Consider the convolutional neural network defined by the layers in the left column

below. Fill in the shape of the output volume and the number of parameters at each

layer. You can write the activation shapes in the format $(H,W,C),$ where $H,W,C$ are the

height, width and channel dimensions, respectively. Unless specified, assume padding $1,$

stride $1$ where appropriate. $[38$ points$]$

Notation :

CONV $-N$ denotes a convolutional layer with $N$ filters with height and width

equal

to $x.$

POOL$-$n denotes a $nn$ max$-$pooling layer with stride of $n$ and $0$ padding.

FLATTEN flattens its inputs,

FC$-$N denotes a fully$-$connected layer with N neuronsConsider the convolutional neural network defined $by$ the layers $in$ the left column

below. Fill $in$ the shape $of$ the output volume and the number $of$ parameters $at$ each

layer. You can write the activation shapes $in$ the format $(H,W,C),$ where $H,W,C$ are the

height, width and channel dimensions, respectively. Unless specified, assume padding $1,$

stride $1$ where appropriate. $[38$ points$]$

Notation :

CONVx$-N$ denotes a convolutional layer with $N$ filters with height and width

equal

$tox.$

POOL$-n$ denotes $ann$ max$-$pooling layer with stride $ofn$ and $0$ padding.

FLATTEN flattens its inputs,

$FC-N$ denotes a fully$-$connected layer with $N$ neurons$(iii)(2$ points$)$ What $is$ del$\frac{z_3}{d}$ela $?$ Refer $to$ this result $as{}_2^{(i)}.$

$(iv)(2$ points$)$ What $is$ del$\frac{a}{d}el{z}_2?$ Refer $to$ this result $as{}_3^{(i)}.$

$(v)(2$ points$)$ What $is$ del$\frac{a}{d}el{z}_1?$ Refer $to$ this result $as{}_4^{(i)}.$

$(vi)(2$ points$)$ What $is$ del$\frac{z_1}{d}el{W}_1?$

$(vii)(6$ points$)$ What $is$ del$\frac{J}{d}el{W}_1?It$ may help $to$ reuse work from the previous parts.

Hint: $Be$ careful with the shapes!

$(viii)(10$ points$)$ Write down the update rules for $W_1,b_1$ and $W_2,b_2$ using simple gradient

descent with learning rate $.$ All gradients should $be$ expanded reusing work from

previous parts.