Do grouped convolutions actually improve learning?

Question

My Understanding of Grouped Convolutions

Let say we have some data with the dimensions [100,100,32] (lets ignore batch size and assume channels last) and we want to pass it to a convolutional layer with 64 filters. Without grouping, we could pass the input directly into the second convolutional layer and get one output with a shape [100,100,64].

Alternatively we can split the input into n groups. For example lets say n=2. This changes the input from 1 [100,100,32] tensor to 2 [100,100,16] tensors. Then we pass each input to a different convolutional layer with 64/n = 32 filters to get two outputs with a shape of [100,100,32]. These two inputs are than concatenated channel wise to get a single output with a shape of [100,100,64].

The Problem

If this is correct, I understand how this can be useful for distributed training on multiple GPUs/CPUs (which I believe is what AlexNet did). However, I have seen claims that grouped convolutions improve performance and I feel that these two approaches (grouped and ungrouped) are mathematically identically and should have no difference in performances.

My Reasoning

Each filter is made up of c kernels; where c is the number of channels in the input. This is because each kernel is applied to a single channel. There is no interaction between kernels in the same filter. Therefore, regardless of how the channels are placed (ie. in one stack or in a groups) the resulting filter will be the same.

Am I mistaken?

Places that claim that grouped convolutions improve performnces

• https://towardsdatascience.com/grouped-convolutions-convolutions-in-parallel-3b8cc847e851
• https://blog.yani.ai/filter-group-tutorial/

Answer 1

As mentioned in the article also, the different groups learn different representations for the data.

In a normal convolutional network, each layer learns a unique representation. But, here, in the same layer, we are able to derive different representations. It can also related to the software engineering principle of Separation of Concerns. Since, different filter groups are trained separately, they are bound to learn things differently.

From a statistical perspective, when a traditional convolutional layers is trained, the correlation between the kernel weights will be there. Since, here we have separated them into groups, the correlation won't happen since they are trained separately.