Max pooling

As explained in Math and Architectures of Deep Learning

Max pooling is an aggregation operation that replaces each local or grouped region with its maximum value, often to downsample a representation.

Max pooling downsamples a feature map by sliding a kernel over local patches and replacing each patch with its largest value. This preserves strong local responses while reducing spatial precision and can make features more robust to small location changes. section 10.7 section 10.8

For each kernel position, the output is max(patch). Output size depends on kernel size and stride: a 2 × 2 kernel with stride 2 produces an output feature map half the input height and width; a 3 × 3 kernel with stride 3 reduces each dimension to one-third. section 10.7

A 2 × 2 pooling pass

Partition a 4 × 4 feature map into 2 × 2 patches with stride 2. Max pooling emits one maximum per patch, creating a 2 × 2 feature map. In PyTorch, create torch.nn.MaxPool2d(kernel_size=2, stride=2) and apply it to an N × C × H × W input tensor. section 10.7

In VGG-style convolutional blocks, convolution and ReLU layers retain spatial resolution, then a max-pool layer halves it. Repeating this across five blocks reduces a 224 × 224 input to a 7 × 7 feature map while channel counts increase. section 11.2.1

Max pooling also supports region-based detection. RoI pooling applies max pooling to regions of different sizes on a shared convolutional feature map, yielding fixed-sized features for classifier and regressor layers. section 11.4.3

Figure 10.19 Max pooling using a 2 × 2 kernel with stride 2. The resulting output feature map is half the size of the input feature map. Each value of the output feature map is a max of the corresponding local patch in the input feature map.

This diagram traces each 2 × 2 local patch to one maximum, making the halved spatial dimensions explicit. section 10.7

How Math and Architectures of Deep Learning covers it

How deep it goes

Defines local maximum aggregation and relates kernel size and stride to output resolution, with a PyTorch implementation.

Examples

Uses 2 × 2 stride-2 pooling on a 4 × 4 tensor and max-pool layers at the ends of VGG blocks.

What it assumes

Uses feature maps, kernels, strides, and tensor dimensions while introducing pooling as local-patch summarization.

What you can do after

Apply it via PyTorch MaxPool2d to downsample feature maps and place spatial reductions in convolutional architectures.

How it connects

Connects pooling to convolutional neural networks, average pooling, local translation invariance, VGG, and RoI pooling.

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Also explained in

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  Deep Learning with R, Third EditionA max-pooling layer down-samples local regions by retaining their maximum values.
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  Deep Learning with Python, Third EditionA two-dimensional pooling layer that downsamples feature maps by taking local maxima.
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  Deep Learning with PyTorch, Second Edition
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  Build a Text-to-Image Generator (from Scratch)Max pooling is a spatial downsampling operation that retains the maximum activation within each local window.
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  Graph Neural Networks in Actionmax_pool is a PyTorch Geometric pooling function that coarsens a graph by pooling clustered nodes using maximum-valued features.
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  Natural Language Processing in Action, Second EditionMax pooling is a downsampling operation that retains the largest activation within each local region of a feature map.
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  Evolutionary Deep Learning: Genetic algorithms and neural networksMax pooling is a neural-network operation that downsamples local activation regions by retaining their maximum values.
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  Machine Learning Algorithms in DepthMax pooling is a downsampling operation that retains the largest value within each local window of a feature sequence.
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  Sutskever's ListA downsampling operation that retains the largest activation within each local spatial window.

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Related concepts

• downsamplingkind of · Downsampling is the reduction of data quantity, spatial resolution, temporal resolution, or sampling rate by retaining, selecting, or aggregating fewer representative values or observations.
• poolingkind of · Pooling is an operation that aggregates values or representations across regions or axes to produce a reduced or summarized representation.
• convolutional neural networkpart of · A convolutional neural network is a neural-network architecture that applies learned convolutional operations to extract patterns from structured data.
• strided convolutioncontrasts with · A strided convolution is a convolution whose filter moves across input positions by more than one step, typically reducing spatial or temporal resolution.
• convolutional layeruses · A convolutional layer is a neural-network layer that applies shared learned filters to local regions of structured input to produce feature representations.
• neural network layerkind of · A neural network layer is a computational stage or component that transforms input representations into outputs within a neural network.

This explainer was generated by Manning's knowledge graph from the text of Math and Architectures of Deep Learning. The section links point to the parts of the book it draws on.