Q$1(20$ points$)$ Consider the following given neural network with three layers of two inputs neurons, two hidden neu$-$

rons, and two output neurons. Additionally, the hidden and output neurons will include a bias. Suppose the initial

weights $(w_i\text{'}$s based on node number top to down at each layers $),$ the biases, and training input$/$outputs$($targets$)$

values are as given in the Figure. For the hidden layer and output layer, we consider the Sigmoid activation

function to get the output of neurons. For the single training data set: given inputs $0\mathrm{.}50$ and $0\mathrm{.}10,$ we want the

neural network to output $0\mathrm{.}10$ and $0\mathrm{.}90$

$($i$)$ Calculate the error for each output neuron and sum them to get the total error:

$E_{\text{t}\text{o}\text{t}\text{a}\text{l}}={\displaystyle \underset{?}{\overset{?}{}}}\frac{1}{2}($ target $-$ output ${)}^2$

$($ii$)$ Consider the parameter $w_5.$ We want to know how much a change in $w_5$ affects the total error, so calculate

$\frac{del{E}_{\text{t}\text{o}\text{t}\text{a}\text{l}}}{del{w}_5}.$

$($iii$)$ Now consider the parameter $w_1.$ We want to know how much a change in $w_1$ affects the total error, so

calculate $\frac{del{E}_{\text{t}\text{o}\text{t}\text{a}\text{l}}}{del{w}_1}.$

$($iv$)$ By following the gradient descent updating rule of

$w_i^{k+1}=w_i^k-\frac{del{E}_{\text{t}\text{o}\text{t}\text{a}\text{l}}}{del{w}_i^k},k=0,1,2$dots

Find the new updating value of $w_1,w_2,w_3,w_4$ parameters after one iteration. Take $=0\mathrm{.}1.$