Optimal storage capacity of neural networks at finite temperatures
Gardner's analysis of the optimal storage capacity of neural networks is extended to study finite-temperature effects. The typical volume of the space of interactions is calculated for strongly-diluted networks as a function of the storage ratio $\alpha$, temperature $T$, and the tolerance para...
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| creator | Shimi, G. M Kim, D Choi, M. Y |
| description | Gardner's analysis of the optimal storage capacity of neural networks is
extended to study finite-temperature effects. The typical volume of the space
of interactions is calculated for strongly-diluted networks as a function of
the storage ratio $\alpha$, temperature $T$, and the tolerance parameter $m$,
from which the optimal storage capacity $\alpha_c$ is obtained as a function of
$T$ and $m$. At zero temperature it is found that $\alpha_c = 2$ regardless of
$m$ while $\alpha_c$ in general increases with the tolerance at finite
temperatures. We show how the best performance for given $\alpha$ and $T$ is
obtained, which reveals a first-order transition from high-quality performance
to low-quality one at low temperatures. An approximate criterion for recalling,
which is valid near $m=1$, is also discussed. |
| doi_str_mv | 10.48550/arxiv.cond-mat/9306032 |
| format | Article |
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extended to study finite-temperature effects. The typical volume of the space
of interactions is calculated for strongly-diluted networks as a function of
the storage ratio $\alpha$, temperature $T$, and the tolerance parameter $m$,
from which the optimal storage capacity $\alpha_c$ is obtained as a function of
$T$ and $m$. At zero temperature it is found that $\alpha_c = 2$ regardless of
$m$ while $\alpha_c$ in general increases with the tolerance at finite
temperatures. We show how the best performance for given $\alpha$ and $T$ is
obtained, which reveals a first-order transition from high-quality performance
to low-quality one at low temperatures. An approximate criterion for recalling,
which is valid near $m=1$, is also discussed.</description><identifier>DOI: 10.48550/arxiv.cond-mat/9306032</identifier><language>eng</language><subject>Physics - Disordered Systems and Neural Networks ; Physics - Materials Science ; Physics - Mesoscale and Nanoscale Physics ; Physics - Other Condensed Matter ; Physics - Quantum Gases ; Physics - Soft Condensed Matter ; Physics - Statistical Mechanics ; Physics - Strongly Correlated Electrons ; Physics - Superconductivity</subject><creationdate>1993-06</creationdate><oa>free_for_read</oa><woscitedreferencessubscribed>false</woscitedreferencessubscribed></display><links><openurl>$$Topenurl_article</openurl><openurlfulltext>$$Topenurlfull_article</openurlfulltext><thumbnail>$$Tsyndetics_thumb_exl</thumbnail><link.rule.ids>228,230,777,882</link.rule.ids><linktorsrc>$$Uhttps://arxiv.org/abs/cond-mat/9306032$$EView_record_in_Cornell_University$$FView_record_in_$$GCornell_University$$Hfree_for_read</linktorsrc><backlink>$$Uhttps://doi.org/10.48550/arXiv.cond-mat/9306032$$DView paper in arXiv$$Hfree_for_read</backlink></links><search><creatorcontrib>Shimi, G. M</creatorcontrib><creatorcontrib>Kim, D</creatorcontrib><creatorcontrib>Choi, M. Y</creatorcontrib><title>Optimal storage capacity of neural networks at finite temperatures</title><description>Gardner's analysis of the optimal storage capacity of neural networks is
extended to study finite-temperature effects. The typical volume of the space
of interactions is calculated for strongly-diluted networks as a function of
the storage ratio $\alpha$, temperature $T$, and the tolerance parameter $m$,
from which the optimal storage capacity $\alpha_c$ is obtained as a function of
$T$ and $m$. At zero temperature it is found that $\alpha_c = 2$ regardless of
$m$ while $\alpha_c$ in general increases with the tolerance at finite
temperatures. We show how the best performance for given $\alpha$ and $T$ is
obtained, which reveals a first-order transition from high-quality performance
to low-quality one at low temperatures. An approximate criterion for recalling,
which is valid near $m=1$, is also discussed.</description><subject>Physics - Disordered Systems and Neural Networks</subject><subject>Physics - Materials Science</subject><subject>Physics - Mesoscale and Nanoscale Physics</subject><subject>Physics - Other Condensed Matter</subject><subject>Physics - Quantum Gases</subject><subject>Physics - Soft Condensed Matter</subject><subject>Physics - Statistical Mechanics</subject><subject>Physics - Strongly Correlated Electrons</subject><subject>Physics - Superconductivity</subject><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>1993</creationdate><recordtype>article</recordtype><sourceid>GOX</sourceid><recordid>eNotzz1vwjAQBmAvDBXwG-qlY-DsI44zUtQvCYmFPbo458qCfMgxbfn3pC3LvcNJr95HiEcFq43Nc1hT_AlfK9d3TdZSWpcIBlA_iOfDkEJLZzmmPtInS0cDuZCusvey40ucXh2n7z6eRklJ-tCFxDJxO3CkdIk8LsTM03nk5T3n4vj6cty9Z_vD28duu8-oKPV0MHcMJRpDyDZHj1oVDYPVrI0HxYVrlOUNs6tBkeba1MTgfGO9cQrn4um_9o9SDXGaHa_VL6maSNWdhDeAEkun</recordid><startdate>19930614</startdate><enddate>19930614</enddate><creator>Shimi, G. M</creator><creator>Kim, D</creator><creator>Choi, M. Y</creator><scope>GOX</scope></search><sort><creationdate>19930614</creationdate><title>Optimal storage capacity of neural networks at finite temperatures</title><author>Shimi, G. M ; Kim, D ; Choi, M. Y</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-a792-a735ce09366a3e853f3217de082e26f01e7cd18e4eecb01a2eb6bae0cfd8f6c13</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>1993</creationdate><topic>Physics - Disordered Systems and Neural Networks</topic><topic>Physics - Materials Science</topic><topic>Physics - Mesoscale and Nanoscale Physics</topic><topic>Physics - Other Condensed Matter</topic><topic>Physics - Quantum Gases</topic><topic>Physics - Soft Condensed Matter</topic><topic>Physics - Statistical Mechanics</topic><topic>Physics - Strongly Correlated Electrons</topic><topic>Physics - Superconductivity</topic><toplevel>online_resources</toplevel><creatorcontrib>Shimi, G. M</creatorcontrib><creatorcontrib>Kim, D</creatorcontrib><creatorcontrib>Choi, M. Y</creatorcontrib><collection>arXiv.org</collection></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext_linktorsrc</fulltext></delivery><addata><au>Shimi, G. M</au><au>Kim, D</au><au>Choi, M. Y</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Optimal storage capacity of neural networks at finite temperatures</atitle><date>1993-06-14</date><risdate>1993</risdate><abstract>Gardner's analysis of the optimal storage capacity of neural networks is
extended to study finite-temperature effects. The typical volume of the space
of interactions is calculated for strongly-diluted networks as a function of
the storage ratio $\alpha$, temperature $T$, and the tolerance parameter $m$,
from which the optimal storage capacity $\alpha_c$ is obtained as a function of
$T$ and $m$. At zero temperature it is found that $\alpha_c = 2$ regardless of
$m$ while $\alpha_c$ in general increases with the tolerance at finite
temperatures. We show how the best performance for given $\alpha$ and $T$ is
obtained, which reveals a first-order transition from high-quality performance
to low-quality one at low temperatures. An approximate criterion for recalling,
which is valid near $m=1$, is also discussed.</abstract><doi>10.48550/arxiv.cond-mat/9306032</doi><oa>free_for_read</oa></addata></record> |
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| subjects | Physics - Disordered Systems and Neural Networks Physics - Materials Science Physics - Mesoscale and Nanoscale Physics Physics - Other Condensed Matter Physics - Quantum Gases Physics - Soft Condensed Matter Physics - Statistical Mechanics Physics - Strongly Correlated Electrons Physics - Superconductivity |
| title | Optimal storage capacity of neural networks at finite temperatures |
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