$[2$ pts$/$ea$]$ Comparing MAE and MSE

What is the advantages of MSE over SSE?

show the error function formula of MAE and MSE, respectively.

Explain why MSE is more sensitive to outliers than MAE using the definition of the formula

$[3$ pts$]$ Explain why $($in most cases$)$ minimizing KL divergence is equivalent to minimizing cross$-$entropy

$[3$ pts$]$ Explain why sigmoid causes vanishing gradient

$[3$ pts$]$ Explain NAG method using the following picture.

$[3$ pts$]$ Using the following formula, explain how RMSProp improves AdaGrad

$G_t=G_{t-1}+(1-)(gra{d}_{w}J(w_t){)}^2$

$[3$ pts$]$ In LeCun or Xavier initialization, explain why variance is divided by $n_{in}($or $n_{in}+n_{\text{o}\text{u}\text{t}})$

$[3$ pts$]$ normalizing with Gaussian $N(0,1)$ with sigmoid function might make DNN a linear classifier.

Explain it$.$