Gating

$1$ point possible $($graded$)$

Recall that the most simple, single$-$layered RNN can be written in equation as:

Recognize that, in the above formulation, is always overwritten with the calculated result $.$

Now, we introduce a gate vector of the same dimension as $,$ which determines "how much information to overwrite in the next state." In equation, a single$-$layered gated RNN can be written as:

where the sign denotes element$-$wise multiplication. Now, which of the following is true about the gate $?$

$($Choose all those apply.$)$

If the th element of is $1,$ the th element of and that of are equal

If the th element of is $0,$ the th element of and that of are equal

If is a vector whose elements are all $1,$ and are equal

If is a vector whose elements are all $0,$ and are equal