Team:USP-UNESP-Brazil/Associative Memory/Background

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(Hopfield Associative Memory Networks)
(Hopfield Associative Memory Networks)
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===Hopfield Associative Memory Networks===
===Hopfield Associative Memory Networks===
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The idea of this project is based on the associative memory network introduced by J.J. Hopfield in the 80’s. On this network, the system tends to converge to a pre-determined equilibrium, restoring the same pattern when exposed to variations of this pattern.
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The idea of this project is based on the associative memory network introduced by J.J. Hopfield in the 80’s. The structure of a Hopfield network is simple, all neurons connect among them. This brings some interesting memory properties and provide a model for understanding human memory.
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On this network, the system tends to converge to a pre-determined equilibrium, restoring the same pattern when exposed to variations of this pattern.
The architecture, or geometry of the system, is composed in a way that all neurons are connected among them. In math terms, a Hopfield Network can be represented as an “Energy” (E) function:
The architecture, or geometry of the system, is composed in a way that all neurons are connected among them. In math terms, a Hopfield Network can be represented as an “Energy” (E) function:
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[[File:equation2.jpg|center|400px|caption|]]
[[File:equation2.jpg|center|400px|caption|]]
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In this equation, “wij” is the wheight
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In this equation, “wij” is the weight
Where "wij" is the weight assigned to the connection from neuron i to neuron j. The summation over j is the sum of all connections made by the neuron i. This dynamics (equation 2) is sufficient  for the network to converge the most similar memorized pattern.  
Where "wij" is the weight assigned to the connection from neuron i to neuron j. The summation over j is the sum of all connections made by the neuron i. This dynamics (equation 2) is sufficient  for the network to converge the most similar memorized pattern.  
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[[File:009.JPG|center|570px|caption|]]
[[File:009.JPG|center|570px|caption|]]
"Figure 1"
"Figure 1"
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The Hopfield model as an associative memory network is a good choice because of its simplicity and robustness. The same methodology can be used to the construction of networks with other architectures, such as the called “perceptrons”. In contrast to a Hopfield network a perceptron is commonly used as a classifier and its structure is feed-forward.
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The Hopfield model for the construction of an associative memory network using bacteria is a good choice because of its simplicity and strength. The same methodology can be used to the construction of networks with other architectures, such as the “perceptrons”. One step forward is the way how to deal with continuous biological variables, because the standard model uses discrete ones.
 
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[[File:0018.JPG|center|620px|caption|]]
[[File:0018.JPG|center|620px|caption|]]
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"Figure 2"
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"Figure 2"-->
===Biological Mechanism===
===Biological Mechanism===

Revision as of 23:35, 25 September 2012