An Introduction to Neural Networks (8th Edition) by Ben Krose, Patrick van der Smagt

By Ben Krose, Patrick van der Smagt

This manuscript makes an attempt to supply the reader with an perception in man made neural networks.

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Extra resources for An Introduction to Neural Networks (8th Edition)

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This is not the case anymore for nonlinear systems such as multiple layer networks, as we will see in the next chapter. 32 CHAPTER 3. PERCEPTRON AND ADALINE 4 Back-Propagation As we have seen in the previous chapter, a single-layer network has severe restrictions: the class of tasks that can be accomplished is very limited. In this chapter we will focus on feed-forward networks with layers of processing units. Minsky and Papert (Minsky & Papert, 1969) showed in 1969 that a two layer feed-forward network can overcome many restrictions, but did not present a solution to the problem of how to adjust the weights from input to hidden units.

The solid line depicts the desired trajectory x d the dashed line the realised trajectory. The third line is the error. 50 CHAPTER 5. RECURRENT NETWORKS feed-forward network with sliding window input. We tested this with a network with ve inputs, four of which constituted the sliding window x;3 , x;2 , x;1 , and x0 , and one the desired next position of the object. 4. 4: Training a feed-forward network to control an object. The solid line depicts the desired trajectory x d the dashed line the realised trajectory.

The total input of a hidden unit or output unit can therefore reach very high (either positive or negative) values, and because of the sigmoid activation function the unit will have an activation very close to zero or very close to one. 21), the weight 40 CHAPTER 4. 5: The periodic function f (x) = sin(2x) sin(x) approximated with sigmoid activation functions. ) adjustments which are proportional to ykp(1 ; ykp ) will be close to zero, and the training process can come to a virtual standstill. Local minima.

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