{"id":"https://openalex.org/W4289655351","doi":"https://doi.org/10.1109/isit50566.2022.9834401","title":"On Algebraic Constructions of Neural Networks with Small Weights","display_name":"On Algebraic Constructions of Neural Networks with Small Weights","publication_year":2022,"publication_date":"2022-06-26","ids":{"openalex":"https://openalex.org/W4289655351","doi":"https://doi.org/10.1109/isit50566.2022.9834401"},"language":"en","primary_location":{"id":"doi:10.1109/isit50566.2022.9834401","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834401","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"},"type":"article","indexed_in":["crossref"],"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/A5050848712","display_name":"Kordag Mehmet Kilic","orcid":null},"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"]}],"countries":["US"],"is_corresponding":true,"raw_author_name":"Kordag Mehmet Kilic","raw_affiliation_strings":["California Institute of Technology,Electrical Engineering,USA","Electrical Engineering, California Institute of Technology, USA"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology,Electrical Engineering,USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Electrical Engineering, California Institute of Technology, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"middle","author":{"id":"https://openalex.org/A5051523017","display_name":"Jin Sima","orcid":"https://orcid.org/0000-0003-4588-9790"},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jin Sima","raw_affiliation_strings":["California Institute of Technology,Electrical Engineering,USA","Electrical Engineering, California Institute of Technology, USA"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology,Electrical Engineering,USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Electrical Engineering, California Institute of Technology, USA","institution_ids":["https://openalex.org/I122411786"]}]},{"author_position":"last","author":{"id":"https://openalex.org/A5043861677","display_name":"Jehoshua Bruck","orcid":"https://orcid.org/0000-0001-8474-0812"},"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"]}],"countries":["US"],"is_corresponding":false,"raw_author_name":"Jehoshua Bruck","raw_affiliation_strings":["California Institute of Technology,Electrical Engineering,USA","Electrical Engineering, California Institute of Technology, USA"],"affiliations":[{"raw_affiliation_string":"California Institute of Technology,Electrical Engineering,USA","institution_ids":["https://openalex.org/I122411786"]},{"raw_affiliation_string":"Electrical Engineering, California Institute of Technology, USA","institution_ids":["https://openalex.org/I122411786"]}]}],"institutions":[],"countries_distinct_count":1,"institutions_distinct_count":3,"corresponding_author_ids":["https://openalex.org/A5050848712"],"corresponding_institution_ids":["https://openalex.org/I122411786"],"apc_list":null,"apc_paid":null,"fwci":0.6432,"has_fulltext":false,"cited_by_count":2,"citation_normalized_percentile":{"value":0.55862384,"is_in_top_1_percent":false,"is_in_top_10_percent":false},"cited_by_percentile_year":{"min":89,"max":94},"biblio":{"volume":null,"issue":null,"first_page":"3007","last_page":"3012"},"is_retracted":false,"is_paratext":false,"is_xpac":false,"primary_topic":{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic Engineering"},"field":{"id":"https://openalex.org/fields/22","display_name":"Engineering"},"domain":{"id":"https://openalex.org/domains/3","display_name":"Physical Sciences"}},"topics":[{"id":"https://openalex.org/T10502","display_name":"Advanced Memory and Neural Computing","score":0.9961000084877014,"subfield":{"id":"https://openalex.org/subfields/2208","display_name":"Electrical and Electronic 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/T10320","display_name":"Neural Networks and Applications","score":0.9939000010490417,"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/T12536","display_name":"Topological and Geometric Data Analysis","score":0.9918000102043152,"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/mathematics","display_name":"Mathematics","score":0.6773264408111572},{"id":"https://openalex.org/keywords/artificial-neural-network","display_name":"Artificial neural network","score":0.5462867021560669},{"id":"https://openalex.org/keywords/lemma","display_name":"Lemma (botany)","score":0.5355377793312073},{"id":"https://openalex.org/keywords/context","display_name":"Context (archaeology)","score":0.5172215700149536},{"id":"https://openalex.org/keywords/discrete-mathematics","display_name":"Discrete mathematics","score":0.4981653690338135},{"id":"https://openalex.org/keywords/exponential-function","display_name":"Exponential function","score":0.486539751291275},{"id":"https://openalex.org/keywords/binary-number","display_name":"Binary number","score":0.4675620496273041},{"id":"https://openalex.org/keywords/algebraic-number","display_name":"Algebraic number","score":0.46700963377952576},{"id":"https://openalex.org/keywords/constant","display_name":"Constant (computer programming)","score":0.450599730014801},{"id":"https://openalex.org/keywords/matrix","display_name":"Matrix (chemical analysis)","score":0.4449983537197113},{"id":"https://openalex.org/keywords/applied-mathematics","display_name":"Applied mathematics","score":0.35219067335128784},{"id":"https://openalex.org/keywords/computer-science","display_name":"Computer science","score":0.18827515840530396},{"id":"https://openalex.org/keywords/arithmetic","display_name":"Arithmetic","score":0.18390703201293945},{"id":"https://openalex.org/keywords/mathematical-analysis","display_name":"Mathematical analysis","score":0.0974036455154419}],"concepts":[{"id":"https://openalex.org/C33923547","wikidata":"https://www.wikidata.org/wiki/Q395","display_name":"Mathematics","level":0,"score":0.6773264408111572},{"id":"https://openalex.org/C50644808","wikidata":"https://www.wikidata.org/wiki/Q192776","display_name":"Artificial neural network","level":2,"score":0.5462867021560669},{"id":"https://openalex.org/C2777759810","wikidata":"https://www.wikidata.org/wiki/Q149316","display_name":"Lemma (botany)","level":3,"score":0.5355377793312073},{"id":"https://openalex.org/C2779343474","wikidata":"https://www.wikidata.org/wiki/Q3109175","display_name":"Context (archaeology)","level":2,"score":0.5172215700149536},{"id":"https://openalex.org/C118615104","wikidata":"https://www.wikidata.org/wiki/Q121416","display_name":"Discrete mathematics","level":1,"score":0.4981653690338135},{"id":"https://openalex.org/C151376022","wikidata":"https://www.wikidata.org/wiki/Q168698","display_name":"Exponential function","level":2,"score":0.486539751291275},{"id":"https://openalex.org/C48372109","wikidata":"https://www.wikidata.org/wiki/Q3913","display_name":"Binary number","level":2,"score":0.4675620496273041},{"id":"https://openalex.org/C9376300","wikidata":"https://www.wikidata.org/wiki/Q168817","display_name":"Algebraic number","level":2,"score":0.46700963377952576},{"id":"https://openalex.org/C2777027219","wikidata":"https://www.wikidata.org/wiki/Q1284190","display_name":"Constant (computer programming)","level":2,"score":0.450599730014801},{"id":"https://openalex.org/C106487976","wikidata":"https://www.wikidata.org/wiki/Q685816","display_name":"Matrix (chemical analysis)","level":2,"score":0.4449983537197113},{"id":"https://openalex.org/C28826006","wikidata":"https://www.wikidata.org/wiki/Q33521","display_name":"Applied mathematics","level":1,"score":0.35219067335128784},{"id":"https://openalex.org/C41008148","wikidata":"https://www.wikidata.org/wiki/Q21198","display_name":"Computer science","level":0,"score":0.18827515840530396},{"id":"https://openalex.org/C94375191","wikidata":"https://www.wikidata.org/wiki/Q11205","display_name":"Arithmetic","level":1,"score":0.18390703201293945},{"id":"https://openalex.org/C134306372","wikidata":"https://www.wikidata.org/wiki/Q7754","display_name":"Mathematical analysis","level":1,"score":0.0974036455154419},{"id":"https://openalex.org/C46757340","wikidata":"https://www.wikidata.org/wiki/Q43238","display_name":"Poaceae","level":2,"score":0.0},{"id":"https://openalex.org/C18903297","wikidata":"https://www.wikidata.org/wiki/Q7150","display_name":"Ecology","level":1,"score":0.0},{"id":"https://openalex.org/C86803240","wikidata":"https://www.wikidata.org/wiki/Q420","display_name":"Biology","level":0,"score":0.0},{"id":"https://openalex.org/C159985019","wikidata":"https://www.wikidata.org/wiki/Q181790","display_name":"Composite material","level":1,"score":0.0},{"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/C151730666","wikidata":"https://www.wikidata.org/wiki/Q7205","display_name":"Paleontology","level":1,"score":0.0},{"id":"https://openalex.org/C192562407","wikidata":"https://www.wikidata.org/wiki/Q228736","display_name":"Materials science","level":0,"score":0.0},{"id":"https://openalex.org/C199360897","wikidata":"https://www.wikidata.org/wiki/Q9143","display_name":"Programming language","level":1,"score":0.0}],"mesh":[],"locations_count":1,"locations":[{"id":"doi:10.1109/isit50566.2022.9834401","is_oa":false,"landing_page_url":"https://doi.org/10.1109/isit50566.2022.9834401","pdf_url":null,"source":{"id":"https://openalex.org/S4363604560","display_name":"2022 IEEE International Symposium on Information Theory (ISIT)","issn_l":null,"issn":null,"is_oa":false,"is_in_doaj":false,"is_core":false,"host_organization":null,"host_organization_name":null,"host_organization_lineage":[],"host_organization_lineage_names":[],"type":"conference"},"license":null,"license_id":null,"version":"publishedVersion","is_accepted":true,"is_published":true,"raw_source_name":"2022 IEEE International Symposium on Information Theory (ISIT)","raw_type":"proceedings-article"}],"best_oa_location":null,"sustainable_development_goals":[],"awards":[],"funders":[],"has_content":{"grobid_xml":false,"pdf":false},"content_urls":null,"referenced_works_count":30,"referenced_works":["https://openalex.org/W1495580177","https://openalex.org/W1539389345","https://openalex.org/W1575761830","https://openalex.org/W1662824729","https://openalex.org/W1862379263","https://openalex.org/W1984744318","https://openalex.org/W1990284858","https://openalex.org/W2047705353","https://openalex.org/W2062929592","https://openalex.org/W2081131431","https://openalex.org/W2098730982","https://openalex.org/W2102956735","https://openalex.org/W2104245397","https://openalex.org/W2163904244","https://openalex.org/W2246078215","https://openalex.org/W2405920868","https://openalex.org/W2762433659","https://openalex.org/W2963122961","https://openalex.org/W3037052212","https://openalex.org/W3134883592","https://openalex.org/W3197797236","https://openalex.org/W4206503652","https://openalex.org/W4289655351","https://openalex.org/W4295262505","https://openalex.org/W6632200440","https://openalex.org/W6691026509","https://openalex.org/W6693397755","https://openalex.org/W6714058667","https://openalex.org/W6778912003","https://openalex.org/W6838240329"],"related_works":["https://openalex.org/W3006682748","https://openalex.org/W1097487277","https://openalex.org/W2768610039","https://openalex.org/W4308265086","https://openalex.org/W4293392396","https://openalex.org/W2149223108","https://openalex.org/W2004969663","https://openalex.org/W2019915549","https://openalex.org/W3099676387","https://openalex.org/W2091797280"],"abstract_inverted_index":{"Neural":[0],"gates":[1,17],"compute":[2,147,185],"functions":[3,21],"based":[4,116],"on":[5,26,117,210],"weighted":[6],"sums":[7],"of":[8,15,19,39,66,103,131,177,199],"the":[9,27,37,44,47,64,121,126,136,148,175,178,186,197,200,207,211,215],"input":[10],"variables.":[11],"The":[12,111],"expressive":[13],"power":[14],"neural":[16,67],"(number":[18],"distinct":[20],"it":[22,99],"can":[23],"compute)":[24],"depends":[25],"weight":[28,48,180,212],"sizes":[29,213,218],"and,":[30],"in":[31,36,59,156,194],"general,":[32],"large":[33,169],"weights":[34],"(exponential":[35],"number":[38],"inputs)":[40],"are":[41,115,158],"required.":[42],"Studying":[43],"trade-offs":[45,78],"among":[46],"sizes,":[49],"circuit":[50,60,201,217],"size":[51,144,181],"and":[52,63,129,221],"depth":[53],"is":[54],"a":[55,71,81,87,101,140,163],"well-studied":[56],"topic":[57],"both":[58],"complexity":[61,77,202],"theory":[62],"practice":[65],"computation.":[68],"We":[69],"propose":[70],"new":[72],"approach":[73],"for":[74,120,125,135,214,219],"studying":[75],"these":[76],"by":[79],"considering":[80],"related":[82],"algebraic":[83],"framework.":[84],"Specifically,":[85],"given":[86],"single":[88,164],"linear":[89,104,165],"equation":[90,166],"with":[91,106,162],"arbitrary":[92],"coefficients,":[93],"we":[94,113,173],"would":[95],"like":[96],"to":[97,146,184],"express":[98],"using":[100],"system":[102],"equations":[105],"smaller":[107],"(even":[108],"constant)":[109],"coefficients.":[110],"techniques":[112],"developed":[114],"Siegel\u2019s":[118],"Lemma":[119],"bounds,":[122],"anti-concentration":[123],"inequalities":[124],"existential":[127],"results":[128,205],"extensions":[130],"Sylvester-type":[132],"Hadamard":[133],"matrices":[134,183],"constructions.We":[137],"explicitly":[138],"construct":[139],"constant":[141],"weight,":[142],"optimal":[143],"matrix":[145],"EQUALITY":[149,161,220],"function":[150,188],"(checking":[151],"if":[152],"two":[153,191],"integers":[154,192],"expressed":[155,193],"binary":[157],"equal).":[159],"Computing":[160],"requires":[167],"exponentially":[168],"weights.":[170],"In":[171,196],"addition,":[172],"prove":[174],"existence":[176],"best-known":[179,216],"(linear)":[182],"COMPARISON":[187],"(comparing":[189],"between":[190],"binary).":[195],"context":[198],"theory,":[203],"our":[204],"improve":[206],"upper":[208],"bounds":[209],"COMPARISON.":[222]},"counts_by_year":[{"year":2024,"cited_by_count":1},{"year":2022,"cited_by_count":1}],"updated_date":"2026-03-14T06:41:57.775601","created_date":"2025-10-10T00:00:00"}
