na two$-$layer neural network fone hidden loyer$)$ whe sigmoid activetions, the outputs are given by two$-$layer neurai network $($one hidden layer$)$ with sigmoid activations, the outputs are given by

f$($ ; $\backslash$theta $)=\backslash$sigma $(^(2)\backslash$sigma $(^(1)+^(1))+^(2))$

where $\backslash$sigma $($a$)=1/1+$exp $(-$a$).$ This equation simply combines all the stages of the network into a single equation. Instead of the sigmoid unction, we could use hyperbolic tangent functions

tanh $($a$)=$exp $($a$)-$exp $(-$a$)/$exp $($a$)+$exp $(-$a$)$

Is an activation function. Consider the two$-$layer neural network with sigmoid activations described above. Show that there exists an equivalent network, which omputes exactly the same function, but with hidden unit activation functions given by tanh $($a$).$ Define the parameters of your newhy :onstructed network explicitly. You are allowed to use an additional affine transformation on the output of your tanh network, since th$.$ ange of tanh and $\backslash$sigma are different. Alint: begin by re$-$writing the equation abolle with tanh hidden unit activations, then find the relation between $\backslash$sigma $($a$)$ and tanh $($a$),$ and how that the parameters of the two networks differ by linear transformations.