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In the paper Progressive growing of gans for improved quality, stability, and variation (ICLR, 2018) by Nvidia researchers, the authors write

Furthermore, we observe that mode collapses traditionally plaguing GANs tend to happen very quickly, over the course of a dozen minibatches. Commonly they start when the discriminator overshoots, leading to exaggerated gradients, and an unhealthy competition follows where the signal magnitudes escalate in both networks. We propose a mechanism to stop the generator from participating in such escalation, overcoming the issue (Section 4.2)

What do they mean by "the discriminator overshoots" and "the signal magnitudes escalate in both networks"?

My current intuition is that the discriminator gets too good too soon, which causes the generator to spike and try to play catch up. That would be the unhealthy competition that they are talking about. Model collapse is the side effect where the generator has trouble playing catch up and decides to play it safe by generating slightly varied images to increase its accuracy. Is this way of interpreting the above paragraph correct?

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  • $\begingroup$ Note that it's not "Model collapse" (as you write) but "mode collapse". This refers to the mode of a distribution (if I remember correctly). $\endgroup$
    – nbro
    Jun 26, 2022 at 9:00

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A discriminator overshooting may result in a dataset that has not been thoroughly clean and probably has too many identical feature, as a result there will be an early convergence from the discriminator as there is little variation. The drawback from this is that the model will not bee able to generalize well.

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  • $\begingroup$ In other words, the generator can no longer effective learn how to fool the discriminator because everything fails. $\endgroup$
    – David Hoelzer
    Mar 5, 2020 at 14:40
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Yes, your intuition is correct. The effect of this problem is that the generator can no longer improve its output to marginally fool the discriminator - the discriminator isn't buying any of the generated output. In this case, the generator gets stuck in a local minimum and typically produces nonsense results.

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Your intuition doesn't coincide with my interpretation. This is how I see it:

The generator might have some problem early on, for simplicity lets consider the example where the generator always outputs a black pixel in the top left corner. Then the discriminator learns to select on that particular feature, and the generator might take several update steps to resolve the issue, during which the discriminator might shift toward only selecting for the color of the first pixel instead of whether the whole image looks like a face.

Because there is this interplay between the generator and discriminator and because they are constantly lacking behind each other they might start to oscillate. The generator might overcompensate for some random pixel which gave him away to the discriminator and then the discriminator might overcompensate by selecting for a single different pixel which the generator wasn't focused on.

Of course this example is oversimplified by talking about the value of a single pixel, but you get the idea: the two networks are too focused on small problems.

It's not about the discriminator getting too good, but about it getting too focused on one of the mistakes the generator is currently making.

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