Question $3$:

Suppose we have input $1,2,2,3+x$ and kernel $-1,2,-1.$

$($a$)$ Calculate the convolution of these two signals.

$($b$)$ Calculate the transposed convolution of these two signals.

Question $4$:

Calculate the cosine distance between the vectors $1,2+x,2$ and $2,3,2+Y.$

Question $5$:

Which of the following statements are TRUE about autoencoders and variational autoencoders?

$($i$)$ Variational autoencoders enforce latent space distribution priors while autoencoders do not.

$($ii$)$ Autoencoders can be trained for denoising while variational autoencoders cannot.

$($iii$)$ Both autoencoders and variational autoencoders use KL$-$divergence as the regularization term.

Question $6$: $(5$ points$)$

Which of the following statements are TRUE about recurrent neural networks?

$($i$)$ Elman network is less likely to suffer from "vanishing gradient" or "exploding gradient" issues than LSTM network.

$($ii$)$ For an RNN model, if the sequence length is increased, the number of parameters increases.

$($iii$)$ RNNs can be stacked to create multiple layers.

Please provide explanations on why things are done the way they are. Would be super if you could provide brief descriptions on topics as well. Thanks!