Question $3[3$ pts$].$ Given a neuron with n dimensional input features $[$x$1,$ x$2,...,$ xn$],$ assuming the output from the neuron is defined by

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$(2)),...,($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 wi $[1$ pt$]$