In this problem, you will use the Perceptron training rule to learn a separating line for the following six data points: I1 1 ** 3 -3 3 OLA 0 X2 6 3 2 -5 -2 5 class -1 -1 +1 -1 +1 +1 Assume that we have two features 21 and 22 and we initialize the weights to ww = 0. Let f(x) be given by the following function f(x) = sgn(w1+ w2r2 + woro) where to is the bias term. (a) [5 points] Assume that the bias term (woro) is always equal to 0. Can a perceptron trained using perceptron training rule be able to perfectly classify this data? Yes or No? Explain your answer. (Hint: Plot the points) (b) 5 points] Consider adding a new data point: = (0.5, 0). Assume that the Perceptron algorithm will not be given the class label of a until it has started training. Can a percep- tron trained using perceptron training rule be able to perfectly classify this data (assuming that the bias term to=0)? Yes or No? Explain your answer. (Hint: Plot the points) XI X2 (c) Here is a simple 2-layer neural network with 2 hidden units and a single output unit. Consider the linear activation function y = C-E, wir, where C is a constant multiplied by a which is the weighted sum of its inputs. Also, consider the non-linear logistic activation function y = o(a) where, o(a): = will w10 w12 W22 NI VI w20 N2 V2 WO W2 N3 1 1+e-a Y i. [2 points] Can this 2-layer network represent decision boundaries that a standard linear model cannot? (Assume all units use the linear activation function.) Explain your answer. ii. [2 points] Now, assume the hidden units use the logistic activation function and the output unit still uses a linear activation function. Now, can this neural network repre- sent non-linear decision boundaries? Explain your answer.