Generative adversarial networks (GANs) learn a parameterized density function, p(x).

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The question asks whether Generative Adversarial Networks (GANs) learn a parameterized density function, p(x).
Option 1: True. This statement would imply that GANs explicitly learn and represent a closed-form probability density function p(x) with a tractable form or parameters. In practice, GANs do not learn an explicit density. The generator creates samples from a latent space through a neural network, yielding an implicit distribution p_g(x) that is not available in closed form. The training objective does not require p_g(x) to be known or written down; it relies on a discriminator to distinguish real from fake samples, not on evaluating p(x) directly. Therefore, claiming that GANs learn a parameterized density p(x) is inaccurate.
Option 2: False. This correctly reflects the standard view of GANs. They use a generator to induce an implicit distribution over x, defined by x = G(z; θ), where z is drawn from a simple prior. The density p_g(x) is generally intractable to compute exactly, and GANs do not provide an explicit form for p_g(x). Training emphasizes the ability to generate realistic samples rather than learning an explicit probability density function. This distinction between implicit distributions and explicit densities is central to how GANs operate, making the statement false.
In short, the core misunderstanding in Option 1 is treating GANs as learning an explicit, usable p(x), whereas GANs actually learn an implicit distribution through a generator, with no tractable explicit density provided. The technical framing in Option 2 aligns with the conventional GAN theory and practice.

CS-7643-O01, OAN, OSZ Quiz #5: Module 4

Generative adversarial networks (GANs) learn a parameterized density function, p(x).

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