Amherst, Amherst Center, United States","institution_ids":["https://openalex.org/I24603500"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5051046818","display_name":"Arya Mazumdar","orcid":"https://orcid.org/0000-0003-4605-7996","observed_orcids":["https://orcid.org/0000-0003-4605-7996"]},"institutions":[{"id":"https://openalex.org/I36258959","display_name":"University of California San Diego","ror":"https://ror.org/0168r3w48","country_code":"US","type":"education","lineage":["https://openalex.org/I36258959"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Arya Mazumdar","raw_affiliation_strings":["Halicioglu Data Science Institute, UC San Diego, La Jolla, CA, USA","University of California, San Diego, San Diego, United States"],"raw_orcid":"https://orcid.org/0000-0003-4605-7996","affiliations":[{"raw_affiliation_string":"Halicioglu Data Science Institute, UC San Diego, La Jolla, CA, USA","institution_ids":["https://openalex.org/I36258959"]},{"raw_affiliation_string":"University of California, San Diego, San Diego, United States","institution_ids":["https://openalex.org/I36258959"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":[],"corresponding_institution_ids":[],"apc_list":{"value":2195,"currency":"USD","value_usd":2195},"apc_paid":null,"fwci":3.7473,"has_fulltext":true,"cited_by_count":90,"citation_normalized_percentile":{"value":0.9482965,"is_in_top_1_percent":false,"is_in_top_10_percent":true},"cited_by_percentile_year":{"min":95,"max":100},"biblio":{"volume":"68","issue":"7","first_page":"4573","last_page":"4587"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T11612","display_name":"Stochastic Gradient Optimization Techniques","score":0.9955999851226807,"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":0.9955999851226807,"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/T10249","display_name":"Distributed Control Multi-Agent Systems","score":0.0010999999940395355,"subfield":{"id":"https://openalex.org/subfields/2207","display_name":"Control and Systems Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},{"id":"https://openalex.org/T12879","display_name":"Distributed Sensor Networks and Detection Algorithms","score":0.0010000000474974513,"subfield":{"id":"https://openalex.org/subfields/1705","display_name":"Computer Networks and Communications"},"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/vector-quantization","display_name":"vector quantization","score":0.9929999709129333},{"id":"https://openalex.org/keywords/stochastic-gradient-descent","display_name":"stochastic gradient descent","score":0.9449999928474426},{"id":"https://openalex.org/keywords/distributed-optimization","display_name":"distributed optimization","score":0.9100000262260437},{"id":"https://openalex.org/keywords/communication-overhead-reduction","display_name":"communication cost reduction","score":0.7789999842643738},{"id":"https://openalex.org/keywords/unbiased-gradient-estimation","display_name":"unbiased gradient estimation","score":0.5509999990463257},{"id":"https://openalex.org/keywords/information-theoretic-lower-bounds","display_name":"information-theoretic lower bounds","score":0.7929999828338623},{"id":"https://openalex.org/keywords/convex-hull","display_name":"convex hull","score":0.7210000157356262},{"id":"https://openalex.org/keywords/binary-error-correcting-codes","display_name":"binary error-correcting codes","score":0.9589999914169312},{"id":"https://openalex.org/keywords/privacy-guarantees","display_name":"privacy guarantees","score":0.6779999732971191}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6697344779968262},{"id":"https://openalex.org/C153258448","wikidata":"https://www.wikidata.org/wiki/Q1199743","display_name":"Gradient descent","level":3,"score":0.5235347747802734},{"id":"https://openalex.org/C185429906","wikidata":"https://www.wikidata.org/wiki/Q1130160","display_name":"Estimator","level":2,"score":0.4805324673652649},{"id":"https://openalex.org/C34388435","wikidata":"https://www.wikidata.org/wiki/Q2267362","display_name":"Bounded function","level":2,"score":0.47361254692077637},{"id":"https://openalex.org/C28855332","wikidata":"https://www.wikidata.org/wiki/Q198099","display_name":"Quantization (signal processing)","level":2,"score":0.46017706394195557},{"id":"https://openalex.org/C84316537","wikidata":"https://www.wikidata.org/wiki/Q36255","display_name":"Unit vector","level":2,"score":0.4393324553966522},{"id":"https://openalex.org/C191795146","wikidata":"https://www.wikidata.org/wiki/Q3878446","display_name":"Norm (philosophy)","level":2,"score":0.42842769622802734},{"id":"https://openalex.org/C126255220","wikidata":"https://www.wikidata.org/wiki/Q141495","display_name":"Mathematical optimization","level":1,"score":0.3933866322040558},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.38828545808792114},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.3834018409252167},{"id":"https://openalex.org/C114614502","wikidata":"https://www.wikidata.org/wiki/Q76592","display_name":"Combinatorics","level":1,"score":0.35622507333755493},{"id":"https://openalex.org/C11413529","wikidata":"https://www.wikidata.org/wiki/Q8366","display_name":"Algorithm","level":1,"score":0.30653637647628784},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.21193769574165344},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.10528901219367981},{"id":"https://openalex.org/C119857082","wikidata":"https://www.wikidata.org/wiki/Q2539","display_name":"Machine learning","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/C199539241","wikidata":"https://www.wikidata.org/wiki/Q7748","display_name":"Law","level":1,"score":0.0},{"id":"https://openalex.org/C105795698","wikidata":"https://www.wikidata.org/wiki/Q12483","display_name":"Statistics","level":1,"score":0.0},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.0}],"mesh":[],"locations_count":6,"locations":[{"id":"doi:10.1109/tit.2022.3161620","doi":"https://doi.org/10.1109/tit.2022.3161620","is_oa":false,"landing_page_url":"https://doi.org/10.1109/tit.2022.3161620","pdf_url":null,"source":{"id":"https://openalex.org/S4502562","display_name":"IEEE Transactions on Information Theory","issn_l":"0018-9448","issn":["0018-9448","1557-9654"],"is_oa":false,"is_in_doaj":false,"is_core":true,"listed_in":["anvur-class-a","anvur-scientific","ccf-a","cwts-core","dongbi-a","jufo-3","norway-2","poland-200","russia-white-list-1"],"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 Information Theory","raw_type":"journal-article"},{"id":"pmh:oai:arXiv.org:1911.07971","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.07971","pdf_url":"https://arxiv.org/pdf/1911.07971","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":"mag:2989787172","doi":null,"is_oa":true,"landing_page_url":"https://arxiv.org/pdf/1911.07971","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:escholarship.org:ark:/13030/qt3hr24892","doi":null,"is_oa":false,"landing_page_url":"https://escholarship.org/uc/item/3hr24892","pdf_url":null,"source":{"id":"https://openalex.org/S4306400115","display_name":"eScholarship (California Digital Library)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":"https://openalex.org/I2801248553","host_organization_name":"California Digital Library","host_organization_lineage":["https://openalex.org/I2801248553"],"host_organization_lineage_names":[],"type":"repository"},"license":null,"license_id":null,"version":"submittedVersion","is_accepted":false,"is_published":false,"raw_source_name":"IEEE Transactions on Information Theory, vol 68, iss 7","raw_type":"article"},{"id":"doi:10.48550/arxiv.1911.07971","doi":"https://doi.org/10.48550/arxiv.1911.07971","is_oa":true,"landing_page_url":"https://doi.org/10.48550/arxiv.1911.07971","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:3158434734","doi":null,"is_oa":false,"landing_page_url":"http://proceedings.mlr.press/v130/gandikota21a/gandikota21a.pdf","pdf_url":null,"source":{"id":"https://openalex.org/S4306419146","display_name":"International Conference on Artificial Intelligence and Statistics","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"listed_in":[],"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":null,"is_accepted":false,"is_published":false,"raw_source_name":"International Conference on Artificial Intelligence and Statistics","raw_type":null}],"best_oa_location":{"id":"pmh:oai:arXiv.org:1911.07971","doi":null,"is_oa":true,"landing_page_url":"http://arxiv.org/abs/1911.07971","pdf_url":"https://arxiv.org/pdf/1911.07971","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/G1160231156","display_name":"CCF-BSF: CIF: Small: Collaborative Research: Coding and Information - Theoretic Aspects of Local Data Recovery","funder_award_id":"1618512","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G1754370423","display_name":"CAREER: Reliability in Large-Scale Storage","funder_award_id":"2127929","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3109196640","display_name":"HDR TRIPODS: Institute for Integrated Data Science: A Transdisciplinary Approach to Understanding Fundamental Trade-offs and Theoretical Foundations","funder_award_id":"1934846","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G3385483125","display_name":"CIF: Small: New Directions in Clustering: Interactive Algorithms and Statistical Models","funder_award_id":"1909046","funder_id":"https://openalex.org/F4320306076","funder_display_name":"National Science Foundation"},{"id":"https://openalex.org/G5560006178","display_name":"CAREER: Reliability in Large-Scale Storage","funder_award_id":"1642658","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/W2989787172.pdf","grobid_xml":"https://content.openalex.org/works/W2989787172.grobid-xml"},"referenced_works_count":50,"referenced_works":["https://openalex.org/W1442374986","https://openalex.org/W1571134169","https://openalex.org/W1606480398","https://openalex.org/W1981029888","https://openalex.org/W1994520254","https://openalex.org/W2013823004","https://openalex.org/W2019029889","https://openalex.org/W2027595342","https://openalex.org/W2053637704","https://openalex.org/W2153635508","https://openalex.org/W2162576315","https://openalex.org/W2167372639","https://openalex.org/W2192240806","https://openalex.org/W2337093093","https://openalex.org/W2405578611","https://openalex.org/W2407022425","https://openalex.org/W2473418344","https://openalex.org/W2517104773","https://openalex.org/W2535838896","https://openalex.org/W2547352193","https://openalex.org/W2617766261","https://openalex.org/W2750384547","https://openalex.org/W2769644379","https://openalex.org/W2805997383","https://openalex.org/W2890924858","https://openalex.org/W2891970177","https://openalex.org/W2911327153","https://openalex.org/W2911863041","https://openalex.org/W2911920332","https://openalex.org/W2916967211","https://openalex.org/W2931501180","https://openalex.org/W2935990182","https://openalex.org/W2948092338","https://openalex.org/W2963112712","https://openalex.org/W2963189173","https://openalex.org/W2963326510","https://openalex.org/W2964010583","https://openalex.org/W2979495156","https://openalex.org/W2987693302","https://openalex.org/W2995427991","https://openalex.org/W3102984355","https://openalex.org/W3118608800","https://openalex.org/W3128083813","https://openalex.org/W3132159201","https://openalex.org/W3132435311","https://openalex.org/W3157119899","https://openalex.org/W3157752112","https://openalex.org/W4205228770","https://openalex.org/W4236362309","https://openalex.org/W6787972765"],"related_works":["https://openalex.org/W7202121614","https://openalex.org/W3114950976","https://openalex.org/W2531786980","https://openalex.org/W4390102611","https://openalex.org/W3036607224","https://openalex.org/W3196192308","https://openalex.org/W3005090007","https://openalex.org/W4297383547","https://openalex.org/W2770274930","https://openalex.org/W4412568823"],"abstract_inverted_index":{"In":[0,32,71],"this":[1],"work,":[2],"we":[3,35,73,159],"present":[4],"a":[5,75,84,93,146],"family":[6],"of":[7,83,92,107,119,124,131,140,156],"vector":[8,96],"quantization":[9,133],"schemes":[10],"\\emph{vqSGD}":[11,162],"(Vector-Quantized":[12],"Stochastic":[13],"Gradient":[14],"Descent)":[15],"that":[16,66,87,110,161],"provide":[17,103,145],"an":[18,51,89],"asymptotic":[19],"reduction":[20],"in":[21,28,58,127],"the":[22,33,37,59,64,80,122,138,150,153],"communication":[23,120,151],"cost":[24],"with":[25,97],"convergence":[26],"guarantees":[27],"first-order":[29],"distributed":[30],"optimization.":[31],"process":[34],"derive":[36],"following":[38],"fundamental":[39],"information":[40],"theoretic":[41],"fact:":[42],"$\u0398(\\frac{d}{R^2})$":[43],"bits":[44,118],"are":[45,111,135],"necessary":[46],"and":[47,114,144,152],"sufficient":[48],"to":[49],"describe":[50],"unbiased":[52,90],"estimator":[53,91],"${\\hat{g}}({g})$":[54],"for":[55],"any":[56],"${g}$":[57],"$d$-dimensional":[60,94],"unit":[61],"sphere,":[62],"under":[63],"constraint":[65],"$\\|{\\hat{g}}({g})\\|_2\\le":[67],"R$":[68],"almost":[69,98],"surely.":[70],"particular,":[72],"consider":[74],"randomized":[76],"scheme":[77,134],"based":[78],"on":[79],"convex":[81],"hull":[82],"point":[85],"set,":[86],"returns":[88],"gradient":[95],"surely":[99],"bounded":[100],"norm.":[101],"We":[102],"multiple":[104],"efficient":[105],"instances":[106,130],"our":[108,132],"scheme,":[109],"near":[112],"optimal,":[113],"require":[115],"only":[116],"$o(d)$":[117],"at":[121],"expense":[123],"tolerable":[125],"increase":[126],"error.":[128],"The":[129],"obtained":[136],"using":[137],"properties":[139],"binary":[141],"error-correcting":[142],"codes":[143],"smooth":[147],"tradeoff":[148],"between":[149],"estimation":[154],"error":[155],"quantization.":[157],"Furthermore,":[158],"show":[160],"also":[163],"offers":[164],"strong":[165],"privacy":[166],"guarantees.":[167]},"counts_by_year":[{"year":2026,"cited_by_count":2},{"year":2025,"cited_by_count":11},{"year":2024,"cited_by_count":13},{"year":2023,"cited_by_count":12},{"year":2022,"cited_by_count":21},{"year":2021,"cited_by_count":20},{"year":2020,"cited_by_count":11}],"updated_date":"2026-11-10T11:39:43.021295","created_date":"2019-12-05T00:00:00"}