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I don't have a definite answer, but only a suspicion/idea: Looking at Figure 1 from the WGAN paper, we clear see that the JS divergence on the right is not continuous at $0$, hence not differentiable at $0$. However, the EM plot on the left is continuous also at $0$. You could now argue that we have a kink there, so it should not be differentiable there ...

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First of all, the discriminator in WGAN does not give a value in the range $[0,1]$. Compared to the traditional discriminator, it has a linear activation in the output layer. Therefore, the authors call it critic instead. To calculate the penalty, we sample an image that lies on the line between the real and the generated image. This is done by sampling a ...

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This is from my own experience with (Vanilla) GANs, so it might not translate exactly to your application, but maybe it gives some orientation. your learning rate seems quite high. I've quite frequently found that 1e-5 is a good value for me. The training might take longer but will probably be more stable. have you tried using dropout? It's a good ...

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Figure 3 in the original WGAN paper is actually quite helpful to understand the difference between the score in WGAN and the probability in GAN (see screenshot below). The blue distribution are real samples, and the green one are fake samples. The Vanilla GAN trained in this example identifies the real samples as '100% real' (red curve) and the fake samples ...

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