$1$ Convolutional Neural Networks $[15$ points$]$

$1)[20$ points$]$ Suppose there is a convolutional neural network, the input are images of size $\backslash (32\backslash$times $32\backslash ),$ the first layer uses a convolution layer with $5$ filters, each with a size of $\backslash (7\backslash$times $7\backslash ),$ zero padding and stride of size $1.$

$1)[5$ points$]$ What is the output size and how many parameters are there in the first layer?

$2)[5$ points$]$ Propose a way to reduce the number of parameters, and calculate how many parameters are there in your proposed scheme.

$2)[5$ points$]$ Propose a way to use CNN to model sequence of varying$-$length inputs. Briefly explain your method.