Consider a $3-2-1$ neural network, in which the input layer is linear, the output layer has a nonlinearity

of the form:

$f(x)=\frac{e^{4x}}{1+e^{4x}}$

and the output of the $j$ th node in the hidden layer is given by a polynomial function of the form:

hat$(y{)}_j^{(1)}=w_{j1}{x}_1+w_{j2}{x}_2+w_{j3}{x}_3$

for $j=1$ and $2.$

$($i$)(10$ pts$.)$ Draw this neural network showing all the neurons. Then, clearly list out all the parameters

of this neural network and the operations at each layer $($for $l=1$ and $2).$ Use a superscript $(l)$ to denote

the index of the layer, e$.$g$.,w_{ij}^{(l)}.$ How many trainable parameters does this neural network have?