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Neural Network

  1. May 2, 2015 #1
    1. The problem statement, all variables and given/known data
    I wont go into detail as I am just trying to figure out the methodology of this problem. Having said that:
    I have 3 inputs. These 3 inputs are connected to a hidden layer of 3 other nodes and then a single output node.
    Each node of ABC is connected to each node of DEF and each DEF is connected to G:

    A D
    B E G
    C F

    Each connection has an associated weight and there is a transfer function f(x) between each node. There is also a bias at DEF and G but not ABC.
    2. Relevant equations


    3. The attempt at a solution
    So, I believe if I want to calculate the value of D I should do the following:
    ##D = (f(x_A)W_{AD})+(f(x_B)W_{BD})+(f(x_C)W_{CD})+Bias_D##
    That is the result of the function from input A times the weight from A to D plus the same from B and C. And then at the end the bias value associated with D.
    I should do this for E and F in the same manner with the correct weights. Then, for G, I take the results of D, E and F and perform the same again to get the final result.

    Is this the correct method?
     
  2. jcsd
  3. May 2, 2015 #2
    It's been a number of years since played with this. I modeled my elements as operational amplifiers with programmable gains (this is the weighting factor W), with soft saturation characteristics (the sigmoidal transfer function). I used the inverse tangent.

    Doing it this way, [tex]D_{out} = atan(W_{AtoD} A_{out} + W_{BtoD} B_{out} + W_{CtoD} C_{out} - D_{bias})[/tex]

    The arc tangent function had the convenient feature that [tex]\frac{d}{dx}atan(x)=\frac{1}{x^2+1}[/tex] useful in implementing a Hopfield reverse learning algorithm. But this might be severely dated.
     
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