Suppose you have a convolutional network with the following architecture:

$$ The input is an RGB image of size $256\backslash$times $256.$

$$ The first layer is a convolution layer with $32$ feature maps and filters of size $3\backslash$times $3.$

It uses a stride of $1,$ so it has the same width and height as the original image.

$$ The next layer is a pooling layer with a stride of $2($so it reduces the size of each

dimension by a factor of $2)$ and pooling groups of size $3\backslash$times $3.$

Determine the size of the receptive field for a single unit in the pooling layer. $($I$.$e$.,$

determine the size of the region of the input image which influences the activation of

that unit.$)$ You may assume the receptive field lies entirely within the image. Hint:

you may want to draw a one$-$dimensional conv net to reason about this problem.