Depthwise separable convolutions require more GPU memory

Question

I have read many papers and web articles that claim that depthwise-separable convolutions reduce the memory required by a deep learning model compared to standard convolution. However, I do not understand how this would be the case, since depthwise-separable convolution requires storing an extra intermediate-step matrix as well as the final output matrix.

Here are two scenarios:

• Typical convolution: You have a 3x3 filter, which is applied to a 7x7 RGB input volume. This results in an output of size 5x5x1 which needs to be stored in GPU memory. Suppose activations are float32, this requires 100 bytes of memory

• Depthwise-separable convolution: You have three 3x3x1 filters applied to a 7x7 RGB input volume. This results in three output volumes each of size 5x5x1. You then apply a 1x1 convolution to the concatenated 5x5x3 volume to get a final output volume of size 5x5x1. Hence, with float32 activations, this requires 300 bytes for the intermediate 5x5x3 volume, and 100 bytes for the final output. Hence a total of 400 bytes of memory

As additional evidence, when using an implementation U-Net in pytorch with typical nn.Conv2d convolutions, the model has 17.3M parameters and a forward/backward pass size of 320MB. If I replace all convolutions with depthwise-separable convolutions, the model has 2M parameters, and a forward/backward pass size of 500MB. So fewer parameters, but more memory required

I am sure I am going wrong somewhere, as every article states that depthwise-separable convolutions require less memory. Where am I going wrong with my logic?