A$.$ A $22$ image is given by

$\{$:$I=[25,60],[10,30]]$

A convolution kernel is given by

$F=\left[\begin{array}{ccc}-1& 0& 1\\ -1& 0& 1\\ -1& 0& 1\end{array}\right].$

i$)$ What will be the size of feature map obtained by transposed convolution with valid padding and stride $2?$

ii$)$ What will be the values of the feature map?

B$.$ Consider a fully connected autoencoder $($each hidden node is connected to all inputs and all outputs$)$ with two dimensional binary input

and one hidden layer with tanh activation function.

At iteration $t,$ the weights are shown in the following autoencoder architecture along with the input vector $(x1=1,x2=1).$ All bias values are

zero. Assume learning rate $=0\mathrm{.}25$ and momentum constant $=0\mathrm{.}75.$ Also assume at $t-1,w1=-0\mathrm{.}5,w2=0\mathrm{.}5,w3=0\mathrm{.}5$ and $w4=-0\mathrm{.}5.$

i$)$ What activation function will you choose at the output node?