Padding and stride decide the output size, and nothing else does.

Demonstration

out = ⌊(in + 2·pad − k) / stride⌋ + 1

That is the entire content of the proposition. Everything else is reading it.

Without padding the image shrinks. A 3 × 3 kernel loses one position at each edge, so 7 becomes 5. Stack twenty such layers and a 224-pixel image is 184 pixels, and the corners have been seen by fewer windows than the middle.

Padding of (k−1)/2 keeps the size. For k = 3 that is 1, which is why almost every modern network uses 3 × 3 with padding 1: shapes stay put and the architecture becomes composable.

Stride subsamples. Stride 2 halves each spatial axis and quarters the number of positions. It is the cheap way to downsample, and it is why resolutions in a network go 224, 112, 56, 28, 14, 7.

The floor is where the surprises live. With in = 7, k = 3, pad = 1, stride = 2, the output is ⌊8/2⌋ + 1 = 5, and the last window hangs off the edge — some frameworks silently drop it, some pad again. The two disagree by a row, and in a segmentation network that disagreement surfaces at the decoder as a shape mismatch several layers later.

Corollary

Compute the shapes on paper before writing the model. Most “the tensors do not line up” bugs are this formula, applied by the framework and not by the author, and they are cheaper to prevent than to trace back from the exception.