The same exact patch dot product repeats at every valid location. The result is a feature map of exact integers.

highlighted = computed this step

Slide the kernel

After one cell, slide the same kernel across every valid patch. With a 4 by 4 image and a 3 by 3 kernel, valid stride 1 makes a 2 by 2 feature map.

(43+1)×(43+1)(4\,-\,3\,+\,1)\times(4\,-\,3\,+\,1)
Feature mapEvery valid stride-one cell is exact.feature mapc1c29-66-9valid padding, stride 1kernel is given; valid padding and stride one; one exact forward pass; head softmax is NAMED;NOT training; NOT learning

Every cell is recomputed

Every displayed feature-map cell is recomputed from its own patch. For this image and kernel, the cells are 9, -6, 6, and -9.

feature map=[9669]\text{feature map}=\begin{bmatrix}9&-6\\6&-9\end{bmatrix}
Feature mapEvery valid stride-one cell is exact.feature mapc1c29-66-9valid padding, stride 1kernel is given; valid padding and stride one; one exact forward pass; head softmax is NAMED;NOT training; NOT learning

Summary

The feature map is not a new kind of arithmetic. It is the same exact dot product repeated at each valid location.

feature map cells are exact integer sums\text{feature map cells are exact integer sums}
Feature mapEvery valid stride-one cell is exact.feature mapc1c29-66-9valid padding, stride 1kernel is given; valid padding and stride one; one exact forward pass; head softmax is NAMED;NOT training; NOT learning