$[3$ 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$.$