Consider the logistic regression classier applied to a sample x $($bias feature added$)$ with correct label y using weights vector w $($bias

corrected$).$ The forward propagation for calculating the sample's loss is:

z $=$ wTx $!$ a $=($z$)!$ L $=$log

$$

ay $(1$ a$)1$y

:

Calculate the gradient of the loss using the chain rule rw$($L$)=$ rw$($z$)$ rz$($a$)$ ra$($L$)$ and express it in terms of x; a; and y: