Problem #3: X1 w1 Y X2 w2 1 b a) For the single neuron network described in lecture 1, show derivations for computing the gradients w1,w2 and b. Assume the network will be classifying using the decision boundary given by y = 0.3 x + 2 In the lecture, x in above equation is referred to as x1, and y is referred to as x2. Y is the class that a given point at (x1,x2) belongs to. If the point is below the line, the class is 0, if the point is above the line, the class is 1. For example the training data may appear as: X1 1 Y (class) 0 1 X2 2.2 2.4 2.5 2.7 1 0 2 2 1 b) Program the back propagation algorithm according to the equations developed in part a). Once the network is trained, the test data to use in your program could be: X1 X2 Expected output 0 1 1.5 1.5 2.5 2.5 2.4 2.5 2.7 2.8 0 1 Problem #3: X1 w1 Y X2 w2 1 b a) For the single neuron network described in lecture 1, show derivations for computing the gradients w1,w2 and b. Assume the network will be classifying using the decision boundary given by y = 0.3 x + 2 In the lecture, x in above equation is referred to as x1, and y is referred to as x2. Y is the class that a given point at (x1,x2) belongs to. If the point is below the line, the class is 0, if the point is above the line, the class is 1. For example the training data may appear as: X1 1 Y (class) 0 1 X2 2.2 2.4 2.5 2.7 1 0 2 2 1 b) Program the back propagation algorithm according to the equations developed in part a). Once the network is trained, the test data to use in your program could be: X1 X2 Expected output 0 1 1.5 1.5 2.5 2.5 2.4 2.5 2.7 2.8 0 1