Learning GANs: Game, Theory, Training, Variants

Definition and intuition of GANs

A generative adversarial network (GAN) is a framework for generative AI in which two neural networks compete in a zero-sum game: a generator and a discriminator. The generator produces synthetic samples from a latent space, while the discriminator tries to distinguish generated (fake) samples from real data. Training proceeds indirectly: the generator is updated to “fool” the discriminator rather than to directly minimize a distance to any specific target sample. Mathematically, the original GAN can be described as a minimax game. For a reference data distribution \(\mu_{ref}\) and generator distribution \(\mu_G\), the discriminator \(D\) outputs a probability that an input is real. The objective \(L(\mu_G,\mu_D)\) is maximized by the discriminator and minimized by the generator. Intuitively, the discriminator provides a learning signal about how realistic the generator’s outputs are, and as the generator improves, the discriminator’s task becomes harder. In practice, GANs are trained by alternating updates: first training the discriminator on real samples and current generated samples, then updating the generator based on how well it succeeds at producing samples the discriminator misclassifies as real. This adversarial setup yields an implicit generative model (it does not explicitly model likelihoods), and under the original formulation the optimal discriminator relates the game to a divergence between distributions (Jensen–Shannon divergence), giving a theoretical intuition for why matching the data distribution is the goal.

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GANs as zero-sum generator-discriminator game

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