For the following set of problems, let's consider a simple 2-dimensional classification task. The training set is made up of 4 points listed below: x(1) = (-1,-1) y(1) = 1 2 x(2) = (1, -1) y(2) = -1 2 x(3) = (-1,1) y(3) = -1 x (4) = (1,1) y(4) = 1 2 The dataset is illustrated below (blue - positive, red - negative) 100 0.75 0.50 0.25 0.00 -0.25 -0.50 -0.75 -1.00 0.25 0.50 0.75 1.00 -1.00 -0.75 -0.50 -0.25 0.00 For simplicity, assume that we are only interested in binary classification problems for now. That is, y(i) can be either 1 or -1. Linear Separability After First Layer 0/1 point (graded) For this problem, let us focus on a network with one hidden layer and two units in that layer: W11 fi 21 2012 22 21 W22 F2 Let fra), Fra denote the output of the two units in the hidden layer corresponding to the input æ() respectively, i.e. = f(wo1 + (W11x + W2] 2.))) f (wo2 + (W122) + W222.))) Consider the set D' = {([fr.º., 5.2"],3,6"), i=1,2,3,4} Assume that fis the linear activation function given by f (2) = 2z – 3. For which of the following values of weights would the set D' be linearly separable? (Select all that apply.) W11 = W21 = 0, W12 = W22 = 0, wo1 = W02 = 0 W11 = W21 = 2, W12 = W22 = -2, wo1 = W02 = 1 W11 = W21 = -2, W12 = W22 = 2, w01 = wo2 = 1 None of the above
