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 ï€½ 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 ,ïŒ,x ,x and their corresponding target vectors 1 2 7 8 d ,d ,ïŒ,d ,d in the training set are: ïƒº ïƒ» ïƒ¹ ïƒª ïƒ« ïƒ© ï€½ 0.5242 0.7826 x1 , ïƒº ïƒ» ïƒ¹ ïƒª ïƒ« ïƒ© ï€ ï€½ 0.5377 0.9003 x2 , ïƒº ïƒ» ïƒ¹ ïƒª ïƒ« ïƒ© ï€ ï€ ï€½ 0.9630 0.0871 x3 , ïƒº ïƒ» ïƒ¹ ïƒª ïƒ« ïƒ©ï€ ï€½ 0.7873 0.1795 x4 , ïƒº ïƒ» ïƒ¹ ïƒª ïƒ« ïƒ© ï€½ 0.5839 0.2309 x5 , ïƒº ïƒ» ïƒ¹ ïƒª ïƒ« ïƒ© ï€ ï€½ 0.0280 0.2137 x6 , ïƒº ïƒ» ïƒ¹ ïƒª ïƒ« ïƒ© ï€ ï€ ï€½ 0.1886 0.6475 x7 , ïƒº ïƒ» ïƒ¹ ïƒª ïƒ« ïƒ©ï€ ï€½ 0.2076 0.6026 x8 ï› ï1 d1 ï€½ , ï› ï1 d2 ï€½ ï€ , d3 ï€½ ï› ï1 , ï› 1ï d4 ï€½ ï€ , ï›1ï d5 ï€½ , ï› 1ï d6 ï€½ ï€ , d7 ï€½ ï› ï1 , d8 ï€½ ï› ï ï€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 2 1 1 ( ) ï® ï® ï® ï€½ ï€ ï€« ï€ ï€ . Note that due to the necessary augmentation of inputs and of the hidden layer by one fixed input, the trained network should have 3 input nodes, 4 hidden neurons, and 1 output neuron. Assign -1 to all augmented inputs. 1.1 Assume that the learning constant is ï¨ ï€½ 0.2, and the initial random output layer weight matrix W( ) 1 and hidden layer weight matrix W ( ) 1 are W (1) ï€½ ï› ï 0.3443 0.6762 ï€ 0.9607 0.3626 ïƒº ïƒº ïƒº

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