The storage capacity of the Hopfield model and moderate deviations
نویسندگان
چکیده
منابع مشابه
The storage capacity of the Hopfield model and moderate deviation principles
This note relates the storage capacity of the Hopfield model of neural networks to the existence of a moderate deviation principle for the empirical correlation of the patterns. This moderate deviation principle is satisfied under a certain condition on the moment generating function of these correlations which on the other hand can be verified in many cases by GHSand FKG-type inequalities. Exa...
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For a given 0 < δ < 2 if [Nδ] neurons deviating from the memorized patterns are allowed, we constructively show that if and only if α(δ) := p(N)/N = (1 − 2δ)2/(1 − δ)2 all stored patterns are fixed points of the Hopfield model. If [NδN ] neurons are allowed with δN → 0 then αN = (1−2δN )2/(8−1(1−δN ))2 → 0 where 8 is the distribution function of the normal distribution. The result obtained by A...
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ژورنال
عنوان ژورنال: Statistics & Probability Letters
سال: 2005
ISSN: 0167-7152
DOI: 10.1016/j.spl.2005.06.001