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David C. Silverman |
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The Back-propagation Computing Element The computing element in the back-propagation neural network is also used in other structures to determine when a node "fires". It is described in more detail because of its fairly ubiquitous presence in this technology. This computing element is the heart of the backpropagation neural network itself. The computing element is shown in this figure) .
It performs one simple task. In terms of
the figure, the computing element i multiplies each input signal xj
from each input path j by a weight Wji assigned to that input path,
sums those weighted inputs, passes the sum through an activation function to create
the output, and sends that output oi on to elements often in the next higher layer.
If the next higher layer of computing elements is the output layer, the outputs become the outputs
of the artificial neural network.
The weights are values determined from training the network. Back-propagation training is discussed elsewhere in this tutorial. A number of activation functions have been proposed: step function 
(1)
where the step function has a threshold such that the output is 1 when the summation is greater than the threshold and is 0 when it is less. The subscript "0" on the function means that no offset exists in the equation as presented. sigmoid function 
(2)
where 
Note that the output of the sigmoid ranges between 0 and 1. hyperbolic tangent 
(3)
where 
and
The output ranges between -1 and 1. This transfer function may enable better training over the sigmoid because the output has a larger absolute magnitude. sine function 
(4)
Use of the sine function leads to generalized Fourier analysis. All of the above functions have one attribute in common. They provide a simple measure of the degree of activation of that node as calculated from the inputs. |
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Previous Page: Artificial Neural Network Background |
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David C. Silverman, Ph.D. - Primary Consultant |