Stride: Skipping Positions to Downsample

The problem, from first principles

01-single-filter-conv2d moves the kernel one pixel at a time — every output position overlaps heavily with its neighbors, since a 3x3 kernel shares two full rows/columns with the position right next to it. That's a lot of redundant computation if what you actually want is a smaller output, not a full-resolution one.

Stride is the fix: instead of moving the kernel by 1 pixel between outputs, move it by stride pixels. A stride of 2 skips every other position, roughly halving the output's height and width for free — a cheap way to downsample an image while still applying a learned filter to it, which is exactly how many real CNNs shrink spatial size between blocks instead of using a separate pooling layer.

From theory to code

Theory changes exactly one thing from 01-single-filter-conv2d: the step between consecutive output positions. Output index i now corresponds to image row i * stride, not row i — everything else about computing one output value (patch, elementwise multiply, sum) stays identical.

Implement conv2d_with_stride(image, kernel, stride=1) against that reasoning.

Constraints

• image: shape (H, W). kernel: shape (kH, kW). stride: positive integer.
• Output shape: ((H - kH) // stride + 1, (W - kW) // stride + 1).
• stride=1 must match 01-single-filter-conv2d exactly.
• No padding — this question is stride only, 02-padding's padding modes aren't part of this contract.
• image and kernel are never modified in place.

Hints

Open one at a time. Each gives away a little more than the last.