Building a Convolutional Neural Network

A convolutional neural network, also called a convnet, is a type of deep-learning model used in computer vision. One problem a convnet can address is image classification: assigning an image to a category. In a small-training-dataset setting, the network must extract useful visual evidence while controlling how much information later layers need to process. Max pooling helps with that control by replacing each small local region with its maximum value.

Max pooling examines a small region of a feature map and carries forward the largest value in that region. The output therefore contains one value where the input contained several nearby values. In the source's interpretation, feature maps can represent the spatial presence of a pattern across different tiles. Keeping the maximum emphasizes the strongest local presence of that pattern.

The window size determines how large a local area is examined. The stride determines how far the window advances before producing the next output. With the common 2 × 2 window and stride 2 arrangement, the operation produces fewer window positions along both height and width. Each spatial dimension is reduced by a factor of 2. For example, a 26 × 26 feature map becomes 13 × 13 after max pooling.

Pooling changes the spatial size of a feature map, but it does not remove the channel dimension. Max pooling is applied independently within each channel. A local region in one channel is summarized using that channel's own values; values from another channel are not included in the same maximum. The result keeps one downsampled spatial map for every original channel.

Downsampling has two linked benefits. First, it reduces the number of feature-map coefficients that later layers must process. The source gives a 22 × 22 × 64 feature map containing 30,976 coefficients per sample. Flattening that map before a Dense layer of size 512 would create 15.8 million parameters, which would be far too large for the small model being discussed and could cause intense overfitting.

Second, repeated downsampling supports a spatial hierarchy. Later convolutional windows can cover an increasingly larger fraction of the original input. This matters for tasks such as recognizing a whole digit, because later features need access to information from a larger portion of the input rather than only a small local region.

Max pooling is one way to reduce spatial dimensions. A convolutional layer can also perform reduction by using strides, and a network can use average pooling. These operations should not be treated as interchangeable descriptions. Max pooling keeps the maximum value from each local region. Average pooling keeps the average value of each channel over that region. A strided convolution uses a convolutional layer before the reduction, with strides controlling how the convolution advances.

Convnets are used in computer vision applications. Image classification is one such problem: the input is an image, and the task is to assign that image to a category. Image-classification problems with small training datasets are identified as the most common use case when the organization is not a large technology company.