Programming Neural Networks with Python
by Rheinwerk Publishing, Inc, Dr. Joachim Steinwendner, Dr. Roland Schwaiger
6.3 A Network of Sigmoid Neurons
For the next steps, we assume that all neurons except the input neurons use a sigmoid function as activation function. The big trick is that we represent the learning problem using a small error formula, as we did previously with the gradient descent.
The output of the ANN is a desired output value (e.g., 0.5) and a calculated value (e.g., 0.8). The difference between the two values is of interest here. As the difference can also be negative, for example, 0.5 - 0.8 = -0.3, we need a means to obtain only positive values; otherwise, the gradient descent wouldn’t work. (Where should you go if the value can become arbitrarily small?) In the previous discussion, we recognized the square of the difference (aka squared ...
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