Question $3[3$ pts$].$ Given a neuron with $n$ dimensional input features $x_1,x_2,$dots,$x_n,$ assuming the

output from the neuron is defined by

$o=w_0+w_1{x}_1+w_2{x}_2+w_3{x}_3$dots$+w_n{x}_n$

The neuron uses identify function as the activation function, and an L$-2$ norm regularizer is added

to the objective function, with $$ being the regularizer's coefficient.

Please draw the structure of the neuron $($please show input, output, and the weight$)[1$

$pt$

Given a batch of $N$ training instances $(x(1),d(1)),(x(2),d(2)),$dots,$(x(N),d(N)),$ where $d(i)$

denotes label of instance $x(i),$ show gradient descent learning objective function of the

neuron $[1$ pt$]$

Derive gradient descent learning weight updating rule for weight $w_i[1pt].$