Couches de regroupement : sous-échantillonnage spatial et invariance

Pooling layers reduce the spatial dimensions of feature maps, decreasing computation and memory while making representations more compact. They also introduce a degree of spatial invariance — small translations of a feature in the input produce the same pooled output. Without pooling (or stride-2 convolutions), the spatial dimensions would remain constant through all layers, making the network computationally prohibitive for large images.

MaxPool2d divides the input feature map into non-overlapping windows and takes the maximum value in each window. The maximum corresponds to the strongest activation of the filter at any position in that window — it captures whether the feature was present anywhere in the region, regardless of its exact position. A 2x2 max pool with stride 2 reduces height and width by half, cutting the total spatial size by 4x.

AvgPool2d takes the average of values in each pooling window instead of the maximum. Average pooling smooths the feature map and retains information from all activations, while max pooling discards the weaker activations. Max pooling is preferred in classification networks where the presence of a feature matters more than its average strength. Average pooling is commonly used for global pooling at the end of a CNN to collapse spatial dimensions.

Global Average Pooling (GAP) collapses the entire spatial dimension to a single value per channel by averaging all spatial positions. For a feature map of shape (B, C, H, W), GAP produces (B, C) — a vector of C values representing the average activation of each filter across the entire image. GAP replaces the flatten + large fully connected layers at the top of classic CNNs (VGG), drastically reducing parameters and acting as a powerful regulariser. It is used in ResNet, MobileNet, and EfficientNet.

Computing the output spatial dimensions after pooling is straightforward: output_size = floor((input_size - kernel_size) / stride) + 1. For a 2x2 pool with stride 2 on a 28x28 input, the output is 14x14. Misjudging dimensions is a common source of shape errors. AdaptiveMaxPool2d and AdaptiveAvgPool2d solve this by accepting the desired output size directly, automatically computing the required kernel and stride — ideal when you want a fixed output regardless of input size.

Pooling provides local translation invariance: if a feature shifts by a few pixels, it likely still falls within the same pooling window and produces the same maximum activation. This means the network recognises a cat whether it is slightly to the left or right in the image. However, pooling is only locally invariant — large translations still produce different outputs. Data augmentation (random crops, flips) is needed to achieve global translation invariance.

Modern CNN architectures (ResNet, EfficientNet) increasingly use stride-2 convolutions instead of separate max pooling layers. The advantage is that stride-2 convolutions are learnable — the network decides how to downsample, potentially preserving more useful information than the fixed max operation. Max pooling is still used in classic architectures (VGGNet, AlexNet) and for its computational simplicity. Both approaches achieve the same goal: reducing spatial resolution by a factor of 2.

An important property of pooling layers is that they have no learnable parameters. Max pooling simply selects the maximum; average pooling computes the mean. This makes pooling layers very fast and memory-free — they do not contribute to the parameter count. The lack of parameters also means pooling cannot overfit. This is why global average pooling at the end of a network is a strong regulariser — it forces the network to encode information in each channel's average, not in spatial positions.

A standard CNN architecture alternates between convolutional blocks (Conv+BN+ReLU) and pooling layers, progressively reducing spatial dimensions while increasing channel count. After the convolutional blocks, global average pooling collapses spatial dimensions, and a linear layer maps to class scores. This pattern produces a network with manageable parameter count, good generalisation, and strong image classification performance.

AdaptiveMaxPool2d(output_size) automatically computes the kernel size and stride needed to produce the specified output dimensions, regardless of input size. This is invaluable when you want a fixed-size vector for the classifier but the input images have varying sizes (e.g., object detection, variable-resolution datasets). FractionalMaxPool2d uses randomised pooling regions to add stochasticity, acting as an additional regulariser in some architectures.

To understand what pooling does visually: a feature map before max pooling shows the raw filter response at each pixel. After pooling, the output is spatially coarser — each value represents the strongest response in its neighbourhood. The feature map becomes more abstract and position-independent. Deep in a network, after many rounds of pooling, each neuron's receptive field covers most of the original image, enabling global pattern recognition.

In this lesson you learned: MaxPool2d and AvgPool2d reduce spatial dimensions by taking the max or average in each pooling window, providing compact representations and local translation invariance, AdaptiveAvgPool2d produces a fixed output size regardless of input dimensions (used as Global Average Pooling), and pooling has no learnable parameters, making it fast and non-overfitting. Next up we build and train a complete CNN on CIFAR-10.