Max Pooling: Downsampling by Keeping the Strongest Response

The problem, from first principles

01-convolutions/03-stride showed one way to shrink a feature map: skip positions while still running the full weighted-sum computation at each one. Pooling is a second, even simpler way — instead of a learned weighted sum, just look at a small window and keep the single strongest value in it, throwing the rest away entirely.

The intuition is that a feature map's job is usually to say "how strongly does this pattern show up here" — if it fired strongly ANYWHERE in a small neighborhood, that's usually the information worth keeping, and exactly where within that neighborhood it fired is often noise you can safely discard.

From theory to code

Theory says: divide the image into small windows (non-overlapping by default), and for each window, keep only its maximum value, once per channel.

Implement max_pool2d(image, kernel_size, stride=None) against that reasoning.

Constraints

• image: shape (C, H, W).
• kernel_size: the pooling window's height and width.
• stride: step between windows; if None, defaults to kernel_size (non-overlapping pooling).
• Output: shape (C, (H - kernel_size)//stride + 1, (W - kernel_size)//stride + 1).
• Pooling has no learned weights and no bias — it's a pure reduction, applied identically to every channel independently.
• image is never modified in place.

Hints

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