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Family name …………………………………………………. First Name ……………………………… ID……………………………………… 1 Scuola di Ingegneria Industriale e dell'Informazione ‐ Politecnico di Milano NeuroEngineering (I) – Prof. Pietro Cerveri II Session February 12th 2020 Multiple choice questions Question 1 (score: 2.5pts) Let us consider a perceptron with two inputs x1 and x2. The perceptron learning rule 1. can be applied only to signum activation function 2. operates to orient the decision boundary along the direction orthogonal to weight vector 3. allows training the net to reconstruct a function y = f(x1,x2) 4. always ensures to converge to a stable solution 5. does not require to compute the derivative of the activation function SOLUTION The perceptron rule can be applied to any activation shaped as a step function The decision boundary has equation 0 = w1*x1 + w2*x2 – S ‐> x2 = ‐ w1/w2 *x1 – S/w2 Therefore –w1/w2 is the angular coefficient of the line in the plane (x1, x2). The weight vector has coordinate [w1, w2] so the ration w2/w1 r epresents the slope of the vector which is exactly the inverse opposite of the angular coefficient of the boundary so that there are orthogonal The perceptron rule use the difference between the expected and measured output without requiring the derivative of the output Question 2 (score: 2.5pts) Let us consider a fully‐connected feed‐forward network featuring two inputs, one hidden layer with 4 neurons, and a softmax layer with 3 neurons in the output. It can be stated that: 1. the net is to be used to perform binary classification of input patterns 2. the hidden layer requires neurons featuring linear activation function 3. the network can only solve linearly separable classification 4. the network can map a 2D function into a 3D function 5. the output of each neuron in…