5. Suppose we modify the Perceptron algorithm as follows: In the update step, instead of performing...

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5. Suppose we modify the Perceptron algorithm as follows: In the update step, instead of performing w(t+1) = w(t) + yix; whenever we make a mistake, we perform w(t+1) = w(t) + nyixi for some > 0. Prove that the modified Per- ceptron will perform the same number of iterations as the vanilla Perceptron and will converge to a vector that points to the same direction as the output of the vanilla Perceptron. 5. Suppose we modify the Perceptron algorithm as follows: In the update step, instead of performing w(t+1) = w(t) + yix; whenever we make a mistake, we perform w(t+1) = w(t) + nyixi for some > 0. Prove that the modified Per- ceptron will perform the same number of iterations as the vanilla Perceptron and will converge to a vector that points to the same direction as the output of the vanilla Perceptron.