Pooling

Intuition

Pooling summarises each small window by its maximum (or average), shrinking feature maps while keeping the strongest responses — a bit of translation tolerance for free.

Precise explanation

For window size $k$ and stride $s$ (default $s = k$, non-overlapping), output size per axis is $\lfloor (n - k)/s \rfloor + 1$ (CS231n formula with no padding). Rows/columns that don't fit a full window are dropped. For the non-overlapping case a reshape trick avoids loops:

x[:Ho*k, :Wo*k].reshape(Ho, k, Wo, k).max(axis=(1, 3))

Overlapping pooling (s < k) can use sliding_window_view (NP-14) or a loop over output cells.

Worked example

4×4 [[1,2,3,4],[5,6,7,8],[9,10,11,12],[13,14,15,16]], 2×2 max → [[6, 8], [14, 16]]; average → [[3.5, 5.5], [11.5, 13.5]].

Common mistakes

• Reshaping (H, W) to (Ho, Wo, k, k) directly — mixes rows and columns.
• Forgetting to crop to a multiple of k.
• Off-by-one in the output size with strides.

Why this matters

Pooling layers appear in classic CNNs (LeNet, VGG) and global average pooling feeds classifier heads.

Library implementation

torch.nn.functional.max_pool2d and avg_pool2d (with kernel_size and stride) implement the same windows for batched, multi-channel tensors. The comparison runs when PyTorch is installed.

References

• CS231n: Convolutional Neural Networks notes — Stanford University CS231n (S015)
• Dive into Deep Learning — Aston Zhang, Zachary C. Lipton, Mu Li, Alexander J. Smola (S013)