Question#$1$

Marks $-15$

Calculate the weights change using the backpropagation algorithm in this $3$ layers NN$.$

All baises set to $1.$ Learning rate $=0\mathrm{.}1,$ input $1,0$ with target $0,1.$ Use identity activation fuction, means no activation fuction, so $g(a)=a.$ Consider the cost$-$function as Mean Square Error $($MSE$)$ to update weights. So$,$ to change the weights through the backpropagation algorithm use the equ. $w_{ij}(t+1)=w_{ij}(t)+{}_i(t)z_j(t),$ where $w_{ij}(t+1)$ is the new weight in a connection, $w_{\text{i}\text{j}\text{j}}(t)$ is the current weight in a connection, ${}_{is\text{t}\text{h}\text{e}\text{l}\text{e}\text{a}\text{r}\text{n}\text{i}\text{n}\text{g}\text{r}\text{a}\text{t}\text{e}\text{,}}{}_i(t)$ is the error made by a perceptron unit, ${?}^{z_j(t)}$ is the input to a perceptron unit

Figure $1$: $3$ layers Neural Network $($input$,1-$hidden, output$)$

A Consider the neural network in figure$-1$ and calculate the output using the forward

$5$

propagation algorithm in the $3$ layers NN$.$

B Consider the neural network in figure$-1$ and calculate the weights change using the

$5$

back$-$propagation algorithm in the $3$ layers $NN$

C Consider the neural network in figure$-1$ with updated weights using the backpropagation in

$5$

question no$.2.$ Calculate the output using the forward propagation algorithm with the updated weights in the $3$ layers NN