The capacity of the Hopfield associative memory
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 com...
Gespeichert in:
Veröffentlicht in: | IEEE transactions on information theory 1987-07, Vol.33 (4), p.461-482 |
---|---|
Hauptverfasser: | , , , |
Format: | Artikel |
Sprache: | eng |
Schlagworte: | |
Online-Zugang: | Volltext bestellen |
Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
container_end_page | 482 |
---|---|
container_issue | 4 |
container_start_page | 461 |
container_title | IEEE transactions on information theory |
container_volume | 33 |
creator | McEliece, R. Posner, E. Rodemich, E. Venkatesh, S. |
description | 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. |
doi_str_mv | 10.1109/TIT.1987.1057328 |
format | Article |
fullrecord | <record><control><sourceid>proquest_RIE</sourceid><recordid>TN_cdi_pascalfrancis_primary_7654685</recordid><sourceformat>XML</sourceformat><sourcesystem>PC</sourcesystem><ieee_id>1057328</ieee_id><sourcerecordid>28689394</sourcerecordid><originalsourceid>FETCH-LOGICAL-c450t-df7c7bce246aecdc9e0086889bea391c8dd84c89e654e1544c4b2a630752a25e3</originalsourceid><addsrcrecordid>eNpNUM9LwzAUDqLgnN4FPfQg3roladImRxnqBgMv9Rze0leM9JdJJ-y_N7NDPD0-3veLj5BbRheMUb0sN-WCaVUsGJVFxtUZmTEpi1TnUpyTGaVMpVoIdUmuQviMUEjGZ2RZfmBiYQDrxkPS18kY8bofaodNlUAIvXUwum9MWmx7f7gmFzU0AW9Od07eX57L1Trdvr1uVk_b1ApJx7SqC1vsLHKRA9rKaqRU5UrpHUKmmVVVpYRVGmM7ZFIIK3Yc8owWkgOXmM3J4-Q7-P5rj2E0rQsWmwY67PfB8OimMy0ikU5E6_sQPNZm8K4FfzCMmuMyJi5jjsuY0zJR8nDyhmChqT101oU_XRE75UpG2v1E6yCA6UYffm0ozaXkNL7vprdDxH-hU8YPxkNzqQ</addsrcrecordid><sourcetype>Aggregation Database</sourcetype><iscdi>true</iscdi><recordtype>article</recordtype><pqid>28689394</pqid></control><display><type>article</type><title>The capacity of the Hopfield associative memory</title><source>IEEE Electronic Library (IEL)</source><creator>McEliece, R. ; Posner, E. ; Rodemich, E. ; Venkatesh, S.</creator><creatorcontrib>McEliece, R. ; Posner, E. ; Rodemich, E. ; Venkatesh, S.</creatorcontrib><description>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.</description><identifier>ISSN: 0018-9448</identifier><identifier>EISSN: 1557-9654</identifier><identifier>DOI: 10.1109/TIT.1987.1057328</identifier><identifier>CODEN: IETTAW</identifier><language>eng</language><publisher>Legacy CDMS: IEEE</publisher><subject>Applied sciences ; Cybernetics ; Electronics ; Exact sciences and technology ; Storage and reproduction of information</subject><ispartof>IEEE transactions on information theory, 1987-07, Vol.33 (4), p.461-482</ispartof><rights>1988 INIST-CNRS</rights><lds50>peer_reviewed</lds50><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed><citedby>FETCH-LOGICAL-c450t-df7c7bce246aecdc9e0086889bea391c8dd84c89e654e1544c4b2a630752a25e3</citedby><cites>FETCH-LOGICAL-c450t-df7c7bce246aecdc9e0086889bea391c8dd84c89e654e1544c4b2a630752a25e3</cites></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><linktohtml>$$Uhttps://ieeexplore.ieee.org/document/1057328$$EHTML$$P50$$Gieee$$H</linktohtml><link.rule.ids>314,776,780,792,27901,27902,54733</link.rule.ids><linktorsrc>$$Uhttps://ieeexplore.ieee.org/document/1057328$$EView_record_in_IEEE$$FView_record_in_$$GIEEE</linktorsrc><backlink>$$Uhttp://pascal-francis.inist.fr/vibad/index.php?action=getRecordDetail&idt=7654685$$DView record in Pascal Francis$$Hfree_for_read</backlink></links><search><creatorcontrib>McEliece, R.</creatorcontrib><creatorcontrib>Posner, E.</creatorcontrib><creatorcontrib>Rodemich, E.</creatorcontrib><creatorcontrib>Venkatesh, S.</creatorcontrib><title>The capacity of the Hopfield associative memory</title><title>IEEE transactions on information theory</title><addtitle>TIT</addtitle><description>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.</description><subject>Applied sciences</subject><subject>Cybernetics</subject><subject>Electronics</subject><subject>Exact sciences and technology</subject><subject>Storage and reproduction of information</subject><issn>0018-9448</issn><issn>1557-9654</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1987</creationdate><recordtype>article</recordtype><sourceid>CYI</sourceid><recordid>eNpNUM9LwzAUDqLgnN4FPfQg3roladImRxnqBgMv9Rze0leM9JdJJ-y_N7NDPD0-3veLj5BbRheMUb0sN-WCaVUsGJVFxtUZmTEpi1TnUpyTGaVMpVoIdUmuQviMUEjGZ2RZfmBiYQDrxkPS18kY8bofaodNlUAIvXUwum9MWmx7f7gmFzU0AW9Od07eX57L1Trdvr1uVk_b1ApJx7SqC1vsLHKRA9rKaqRU5UrpHUKmmVVVpYRVGmM7ZFIIK3Yc8owWkgOXmM3J4-Q7-P5rj2E0rQsWmwY67PfB8OimMy0ikU5E6_sQPNZm8K4FfzCMmuMyJi5jjsuY0zJR8nDyhmChqT101oU_XRE75UpG2v1E6yCA6UYffm0ozaXkNL7vprdDxH-hU8YPxkNzqQ</recordid><startdate>19870701</startdate><enddate>19870701</enddate><creator>McEliece, R.</creator><creator>Posner, E.</creator><creator>Rodemich, E.</creator><creator>Venkatesh, S.</creator><general>IEEE</general><general>Institute of Electrical and Electronics Engineers</general><scope>CYE</scope><scope>CYI</scope><scope>IQODW</scope><scope>AAYXX</scope><scope>CITATION</scope><scope>7SC</scope><scope>8FD</scope><scope>JQ2</scope><scope>L7M</scope><scope>L~C</scope><scope>L~D</scope></search><sort><creationdate>19870701</creationdate><title>The capacity of the Hopfield associative memory</title><author>McEliece, R. ; Posner, E. ; Rodemich, E. ; Venkatesh, S.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c450t-df7c7bce246aecdc9e0086889bea391c8dd84c89e654e1544c4b2a630752a25e3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1987</creationdate><topic>Applied sciences</topic><topic>Cybernetics</topic><topic>Electronics</topic><topic>Exact sciences and technology</topic><topic>Storage and reproduction of information</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>McEliece, R.</creatorcontrib><creatorcontrib>Posner, E.</creatorcontrib><creatorcontrib>Rodemich, E.</creatorcontrib><creatorcontrib>Venkatesh, S.</creatorcontrib><collection>NASA Scientific and Technical Information</collection><collection>NASA Technical Reports Server</collection><collection>Pascal-Francis</collection><collection>CrossRef</collection><collection>Computer and Information Systems Abstracts</collection><collection>Technology Research Database</collection><collection>ProQuest Computer Science Collection</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>Computer and Information Systems Abstracts Academic</collection><collection>Computer and Information Systems Abstracts Professional</collection><jtitle>IEEE transactions on information theory</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>McEliece, R.</au><au>Posner, E.</au><au>Rodemich, E.</au><au>Venkatesh, S.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>The capacity of the Hopfield associative memory</atitle><jtitle>IEEE transactions on information theory</jtitle><stitle>TIT</stitle><date>1987-07-01</date><risdate>1987</risdate><volume>33</volume><issue>4</issue><spage>461</spage><epage>482</epage><pages>461-482</pages><issn>0018-9448</issn><eissn>1557-9654</eissn><coden>IETTAW</coden><abstract>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.</abstract><cop>Legacy CDMS</cop><pub>IEEE</pub><doi>10.1109/TIT.1987.1057328</doi><tpages>22</tpages><oa>free_for_read</oa></addata></record> |
fulltext | fulltext_linktorsrc |
identifier | ISSN: 0018-9448 |
ispartof | IEEE transactions on information theory, 1987-07, Vol.33 (4), p.461-482 |
issn | 0018-9448 1557-9654 |
language | eng |
recordid | cdi_pascalfrancis_primary_7654685 |
source | IEEE Electronic Library (IEL) |
subjects | Applied sciences Cybernetics Electronics Exact sciences and technology Storage and reproduction of information |
title | The capacity of the Hopfield associative memory |
url | https://sfx.bib-bvb.de/sfx_tum?ctx_ver=Z39.88-2004&ctx_enc=info:ofi/enc:UTF-8&ctx_tim=2025-02-03T20%3A02%3A04IST&url_ver=Z39.88-2004&url_ctx_fmt=infofi/fmt:kev:mtx:ctx&rfr_id=info:sid/primo.exlibrisgroup.com:primo3-Article-proquest_RIE&rft_val_fmt=info:ofi/fmt:kev:mtx:journal&rft.genre=article&rft.atitle=The%20capacity%20of%20the%20Hopfield%20associative%20memory&rft.jtitle=IEEE%20transactions%20on%20information%20theory&rft.au=McEliece,%20R.&rft.date=1987-07-01&rft.volume=33&rft.issue=4&rft.spage=461&rft.epage=482&rft.pages=461-482&rft.issn=0018-9448&rft.eissn=1557-9654&rft.coden=IETTAW&rft_id=info:doi/10.1109/TIT.1987.1057328&rft_dat=%3Cproquest_RIE%3E28689394%3C/proquest_RIE%3E%3Curl%3E%3C/url%3E&disable_directlink=true&sfx.directlink=off&sfx.report_link=0&rft_id=info:oai/&rft_pqid=28689394&rft_id=info:pmid/&rft_ieee_id=1057328&rfr_iscdi=true |