By Kroese B., van der Smagt P.
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Additional resources for An Introduction to Neural Networks
Note that the learning error increases with an increasing learning set size, and the test error decreases with increasing learning set size. A low 44 CHAPTER 4. 7: Effect of the learning set size on the generalization. The dashed line gives the desired function, the learning samples are depicted as circles and the approximation by the network is shown by the drawn line. 5 hidden units are used. a) 4 learning samples. b) 20 learning samples. learning error on the (small) learning set is no guarantee for a good network performance!
We further set E = p as the summed squared error. We can write p ∂E p ∂E p ∂sk = . 2) we see that the second factor is ∂spk = yjp . 7) When we define δkp = − we will get an update rule which is equivalent to the delta rule as described in the previous chapter, resulting in a gradient descent on the error surface if we make the weight changes according to: ∆p wjk = γδkp yjp . 8) The trick is to figure out what δkp should be for each unit k in the network. The interesting result, which we now derive, is that there is a simple recursive computation of these δ’s which can be implemented by propagating error signals backward through the network.
As multi-layer perceptrons, the Boltzmann machine consists of a non-empty set of visible and a possibly empty set of hidden units. Here, however, the units are binary-valued and are updated stochastically and asynchronously. , 1985). This algorithm works as follows. First, the input and output vectors are clamped. The network is then annealed until it approaches thermal equilibrium at a temperature of 0. It then runs for a fixed time at equilibrium and each connection measures the fraction of the time during which both the units it connects are active.
An Introduction to Neural Networks by Kroese B., van der Smagt P.