By Ben Krose, Patrick van der Smagt
This manuscript makes an attempt to supply the reader with an perception in synthetic neural networks.
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Extra info for An Introduction to Neural Networks (8th Edition)
Programmed with two inputs, 10 hidden units with sigmoid activation function and an output unit with a linear activation function. 20) should be adapted for the linear instead of sigmoid activation function. The network weights are initialized to small values and the network is trained for 5,000 learning iterations with the back-propagation training rule, described in the previous section. 3 (bottom left). 3 (bottom right). We see that the error is higher at the edges of the region within which the learning samples were generated.
This example shows that a large number of hidden units leads to a small error on the training set but not necessarily leads to a small error on the test set. Adding hidden units will always lead to a reduction of the E learning . However, adding hidden units will rst lead to a reduction of the E test , but then lead to an increase of E test . This e ect is called the peaking e ect. 10. 10: The average learning error rate and the average test error rate as a function of the number of hidden units.
For every p x 2 X + a hidden unit h can be reserved of which the activation yh is 1 if and only if the speci c pattern p is present at the input: we can choose its weights wih equal to the speci c pattern xp and the bias h equal to 1 ; N such that yhp = sgn X i wihxpi ; N + 21 ! 7. CONCLUSIONS 31 is equal to 1 for xp = wh only. Similarly, the weights to the output neuron can be chosen such that the output is one as soon as one of the M predicate neurons is one: yop = sgn M X h=1 ! 21) This perceptron will give yo = 1 only if x 2 X + : it performs the desired mapping.
An Introduction to Neural Networks (8th Edition) by Ben Krose, Patrick van der Smagt