I.11.X02

Count the fourth window, not a fifth

numeric▲△△

Compute the output length for input seven, kernel three, dilation one, padding one on each side and stride two. List padded-coordinate origins. Then choose padding for a width-four, stride-one kernel to retain length seven.

Hint

Use the effective span, and require the last tap to stay inside the padded input.

Solution

Equation (I.11.4) gives $\lfloor(7+2-3)/2\rfloor+1=4$ . In a padded input of length nine, origins $0,2,4,6$ end at $2,4,6,8$ . Origin eight would end at ten and does not fit.

For width four at stride one, total padding must be three. Splits $(1,2)$ and $(2,1)$ both preserve length but shift alignment differently. Equal integer padding cannot sum to three. The phrase ‘same size’ does not determine which side gets the extra value.

Draws on

I.11.P02 — Output size is a count of valid kernel origins.