Question $8[4$ pts$]$: Figure $6$ shows a ResNet block where the input a$[$l$]$ is a two$-$dimensional

vector: $[0\mathrm{.}5,-0\mathrm{.}5].$ The two layers inside the ResNet block consist of two dense layers, each

having two nodes. The weight values for the first layer are $[-0\mathrm{.}3,0\mathrm{.}7]$ and $[0\mathrm{.}5,-0\mathrm{.}4],$ respectively.

The weight values for the second layer are $[0\mathrm{.}7,-0\mathrm{.}3]$ and $[-0\mathrm{.}5,-0\mathrm{.}3],$ respectively. Ignore bias

and use ReLu$()$ as the activation functions for all nodes.

$$ Calculate output of the first layer of the ResNet block, i$.$e$.,$ a$[$l$+1]($show calculations$)[1$ pt$]$

$$ Calculate output of the second layer of the ResNet block, i$.$e$.,$ a$[$l$+2]($show calculations$)[1$ pt$]$

$$ If the skip connection of the ResNet block does not exist, what is the output of the block, i$.$e$.,$

a$[$l$+2]($show calculations$)[1$ pt$]$

$$ Explain motivation of ResNet block $($i$.$e$.,$ what is the learning objective of the ResNet block$)[1$ pt$]$

Figure $6$

Question $9[4$ pts$]$: Figure $7$ shows unfolded LSTM network with two consecutive cells. Using

ht and ct to denote output and cell memory of the cell at time point t$.$ Use ft$,$ it$,$ ot to denote forget

gate, input gate, output gate of the cell at time point t$.$ Use t to denote candidate layer output at

time point t$.$

$1.$ Use mathematical equations to show the relationship between cell memory at time

point t$,$ with respect to cell memory and output at time point t$-5[2$ pts$]$

$2.$ Use

$$ Ct to denote change of network error with respect to cell state at time point t$,$ i$.$e$.,$

$.$ Derive relationship between

$$ Ct$-5$ and

$$ Ct $[2$ pts$]$V