For the truth tables below, is it possible for a perceptron to learn the required output?Explain your reasoning.Input X 0 0 1 1Input Y 0 1 0 1Required Output 1 0 1 0Input X 0 0 1 1Input Y 0 1 0 1Required Output 1 0 0 1[6 Marks]
Question
For the truth tables below, is it possible for a perceptron to learn the required output?Explain your reasoning.Input X 0 0 1 1Input Y 0 1 0 1Required Output 1 0 1 0Input X 0 0 1 1Input Y 0 1 0 1Required Output 1 0 0 1[6 Marks]
Solution
For the first truth table, the required output is not possible for a perceptron to learn. This is because the output does not follow a linearly separable pattern. A perceptron can only learn functions that are linearly separable, meaning there exists a line (in 2D) or a hyperplane (in higher dimensions) that can separate the different classes. In this case, the output '1' is not separable from the output '0' by a line or hyperplane, hence a perceptron cannot learn this function.
For the second truth table, the required output is possible for a perceptron to learn. This is because the output follows a linearly separable pattern. The output '1' can be separated from the output '0' by a line or hyperplane. In this case, the perceptron can learn this function. The perceptron will adjust its weights and bias until it finds a decision boundary that can separate the two classes.
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