Neural Network. Consider a three-layer neural network to learn a function f : X → Y, where X = [X1, X2] consists of two features. The weights w1,...,w6 can be arbitrary. There are two possible choices for the function implemented by each unit in this network:
- S: sigmoid function, S(z) = 1/(1+exp(-z))
- L: linear function, L(z) = cz
where in both cases z = Σi wi Xi. Assign proper activation functions (S or L) to each unit in the following graph so that we can generate functions of the form f(X1, X2) = 1/(1+exp(β1 X1 + β2 X2)) at the output of the neural network Y. Derive β1 and β2 as a function of w1,...,w6.