(2) In class on Wednesday, 3/10, we talked about how to extend the boolean X-OR function f : {0,1}{ {0,1} (defined by: f(a,b) = 1 iff (a,b) = (1,0) or (0, 1)) to a two-layer neural network F:R2 F1=H0A1, R2 F2=H0A2, R with Heaviside step activation function. (a) Explain in your own words why a single-layer neural network with Heaviside step activation function cannot possibly extend the X-OR function." (b) We mentioned quickly in class that we can choose the weight & bias parameter matrices for the two layers of F: R2 Fi=H0A1, R2 F2=H0A2, R by describing the X-OR function in terms of elementary logic. I will now ask you to carry this out explicitly here. Note that in the following, we are using the row/column convention that assigns data vectors to rows, not columns, so the weight matrices for affine linear functions are defined by multiplying on the right. According to this convention, x R2 is a row vector, and the output of A1 is computed as XW1 + bi, where W1 is a 2x2 matrix whose columns are the weight vectors associated to the components (nodes) of the multi-output function A1, and b is a row vector (1x2 matrix) whose entries are the biases associated to the components (nodes) of A1. Find W1 and by for A1 and W2 and b2 for A2 so that F = (H o A2) (H o A1) extends X-OR. Are these weight and bias vectors the unique choices ensuring that F extends X-OR? If so, explain why. If not, produce another choice that works. (c) Let Fi be the first layer map of the neural network you constructed above. Plot Fi(0,0) and Fi(1,1) (the inputs for which the X-OR function assigns the output 0). Now plot F1(1,0) and F1(0,1) (the inputs for which the X-OR function assigns the output 1). Do you notice anything interesting? Explain