Q$1.$ Assume that a typical $CNN$ has following input channels $(553),$ two $(333)$ filter volumes and two$(1$x$1)$ bias. A convolutional layer cross$-$correlates the input and kernels and adds a scalar bias to produce an output. Assume that a zero padding $)=(1,$ stride of $2$ is applied to the input volume. ReLU activation function is used on the feature map and then a $22$ avg. pooling with a stride of $1$ is applied. Illustrate the convolution layer computation to pooling output.

$\backslash$table$[[x1,,,,],[1,0,1,0,0],[0,1,2,2,0],[0,1,0,1,0],[1,1,0,2,2],[0,1,2,2,0]]$

x$2$

$\backslash$table$[[1,1,0,0,2],[1,0,1,2,0],[1,2,1,1,0],[0,0,1,0,0],[0,2,2,2,1]]$

$[15$M$]$

w$00$

$\backslash$table$[[0,1,1],[-1,1,-1],[0,-1,0]]$

w$10$

$\backslash$table$[[1,1,0],[1,1,-1],[1,-1,-1]]$

b$0$

$1$

w$01$

$\backslash$table$[[1,-1,0],[1,1,1],[0,1,1]]$

w$11$

$\backslash$table$[[1,0,-1],[-1,1,-1],[0,-1,-1]]$

$w12$

$\backslash$table$[[-1,-1,-1],[1,1,0],[0,1,1]]$

w$02$

$\backslash$table$[[-1,-1,1],[-1,0,-1],[0,-1,-1]]$

x$3$

$\backslash$table$[[1,0,0,0,2],[1,0,1,0,2],[1,2,1,2,2],[1,1,0,1,2],[2,0,2,2,0]]$

$\backslash$table$[[1,0,0,0,2],[1,0,1,0,2],[1,2,1,2,2],[1,1,0,1,2],[2,0,2,2,0]]$

w$02$

$\backslash$table$[[-1,-1,1],[-1,0,-1],[0,-1,-1]]$

b$1$

$0$