How is the backpropagation for Separable Convolution 2D in tensorflow/keras implemented exactly?

How Backpropagation Works in SeparableConv2D

Forward Pass

Let:

• Input shape = [B, H, W, C_in]

• Depthwise kernel = [K, K, C_in, 1]

• Pointwise kernel = [1, 1, C_in, C_out]

The output is computed as:

• First: apply depthwise conv → [B, H, W, C_in]

• Then: apply pointwise conv → [B, H, W, C_out]
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Backward Pass

Backpropagation happens in two parts, just like forward pass:

A. Gradient wrt Pointwise Convolution

• Acts like a standard 1×1 convolution.

• Gradients w.r.t pointwise kernel are computed using standard conv backprop.

• Gradient flows from loss → output → pointwise conv → depthwise output.
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B. Gradient wrt Depthwise Convolution

• Since each filter is applied to one input channel only, gradients are calculated per-channel.

• The chain rule applies:

• From pointwise gradients → through the depthwise output → back to each channel’s depthwise filter.

TensorFlow handles both parts using standard Conv2DBackprop* operations under the hood.