A sigmoid activation function, $\backslash$sigma $($x$)=1/(1+$e$-$x

$),$ having a derivative

$\backslash$sigma $($x$)(1-\backslash$sigma $($x$)),$ is used in a Multi$-$Layer Perceptron $($MLP$)$ Neural

Network. The MLP has $10$ inputs, two hidden layers $($the first has

$5$ neurons and the second has $3$ neurons$)$ and $2$ outputs. The

backpropagation $($BP$)$ algorithm is used for training.

$($i$)$ How many weights exist in this MLP neural network?

$[1$ mark$]$

$($ii$)$ Explain the principles of the backpropagation $($BP$)$ learning

algorithm that is used to train the weights of the MLP$.$ Your

explanation needs to show how the Perceptron Delta Rule is used

in the MLP network. $[3$ marks$]$

$($iii$)$ What are the suggested minimum number of representative

input $$ output training samples required in order to have a high

probability of achieving good generalisation from the MLP

network? $[1$ mark