1. Perceptrons. (7 points) In class, we showed how to learn the OR function using the...

Transcribed Image Text:

1. Perceptrons. (7 points) In class, we showed how to learn the "OR" function using the perceptron learning rule. Now we want to learn the "NAND" function using four patterns, as shown in Table 1. Input Output 00 1 01 1 10 1 11 0 Table 1: The "NAND" function (a) (1 pt) Write down the perceptron learning rule as an update equation. (b) (4 pts) Draw the rest of this table, as we did in class, as the network learns NAND. Initialize wo, w, and w2 to be 0 and fix the learning rate to 1. Add one row for each randomly selected pattern (training example) for the perceptron to learn. Stop when the learning converges. Make sure you show the final learned weights and bias. You may pick a "random" order to make the learning converge faster, if you can (you may not need all of these rows). x1 22 Output Teacher Wo W1 W2 1 1 1 0 0 0 0 0 0 0 1 -1 -1 -1 0 1 0 1 0 -1 -1 (c) (2 pts) Is the solution unique? Why or why not? Justify your answer. 1. Perceptrons. (7 points) In class, we showed how to learn the "OR" function using the perceptron learning rule. Now we want to learn the "NAND" function using four patterns, as shown in Table 1. Input Output 00 1 01 1 10 1 11 0 Table 1: The "NAND" function (a) (1 pt) Write down the perceptron learning rule as an update equation. (b) (4 pts) Draw the rest of this table, as we did in class, as the network learns NAND. Initialize wo, w, and w2 to be 0 and fix the learning rate to 1. Add one row for each randomly selected pattern (training example) for the perceptron to learn. Stop when the learning converges. Make sure you show the final learned weights and bias. You may pick a "random" order to make the learning converge faster, if you can (you may not need all of these rows). x1 22 Output Teacher Wo W1 W2 1 1 1 0 0 0 0 0 0 0 1 -1 -1 -1 0 1 0 1 0 -1 -1 (c) (2 pts) Is the solution unique? Why or why not? Justify your answer.