Pooling

Pooling shrinks the height and width of a feature map while keeping the important information. It reduces computation in later layers, reduces overfitting by summarising regions, and gives some invariance to small shifts and distortions.

Max pooling keeps the largest value in each region: for the 2×2 region $\left[\begin{array}{cc}1& 3\\ 4& 2\end{array}\right]$ (window 2, stride 2) it outputs 4. It preserves strong features like edges but can make representations sparse.

Average pooling keeps the mean of the region — (1 + 3 + 4 + 2)/4 = 2.5 for the same region. It gives a smoother, less noise-sensitive representation.

Global pooling uses the whole feature map as one region, producing one value per channel; it is often used just before the fully connected layers. For the 4×4 matrix 1…16, global average pooling gives 8.5 and global max pooling gives 16. Global average pooling is used in architectures like GoogLeNet.

Fractional pooling uses non-integer pool sizes and strides for gentler downsampling. L2 pooling outputs the L2 norm of each region, $\sqrt{\sum x_i^2}$, preserving the 'energy' of the features.