$[3$ pts$]$ If we want to change perceptron to logistic regression, what do we do$?$

$[2$ pts$/$ea$]$ The following is the error function of perceptron.

$E[W]=\frac{1}{2}{\displaystyle \underset{\text{d}\text{i}\text{n}\text{D}}{\overset{?}{}}}(t_d-o_d{)}^2$

Show $o_d$ in Perceptron training rule$($PTR$)$

Show $o_d$ in Delta rule$($DR$)$

Explain the differences between PTR and DR in terms of convergence

Suppose perceptron uses ReLU activation function. In this case, show the formula of $\frac{\text{d}\text{e}\text{l}\text{E}}{del{w}_i}$

$[2$ pts$/$ea$]$ Given $f(x,y)=2x^2+y^2+y+1$

compute the derivative of $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{x}}$ and $\frac{\text{d}\text{e}\text{l}\text{f}}{\text{d}\text{e}\text{l}\text{y}},$ respectively.

Suppose that we start at position $(x1,y1)=(300,150).$ Compute the gradient vector using q$.1)$

Compute next position $($learning rate $=1)$

$[4$ pts$]$ Perceptron is a linear classifier. To change perceptron non$-$linear classifier, the following two

things must be done

activation function:

layer:

$[6$ pts$]$ We use backpropagation method in the following neural network. Suppose output $o_1=0\mathrm{.}6$ and

target value $($of $o_1)t_1=1.$ Also $w_{11}^{(2)}=0\mathrm{.}5$ and $=1.$

compute ${}_1$

update $w_{11}^{(2)}$