Pooling#

Pooling is a standard operation in convolutional neural networks (CNNs) used to downsample feature maps. It reduces the spatial dimensions (height and width) while keeping the number of channels unchanged.

Pooling is not a learnable operation — it applies a fixed function (like max or average) over small regions of the input.

A pooling layer slides a small window (like a kernel) across the input and applies a function. Like convolution, pooling has:

  • Kernel size: window size (\(k\times k\))

  • Stride: step size (often equals the kernel size for downsampling)

  • Padding: rarely used in pooling, but available

Max Pooling#

The example below shows a Max-Pooling with a \(2\times 2\) window.

In Python, we can apply a max pooling layer as follows.

import torch
import torch.nn as nn

x = torch.tensor([[[[1., 2., 3., 4.],
                    [5., 6., 7., 8.],
                    [9.,10.,11.,12.],
                    [13.,14.,15.,16.]]]])

pool = nn.MaxPool2d(kernel_size=2, stride=2)
y = pool(x)

print(y)  # shape: (1, 1, 2, 2)

tensor([[[[ 6.,  8.],
          [14., 16.]]]])

The effect of max-pooling is mainly the amplification of features. It compresses the input to a summary that contains the most prevalent features of the previous feature map.

Average Pooling#

Average pooling computes the average of the window. The example below shows the input on the right and the average pooling output on the right.

Average pooling smoothes the features in the input feature map.