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2. Perceptron Convergence Rule The following perceptron is being…
2. Perceptron Convergence Rule
The following perceptron is being trained to recognize paperclips. The input units are feature detectors. For example, if the object presented to the perceptron is wooden, then a1=1; otherwise, a1=0. The intended behavior of the perceptron is for a4 to be 1 (indicating the likely presence of a paperclip) in the situation where a1=0, a2=1, and a3=0; and for a4 to be 0 in all other situations.
Paperclip?
OUTPUT: 4
INPUT:
1 2 3
Wood? Metal? Longer than 1″?
Activation function is “Threshold” (fT): fT (x) = 1, if x > 0
0, if x = 0
(Note that fT is slightly different from Heaviside.)
The training process is using the Perceptron Convergence Rule, with a learning rate of e = 0.2. At present, the threshold is set to T = 0.1, and the weights are set as follows: w4,1 = -0.1, w4,2 = 1.0, and w4,3 = -0.7.
a. Suppose that the next input-output pair presented to the model is as follows.
Input: a1=1, a2=1, a3=0 Intended Output: a4 = 0
Calculate the new values of T and the three connection weights after the Perceptron Convergence Rule has applied. (Show your work.)
T : w4,1 : w4,2 : w4,3 :
b. Calculate the output of the percepton when the new values for T and connection weights from (b) are in place, and the input is: a1=1, a2=1, a3=0. (Show your work.)
c. Now suppose that the same input-output pair is presented to the perceptron a second time:
Input: a1=1, a2=1, a3=0 Intended Output: a4 = 0
Once again, calculate the new values of T and the three connection weights after the Perceptron Convergence Rule has applied. (Show your work.)
T : w4,1 : w4,2 : w4,3 :
d. Finally, calculate the output of the percepton when the newest values for T and connection weights, calculated in step (c), are in place and the input is: a1=1, a2=1, a3=0. (Show your work.) Has the training process succeeded at this point?
