Consider a neural network that represents the following function:

hat$(y)=(w_5(w_1{x}_1+w_2{x}_2)+w_6(w_3{x}_3+w_4{x}_4))$

where $x_i$ denotes input variables, hat$(y)$ is the output variable, and $$ is the logistic function:

$(x)=\frac{1}{1+e^{-x}}.$

Suppose the loss function used for training this neural network is the $L2$ loss, i$.$e$.L(y,$hat$(y))=$

$(y-$hat$(y){)}^2.$ Assume that the network has its weights set as:

$(w_1,w_2,w_3,w_4,w_5,w_6)=(-0\mathrm{.}65,-0\mathrm{.}55,1\mathrm{.}74,0\mathrm{.}79,-0\mathrm{.}13,0\mathrm{.}93)$

$[3.$a$](5$ marks$)$ Draw the computational graph for this function. Define appropriate in$-$

termediate variables on the computational graph. $($break the logistic function into smaller

components.$)$

$[3.$b$](5$ marks$)$ Given an input data point $(x_1,x_2,x_3,x_4)=(1\mathrm{.}2,-1\mathrm{.}1,0\mathrm{.}8,0\mathrm{.}7)$ with true

label of $1\mathrm{.}0,$ compute the partial derivative $\frac{\text{d}\text{e}\text{l}\text{L}}{w_3},$ by using the back$-$propagation algorithm.

Indicate the partial derivatives of your intermediate variables on the computational graph.

Round all your calculations to $4$ decimal places.