[{"_1":2,"_3":-5,"_4":-5},"loaderData",{"_5":6,"_7":8,"_9":10},"actionData","errors","root",{"_287":288},"routes/_layout",{"_11":213},"routes/entity.$type.$id",{"_11":12,"_13":14,"_15":16,"_17":18,"_19":20,"_21":22,"_23":24,"_25":26,"_27":28},"dehydratedState",{"_73":74,"_75":76},"type","paper","id","paper_W1984431842","section","technologies","entity",{"_15":16,"_29":30,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":38,"_39":-5,"_40":41,"_42":43,"_44":45,"_46":47,"_48":-5,"_49":50,"_51":30,"_52":53,"_54":55,"_56":57,"_58":59,"_60":61,"_62":-5,"_63":64,"_65":-5,"_66":67,"_68":30,"_69":-5},"canonical","https://www.hugmap.com/entity/paper/paper_W1984431842/technologies","siteBaseUrl","https://www.hugmap.com","sectionCount",3,"jsonLd","{\"@context\":\"https://schema.org\",\"@graph\":[{\"name\":\"The capacity of the Hopfield associative memory\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W1984431842/technologies\",\"@type\":\"ScholarlyArticle\",\"headline\":\"The capacity of the Hopfield associative memory\",\"datePublished\":\"1987-07-01\",\"isPartOf\":{\"@type\":\"Periodical\",\"name\":\"IEEE Transactions on Information Theory\"}},{\"@type\":\"CollectionPage\",\"name\":\"The capacity of the Hopfield associative memory 相关技术\",\"description\":\"The capacity of the Hopfield associative memory 在 HugMap 中的相关技术，共 3 条，含结构化关联信息与详情链接。\",\"url\":\"https://www.hugmap.com/entity/paper/paper_W1984431842/technologies\",\"inLanguage\":\"zh-CN\"},{\"@type\":\"BreadcrumbList\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"首页\",\"item\":\"https://www.hugmap.com/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"论文\",\"item\":\"https://www.hugmap.com/search?type=paper\"},{\"@type\":\"ListItem\",\"position\":3,\"name\":\"The capacity of the Hopfield associative memory\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W1984431842\"},{\"@type\":\"ListItem\",\"position\":4,\"name\":\"相关技术\",\"item\":\"https://www.hugmap.com/entity/paper/paper_W1984431842/technologies\"}]}]}","name","The capacity of the Hopfield associative memory","nameZh","aliases","description","descriptionZh","status","active","externalIds","{\"openalex\":\"W1984431842\",\"doi\":\"10.1109/tit.1987.1057328\"}","properties","source","openalex","createdAt","2026-05-14T17:38:58.332845336","updatedAt","2026-05-21T22:23:20.18651763","doi","10.1109/tit.1987.1057328","arxivId","openalexId","W1984431842","title","abstractText","Techniques from coding theory are applied to study rigorously the capacity of the Hopfield associative memory. Such a memory stores n -tuple of \\pm 1 's. The components change depending on a hard-limited version of linear functions of all other components. With symmetric connections between components, a stable state is ultimately reached. By building up the connection matrix as a sum-of-outer products of m fundamental memories, one hopes to be able to recover a certain one of the m memories by using an initial n -tuple probe vector less than a Hamming distance n/2 away from the fundamental memory. If m fundamental memories are chosen at random, the maximum asympotic value of m in order that most of the m original memories are exactly recoverable is n/(2 \\log n) . With the added restriction that every one of the m fundamental memories be recoverable exactly, m can be no more than n/(4 \\log n) asymptotically as n approaches infinity. Extensions are also considered, in particular to capacity under quantization of the outer-product connection matrix. This quantized memory capacity problem is closely related to the capacity of the quantized Gaussian channel.","publishedDate","1987-07-01","publishedYear",1987,"venue","IEEE Transactions on Information Theory","citationCount",904,"authors","keywords",[70,71,72],"pdfUrl","topVenue",false,"displayName","displayDescription","Advanced Memory and Neural Computing","Neural Networks and Applications","Quantum Computing Algorithms and Architecture","mutations",[],"queries",[77],{"_78":79,"_80":81,"_82":83,"_84":85},"dehydratedAt",1780770339619,"state",{"_87":88,"_89":90,"_91":92,"_93":-5,"_94":95,"_96":95,"_97":95,"_98":-5,"_99":-5,"_100":67,"_35":101,"_102":103},"queryKey",[86,19,14,16],"queryHash","[\"portal\",\"entity\",\"paper\",\"paper_W1984431842\"]","portal","data",{"_19":20,"_104":105,"_106":107,"_108":109,"_110":111,"_18":112,"_62":113},"dataUpdateCount",1,"dataUpdatedAt",1780770339618,"error","errorUpdateCount",0,"errorUpdatedAt","fetchFailureCount","fetchFailureReason","fetchMeta","isInvalidated","success","fetchStatus","idle","entityType","Paper","taxonomies",[174,175,176,177],"events",[],"articles",[],[148,149,150],[114,115,116,117],{"_15":142,"_29":143,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":144,"_39":-5,"_40":41,"_42":145,"_44":146,"_123":147,"_51":-5,"_124":-5,"_125":-5,"_126":-5,"_60":-5,"_127":-5,"_128":-5,"_129":-5,"_130":-5,"_131":-5,"_68":143,"_69":-5},{"_15":137,"_29":138,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":139,"_39":-5,"_40":41,"_42":140,"_44":141,"_123":-5,"_51":-5,"_124":-5,"_125":-5,"_126":-5,"_60":-5,"_127":-5,"_128":-5,"_129":-5,"_130":-5,"_131":-5,"_68":138,"_69":-5},{"_15":132,"_29":133,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":134,"_39":-5,"_40":41,"_42":135,"_44":136,"_123":-5,"_51":-5,"_124":-5,"_125":-5,"_126":-5,"_60":-5,"_127":-5,"_128":-5,"_129":-5,"_130":-5,"_131":-5,"_68":133,"_69":-5},{"_15":118,"_29":119,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":120,"_39":-5,"_40":41,"_42":121,"_44":122,"_123":-5,"_51":-5,"_124":-5,"_125":-5,"_126":-5,"_60":-5,"_127":-5,"_128":-5,"_129":-5,"_130":-5,"_131":-5,"_68":119,"_69":-5},"person_A5032497643","Robert J. McEliece","{\"openalex\":\"A5032497643\"}","2026-05-14T06:37:45.271795924","2026-05-21T22:23:20.194772307","orcid","affiliation","researchArea","paperCount","homepage","linkedin","twitter","github","hindex","person_A5050330289","Edward C. Posner","{\"openalex\":\"A5050330289\"}","2026-05-14T17:38:58.398075411","2026-05-21T22:23:20.246559882","person_A5001508576","E. R. Rodemich","{\"openalex\":\"A5001508576\"}","2026-05-14T17:38:59.180274173","2026-05-21T22:23:20.310847608","person_A5009392214","Santosh S. Venkatesh","{\"openalex\":\"A5009392214\",\"orcid\":\"0000-0002-4453-5061\"}","2026-05-14T17:38:59.260537239","2026-05-21T22:23:20.36998725","0000-0002-4453-5061",{"_15":170,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":171,"_39":-5,"_40":153,"_42":172,"_44":173,"_156":169,"_158":159,"_160":-5,"_161":162,"_163":-5,"_126":-5,"_164":-5,"_68":71,"_69":-5},{"_15":165,"_29":72,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":166,"_39":-5,"_40":153,"_42":167,"_44":168,"_156":169,"_158":159,"_160":-5,"_161":162,"_163":-5,"_126":-5,"_164":-5,"_68":72,"_69":-5},{"_15":151,"_29":70,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":152,"_39":-5,"_40":153,"_42":154,"_44":155,"_156":157,"_158":159,"_160":-5,"_161":162,"_163":-5,"_126":-5,"_164":-5,"_68":70,"_69":-5},"tech_oa_T10502","{\"taxonomy_id\":\"tax_rd_T10502\"}","openalex_topics","2026-05-17T09:00:21.284122589","2026-05-17T09:00:21.284125683","techType","concept","domain","Physical Sciences","proposedYear","maturityLevel","growing","wikipediaUrl","patentCount","tech_oa_T10682","{\"taxonomy_id\":\"tax_rd_T10682\"}","2026-05-17T09:00:16.315436236","2026-05-17T09:00:16.315439876","architecture","tech_oa_T10320","{\"taxonomy_id\":\"tax_rd_T10320\"}","2026-05-17T09:00:01.255985187","2026-05-17T09:00:01.255987331",{"_15":206,"_29":207,"_31":-5,"_32":-5,"_33":208,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":212,"_190":95,"_191":192,"_193":95,"_194":-5,"_68":207,"_69":208},{"_15":201,"_29":71,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":202,"_39":-5,"_40":41,"_42":203,"_44":204,"_182":183,"_184":-5,"_185":26,"_186":199,"_188":205,"_190":95,"_191":192,"_193":95,"_194":-5,"_68":71,"_69":-5},{"_15":195,"_29":72,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":196,"_39":-5,"_40":41,"_42":197,"_44":198,"_182":183,"_184":-5,"_185":26,"_186":199,"_188":200,"_190":95,"_191":192,"_193":95,"_194":-5,"_68":72,"_69":-5},{"_15":178,"_29":70,"_31":-5,"_32":-5,"_33":-5,"_34":-5,"_35":36,"_37":179,"_39":-5,"_40":41,"_42":180,"_44":181,"_182":183,"_184":-5,"_185":26,"_186":187,"_188":189,"_190":95,"_191":192,"_193":95,"_194":-5,"_68":70,"_69":-5},"tax_rd_T10502","{\"openalex_topic\":\"T10502\"}","2026-05-14T00:32:12.294786343","2026-05-23T12:35:55.222922889","taxonomyType","RESEARCH_DOMAIN","code","level","parentId","tax_rd_2208","path","Physical Sciences/Engineering/Electrical and Electronic Engineering/Advanced Memory and Neural Computing","sortOrder","isLeaf",true,"entityCount","children","tax_rd_T10682","{\"openalex_topic\":\"T10682\"}","2026-05-14T00:30:39.395658458","2026-05-23T12:41:03.272911456","tax_rd_1702","Physical Sciences/Computer Science/Artificial Intelligence/Quantum Computing Algorithms and Architecture","tax_rd_T10320","{\"openalex_topic\":\"T10320\"}","2026-05-14T00:27:16.239175777","2026-05-23T12:36:45.268811201","Physical Sciences/Computer Science/Artificial Intelligence/Neural Networks and Applications","tax_ind_quantum","量子计算","Quantum Computing","manual","INDUSTRY","tax_ind_root","科技行业/量子计算",{"_73":214,"_75":215},[],[216],{"_78":217,"_80":218,"_82":219,"_84":220},1780770338831,{"_87":222,"_89":90,"_91":223,"_93":-5,"_94":95,"_96":95,"_97":95,"_98":-5,"_99":-5,"_100":67,"_35":101,"_102":103},[86,221],"[\"portal\",\"industries\"]","industries",[224,225,226,227,228,229,230,231,232,233,234,235],1780770338830,{"_15":280,"_29":281,"_31":-5,"_32":282,"_33":283,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":284,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":281,"_69":283},{"_15":276,"_29":277,"_31":-5,"_32":-5,"_33":278,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":279,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":277,"_69":278},{"_15":270,"_29":271,"_31":-5,"_32":272,"_33":273,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":274,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":271,"_69":273},{"_15":266,"_29":267,"_31":-5,"_32":-5,"_33":268,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":269,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":267,"_69":268},{"_15":262,"_29":263,"_31":-5,"_32":-5,"_33":264,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":265,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":263,"_69":264},{"_15":256,"_29":257,"_31":-5,"_32":258,"_33":259,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":260,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":257,"_69":259},{"_15":206,"_29":207,"_31":-5,"_32":-5,"_33":208,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":212,"_190":95,"_191":192,"_193":95,"_194":-5,"_68":207,"_69":208},{"_15":252,"_29":253,"_31":-5,"_32":-5,"_33":254,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":255,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":253,"_69":254},{"_15":248,"_29":249,"_31":-5,"_32":-5,"_33":250,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":251,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":249,"_69":250},{"_15":244,"_29":245,"_31":-5,"_32":-5,"_33":246,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":247,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":245,"_69":246},{"_15":240,"_29":241,"_31":-5,"_32":-5,"_33":242,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":243,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":241,"_69":242},{"_15":236,"_29":237,"_31":-5,"_32":-5,"_33":238,"_34":-5,"_35":36,"_37":-5,"_39":-5,"_40":209,"_42":-5,"_44":-5,"_182":210,"_184":-5,"_185":90,"_186":211,"_188":239,"_190":95,"_191":67,"_193":95,"_194":-5,"_68":237,"_69":238},"tax_ind_smartphone","智能手机","Smartphone","科技行业/智能手机","tax_ind_robot","机器人","Robotics","科技行业/机器人","tax_ind_wearable","智能穿戴","Smart Wearables","科技行业/智能穿戴","tax_ind_energy","新能源与智能制造","New Energy & Smart Manufacturing","科技行业/新能源与智能制造","tax_ind_biotech","生物科技","Biotech","科技行业/生物科技","tax_ind_blockchain","区块链",[261],"Blockchain","科技行业/区块链","Web3","tax_ind_enterprise","企业软件","Enterprise Software","科技行业/企业软件","tax_ind_security","网络安全","Cybersecurity","科技行业/网络安全","tax_ind_semi","半导体",[275],"Semiconductor","科技行业/半导体","芯片","tax_ind_cloud","云计算","Cloud Computing","科技行业/云计算","tax_ind_ai","人工智能",[285,286],"Artificial Intelligence","科技行业/人工智能","AI","AI 技术","env",{"_289":24},"SITE_BASE_URL"]

The capacity of the Hopfield associative memory 论文

The capacity of the Hopfield associative memory · 相关技术

相关技术