What is a pointwise convolution?

A pointwise convolution is a `1×1` convolution that combines information across the input channels at each spatial location. Unlike a 3×3 convolution, it does not look at neighboring pixels.

How does it work?

• At one pixel location, the input feature map contains one value from each input channel.
• A 1×1 filter computes a weighted combination of those values to produce one output channel.
• Using multiple 1×1 filters produces multiple output channels. The same filters are applied at every spatial location.

Example: Suppose a feature map has 16 input channels and we want 32 output channels.

• Each 1×1 filter has 16 weights, one per input channel.
• With 32 filters, the layer has 16 × 32 = 512 weights (excluding biases).
• The output has 32 channels, while its height and width stay unchanged when stride is 1.

PyTorch example:

nn.Conv2d(16, 32, kernel_size=1)

Why is it useful?

• Channel mixing: Combines features from different channels at the same image position.
• Channel projection: Increases or reduces channel count—for example, from 64 channels to 16 in a bottleneck block.
• Efficient CNN design: Often follows a depthwise convolution, which processes each channel separately.

Pointwise vs. depthwise convolution

• Depthwise `3×3`: Learns spatial patterns *within* each channel, without mixing channels.
• Pointwise `1×1`: Mixes *across* channels at each location, without directly expanding spatial context.

Together, they form a depthwise separable convolution. Its computational savings compared with a standard spatial convolution are explored in the next question.

Related concepts: “What is a depthwise convolution?” and “What is a grouped convolution in a CNN?”

Research: MobileNets: Efficient Convolutional Neural Networks for Mobile Vision Applications. Documentation: PyTorch Conv2d.