# How different should discriminator be from generator in GAN

When training a GAN, the generator $$G$$ strives to fool the discriminator $$D$$, while $$D$$ attempts to catch any output generated $$G$$ and isolate it from a real data point. They grow together training in turns for each epoche.

Assuming $$D$$ is already an expert classifier (for example, classifying birds and nonbirds images). What will happen if I freeze the weights of $$D$$ and only train $$G$$ (to generate high-resolution bird images from low-resolution ones for example)? Is there a mathematical problem here? Is $$D$$ so good that the generator will not be able to learn due to a very high initial error? I have obviously simulated it and failed.

Generator cant learn if the discriminator error is too small. But generator should always be "ahead" of generator in order to learn.

There is a paper explaining why the generator's gradient vanishes if the discriminator gets too strong. And how does this proportion look mathemactically optimal

TL;DR Dont make it too strong, but make sure D is ahead to ensure optimal learning. GANS are notoriously unstable (expensive also)