Well, I would try to scale the classification loss to match the discriminator loss.
But before you are doing that, let’s dig a bit deeper into the CrossEntropyLoss.
You’ve said, that elementwise_mean doesn’t reduce the loss and it stays approx. at >400.
However, you’re using a batch size of 128. So the sum and mean should definitely change the loss value.
Could you explain your setup a bit?
How many classes are you dealing with?