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In CNNs, convolution and pooling are two fundamental operations that are often used together to process and analyze input data, typically images. They are sequential operations within a CNN layer.

Max-pooling is a type of pooling operation commonly used in machine learning and convolutional neural networks (CNNs). It involves dividing the input data into non-overlapping regions and selecting the maximum value from each region to create a downsampled version of the input. 

Here's how max-pooling works: 

1.  Input Regions: 

   The input data is divided into small, non-overlapping regions (usually square or rectangular) known as pooling windows. 

2.  Maximum Value: 

   For each region, the maximum value is determined. This operation is applied independently to each region. 

3.  Downsampling: 

   The selected maximum values form a downsampled version of the input data, resulting in a reduced spatial resolution. 

Figure 3545a shows a max-pooling with a pool size of 2 x 2.

 Figure 3545a. Max-pooling with a pool size of 2 x 2 (code).

Max-pooling is used for several reasons in convolutional neural networks: 

1.  Translation Invariance: 

   Max-pooling helps to make the representation of an object invariant to small translations. The network becomes less sensitive to the precise location of features. 

2.  Reducing Dimensionality: 

   By selecting only the maximum values, max-pooling reduces the spatial dimensions of the input, which can help reduce the computational complexity of subsequent layers and prevent overfitting. 

3.  Feature Selection: 

   The maximum value in each region represents the most activated feature, helping to retain important information and discard less relevant details.

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