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For questions related to the concept of cross-entropy in the context of artificial intelligence. For example, when the cross-entropy is used as a loss function to train a neural network.

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Where is the mistake in my derivation of the GAN loss function?

I guess the issue is you lost track of where the samples came from and since you requested a math explanation I'll try to go step by step using my notation and without checking other material to avoid …
Nicola Bernini's user avatar