Question $1[2$ pts$]$: In Figure $1,$ the upper panel shows a $\backslash (2\backslash$times $2\backslash )$ convolutional filter being applied to an image with $\backslash (6\backslash$times $6\backslash )$ pixels to generate output $($no padding and using stride$=1),$ and the lower panel shows a fully connected dense network to process the same image.

$-$ Find feature map in the blue box marked with a question mark $[0\mathrm{.}5$ pt$]$

$-$ For the dense network, how many neurons are needed to produce the results which are the same as the convolutional filter? How many parameters are need for the dense network? $\backslash ([0\mathrm{.}5\backslash$mathrm$\{$pt$\}]\backslash )$

$-$ How many weight values does the convolutional filter have? $[0\mathrm{.}5$ pt$]$

$-$ Explain why the dense network is designed to find global pattern, whereas the convolutional filter is designed to find local patterns? $[0\mathrm{.}5$ pt$]$