In a backprop context, you’d use groupwise convolution to either make the model splittable into more than one GPU (since the groups won’t have to “cross” data), or to force the training to split channels into different groupings of features (you can google on this, there are some nice explanations available). In a more general context, you could find any number of applications, lets say for simplicity that you just want to blur each R, G and B channel separately with a blur kernel and want RGB output (and you definitely don’t want to blur R with G etc.).