Consider a two$-$layer network function of the form $(5\mathrm{.}7)$ in which the hidden$-$ unit nonlinear activation functions g$()$ are given by logistic sigmoid functions of the

form

$1$

$\backslash$sigma $($a$)=\{1+$ exp$($a$)\}.(5\mathrm{.}191)$

Show that there exists an equivalent network, which computes exactly the same func$-$ tion, but with hidden unit activation functions given by tanh$($a$)$ where the tanh func$-$ tion is defined by $(5\mathrm{.}59).$ Hint: first find the relation between $\backslash$sigma $($a$)$ and tanh$($a$),$ and then show that the parameters of the two networks differ by linear transformations.