Max Pooling - CNNs & Computer Vision

Max Pooling

What you'll build

Non-overlapping 2D max pooling on a single-channel (H, W) feature map: split it into pool_size x pool_size windows (stride = window size) and keep the maximum of each.

Background

Pooling shrinks feature maps, which cuts compute in later layers, grows the receptive field, and makes the network a little tolerant to small shifts (a feature that moves by one pixel inside a window gives the same max). Classic CNNs (LeNet, VGG, the ResNet stem) use 2x2 or 3x3 max pooling; many modern networks use strided convolutions instead.

Formula

With p = pool_size (window size and stride):

out[i, j] = max(image[i*p:(i+1)*p, j*p:(j+1)*p])

H_out = H // p
W_out = W // p

Inputs

• image: 2D array of shape (H, W) (ints or floats; a nested list is fine).
• pool_size: positive int p, default 2.

Expected return format

A NumPy array of shape (H // p, W // p) holding the window maxima (same dtype as the input; float inputs stay floats).

Edge cases and conventions

• If H or W is not a multiple of p, the leftover rows/columns at the bottom/right are dropped (floor), like F.max_pool2d with no padding and ceil_mode=False.
• Negative values: the max of [-1, -2] is -1; don't initialise the output with zeros and compare.

Constraints

NumPy only. A double loop over windows is fine; the reshape trick is fully vectorised.

Follow-up

• In the backward pass, which input receives the gradient of each output?
• How do average pooling and global average pooling differ, and why did global average pooling replace big fully connected heads?

Input: [[1, 2, 3, 4], [5, 6, 7, 8], [9, 10, 11, 12], [13, 14, 15, 16]]
Output: [[6, 8], [14, 16]]

Input: image = np.arange(30).reshape(5, 6) * 0.5, pool_size = 3
Output: [[7.0, 8.5]]

import numpy as np

def max_pool2d(image, pool_size=2):
    """
    Apply 2D max pooling with window = stride = pool_size.

    Args:
        image: Input feature map, shape (H, W)
        pool_size: Window size and stride p (default 2)

    Returns:
        output: Array of shape (H // p, W // p); leftover rows/columns are dropped
    """
    # Your code here
    pass