Greetings!
I am confused by the Batchnorm2d documentation:
https://pytorch.org/docs/stable/generated/torch.nn.BatchNorm2d.html 2

The mean and standard-deviation are calculated per-dimension over the mini-batches

What does per dimension mean?
As far as I know, I want to normalize every feature map, i.e. every channel. But how exactly is a single feature map normalized? They say that \gamma and \beta have the same dimension as the channel number C, so y also has dimension C. Yet, the layer output is supposed to have the same shape as the input… what are y and x in this formula then?
Best,
PiF