averagepooling

Average pooling, or mean pooling, is a pooling operation used in convolutional neural networks to downsample feature maps. It partitions a feature map into regions and replaces each region with the average value of its elements. The common parameters are the pooling window size k x k, the stride s, and optionally padding p. For each channel, the output dimensions follow the usual pooling formulas, and each output location corresponds to the average of the k x k neighborhood in the input.

Mathematically, for a 2D input with a single channel, the output at position (i, j) is given by y[i, j] = (1/k^2) sum_{m=0}^{k-1} sum_{n=0}^{k-1} x[i*s + m, j*s + n]. This operation is applied independently across channels. Global average pooling is a special case where the pooling window covers the entire spatial extent, producing one value per channel, often used before a dense classifier to reduce parameters and model size.

Compared with max pooling, average pooling replaces each region with its mean rather than its maximum. This tends to preserve background information and produce smoother feature maps, at the cost of potentially blurring sharp activations. It distributes gradient more evenly during training and can be more robust to small translations in the input.

Applications and variants: average pooling is widely used for downsampling within CNNs and can be followed by a fully connected layer or used as a final global pooling layer before classification. Adaptive average pooling, which outputs a fixed spatial size regardless of input dimensions, is another common variant.