Consider a $$2	imes 2$$ max-pooling layer applied to an input tensor. The pooling window starts from the upper-left and slides across the tensor. At each location, it outputs the maximum value of the input subtensor in the window. For example, if the elements in a given window are $$0, 1, 3, 4$$, the output is $$\max(0, 1, 3, 4)=4$$. This operation is repeated for all regions traversed by the window, generating an output tensor where each element is derived from the maximum value in its respective pooling window.

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Max-pooling is a deterministic operation that selects the maximum value from the elements within a fixed-shape pooling window as it slides across an input tensor. Originally introduced in cognitive neuroscience research on hierarchical object recognition, max-pooling has become the dominant pooling method in modern convolutional neural networks. It is generally preferred over average pooling because it confers a degree of invariance to the output—small translations or distortions in the input are less likely to affect the maximum value within a window, making the learned features more robust to spatial shifts.

Max Pooling in Convolutional Deep Learning

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Max-Pooling Computation Example

Max-pooling can provide translation invariance to features extracted by convolutional layers. For instance, in edge detection, passing the output of a convolutional layer through a $$2	imes 2$$ max-pooling layer ensures that the detected edge pattern will still be recognized even if the input shifts by one element in height or width. As long as the high activation value remains within the pooling window, the pooling layer will consistently output the same maximum value.

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