$[20$ points$]$ The feedforward neural network in the figure below has $4$ input units, $2$ neurons in the

hidden layer and $2$ neurons in the output layer. The neurons in the network do not have bias inputs

and bias weights. Note that the input layer and the hidden layer are not fully connected. All six

connections between the input layer and the hidden layer have a current value of $0\mathrm{.}2$ and all three

connections between the hidden layer and the output layer have a current value of $0\mathrm{.}4.$

Train the neural network using back propagation and gradient descent one time $($one epoch$)$ with the

updating rules and the training sample below. The ReLu activation function is used in neurons a$3$ and

a$4,$ and the Sigmoid activation function is used in the output neurons al and a$2.$ Let the learning rate

$=0\mathrm{.}2$ What are the values of the links between the output layer and the hidden layer, and between

the hidden layer and the input layer after training? Show all work to get full credits.

Training sample: $(I1,I2,I3,I4)=(1\mathrm{.}0,-1\mathrm{.}5,-2\mathrm{.}0,5\mathrm{.}0)$;$(y1,y2)=(1\mathrm{.}0,0\mathrm{.}0).$

Updating rules:

$W_{ji}larr{W}_{ji}-\frac{del{E}_i}{del{W}_{ji}}=W_{ji}+{}_i{a}_j,$ with ${}_i=Er{r}_i{g}^{\text{'}}(i{n}_i)$

$W_{kj}larr{W}_{kj}+{}_j{a}_k,$ with ${}_j=g^{\text{'}}(i{n}_j){\displaystyle \underset{i}{\overset{?}{}}}{W}_{ji}{}_i$

Hints: Sigmoid function $S(x)=\frac{1}{1+e^{-x}}$;ReLu function $=$max$(0,x).$