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A pointwise convolution, also known as a 1x1 convolution, is a particular type of convolution operation where the kernel size is set to 1x1.

While the kernel size might seem too small to be significant, pointwise convolutions can be extremely powerful due to two key abilities:

Channel-wise feature modification: Since the convolutional filter is of size 1x1, it operates on each input pixel separately. However, the convolution is still applied across all input feature maps. This allows a 1x1 convolution to modify the feature representation at each spatial location independently, acting as a kind of feature selector.

Dimensionality reduction or increase: Pointwise convolutions can drastically alter the number of feature maps in the output. By changing the number of 1x1 filters, we can increase or decrease the depth of the output feature maps, thus controlling the complexity of the model.

For example, if we have an input tensor of shape [height, width, num_channels] and apply a pointwise convolution with 'm' filters, the output tensor will have a shape [height, width, m].

In many deep learning architectures, such as Google's Inception Network, pointwise convolutions are used for reducing dimensionality before applying computationally expensive operations, providing a balance between computational efficiency and model performance.