Pointwise Convolution

Pointwise Convolution is a 1×1 convolution that operates across channels at each spatial position independently — used to change the number of channels (projection), mix channel information, and add nonlinearity without any spatial interaction.

Properties of Pointwise Convolution

• Kernel Size: 1×1 (no spatial extent).
• Operation: Linear combination of channels at each pixel: $y_j(h,w) = \sum_i W_{ji} \cdot x_i(h,w)$.
• Parameters: $C_{in} \times C_{out}$ per layer.
• Equivalent To: A fully connected layer applied to each spatial position independently.

Why It Matters

• Channel Mixing: The primary mechanism for inter-channel communication in depthwise-separable convolutions.
• Projection: Used to reduce or expand channel dimensions (bottleneck design).
• Ubiquitous: Used in every MobileNet, EfficientNet, ShuffleNet, and modern lightweight architecture.

Pointwise Convolution is the channel mixer — the 1×1 operation that connects information across feature channels at every spatial position.