Question $2$:

Let $M$ be a neural network with $2$ inputs and $2$ sigmoidal hidden units and a linear output. Let

$w_{10},w_{11},w_{12}$ and $w_{20},w_{21},w_{22}$ be the first layer weights, and $v_0,v_1$ and $v_2$ be the output layer

weights. Let $f(x,w,v)$ be a function that is implemented by $M.$ Let $M^{\text{'}}$ be another neural network

with tanh hidden units and same layer sizes, and let $f(x,w,v)=f^{\text{'}}(x,w^{\text{'}},v^{\text{'}})$ for all $x.$ Calculate

the weights $w^{\text{'}}$ and $v^{\text{'}}$ of $M^{\text{'}}$ in terms of $w$ and $v$ to ensure that $f(x,w,v)=f^{\text{'}}(x,w^{\text{'}},v^{\text{'}}).$

sigm$(x)=\frac{1}{1+e^{-x}},$ and $,tanh(x)=\frac{e^x-e^{-x}}{e^x+e^{-x}}=\frac{2}{1+e^{-2x}}-1$