Suppose you had a neural network with linear activation functions. That is$,$ for each unit the

output is some constant $c$ times the weighted sum of the inputs.

a$.$ Assume that the network has one hidden layer. For a given assignment to the weights

$w,$ write down equations for the value of the units in the output layer as a function of $w$

and the input layer $x,$ without any explicit mention of the output of the hidden layer.

Show that there is a network with no hidden units that computes the same function.

b$.$ Repeat the calculation in part $($a$),$ but this time do it for a network with any number of

hidden layers.

c$.$ Suppose a network with one hidden layer and linear activation functions has $n$ input

and output nodes and $h$ hidden nodes. What effect does the transformation in part $($a$)$

to a network with no hidden layers have on the total number of weights? Discuss the

case