1. (30 points) Consider the Multilayer Perceptron (MLP) for binary classification de- scribed in section 11.7.2 in the textbook. Let's look at the regularized version of MLP when the activation function of each hidden unit becomes the reLU function reLU(x) = max(0, x), and the activation function of the output unit is the sigmoid function. In the regularized version, the error function becomes the following: N H E(W, v X) = -> [rlogy* + (1 - r) log(1 - yb)] + Ellwall3, t=1 h=1 H where y =sigmoid( _ Unzh + vo) and 27 =reLU(what + Who). Derive the update equa- h=1 tions of the regularized MLP using the given activation functions. Hint 1: Given y =sigmoid(@) = 1/(1 + e-"), the derivative an ay = y (1 - y) . Hint 2: Given reLU(f(x)) = max(0, f(x)), the derivative of reLU(f (x) ) is given by f' (x) if f(x) > 0, and 0 otherwise