The Generalised XOR Problem

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NE [ The Generalised XOR Problem ] [ 50 marks ]
A neural network model with two input neurons, three hidden neurons in a single
hidden layer, and an output neuron is used to learn the decision surface of the wellknown
generalised XOR problem:
sgn( ) 1 2 d  x x
The input range is [-1,1]. The desired output value is either –1 (corresponds to logical
zero) or 1 (corresponds to logical one).
This generalised XOR problem has been utilised recently to compare the
effectiveness of various neural network learning algorithms. A simplified version is
used in this question. Eight input samples 1 2 7 8 x ,x ,,x ,x and their corresponding
target vectors 1 2 7 8 d ,d ,,d ,d in the training set are:


 

  0.5242
0.7826
x1 , 

 


  0.5377
0.9003
x2 , 

 



  0.9630
0.0871
x3 , 

 

  0.7873
0.1795
x4 ,


 

  0.5839
0.2309
x5 , 

 


  0.0280
0.2137
x6 , 

 



  0.1886
0.6475
x7 , 

 

  0.2076
0.6026
x8
 1 d1  ,  1 d2   , d3   1 ,  1 d4   , 1 d5  ,  1 d6   , d7   1 , d8    1
Assume that the network as shown in Figure 1 has 3 hidden neurons, 1 output neuron,
and all continuous perceptrons use the bipolar activation function f e
e

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