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Implement the perceptron rule training of the network using f(net) = sgn (net), c = 1, and the following data specifying the initial weights w', and the two training pairs 2 ,d X2 w = Repeat the training sequence (X1,d), (X2,d) until two correct responses in a row are achieved. List the nerk values obtained during training.



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To implement the perceptron rule training using the given parameters, we need to follow these steps:

Initialize the weights w' as specified.

For each training pair (X, d), calculate the net value using the formula: net = X · w, where · represents the dot product.

Apply the activation function f(net) = sgn(net) to determine the output.

If the output matches the desired output d, move on to the next training pair. If not, update the weights using the formula: w_new = w_old + c * d * X, where c = 1.

Repeat steps 2-4 for all training pairs until two correct responses in a row are achieved.

Given:

Initial weights w' = [1, -1, 0.5]

Training pair 1: X1 = [1, 0, -1], d1 = 1

Training pair 2: X2 = [1, -1, 0], d2 = -1

Let's start the training process:

Iteration 1:

For training pair (X1, d1):

net1 = [1, 0, -1] · [1, -1, 0.5] = 1 - 0 - 0.5 = 0.5

f(net1) = sgn(0.5) = 1

Output matches the desired output, so no weight update is needed.

For training pair (X2, d2):

net2 = [1, -1, 0] · [1, -1, 0.5] = 1 + 1 + 0 = 2

f(net2) = sgn(2) = 1

Output does not match the desired output, so we update the weights:

w_new = [1, -1, 0.5] + 1 * (-1) * [1, -1, 0] = [0, 0, 0.5]

Iteration 2:

For training pair (X1, d1):

net1 = [1, 0, -1] · [0, 0, 0.5] = 0 - 0 - 0.5 = -0.5

f(net1) = sgn(-0.5) = -1

Output does not match the desired output, so we update the weights:

w_new = [0, 0, 0.5] + 1 * 1 * [1, 0, -1] = [1, 0, -0.5]

For training pair (X2, d2):

net2 = [1, -1, 0] · [1, 0, -0.5] = 1 + 0 + 0 = 1

f(net2) = sgn(1) = 1

Output does not match the desired output, so we update the weights:

w_new = [1, 0, -0.5] + 1 * (-1) * [1, -1, 0] = [0, 1, -0.5]

Iteration 3:

For training pair (X1, d1):

net1 = [1, 0, -1] · [0, 1, -0.5] = 0 + 0 + 0.5 = 0.5

f(net1) = sgn(0.5) = 1

Output matches the desired output, so no weight update is needed.

For training pair (X2, d2):

net2 = [1, -1, 0] · [0, 1, -0.5] = 0 - 1 + 0 = -1

f(net2) = sgn(-1) = -1

Output matches the desired output, so no weight update is needed.

The training sequence has achieved two correct responses in a row, so the training is complete.

The net values obtained during training are:

Iteration 1: net1 = 0.5, net2 = 2

Iteration 2: net1 = -0.5, net2 = 1

Iteration 3: net1 = 0.5, net2 =

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