gan-equilibrium-generator-matches-data

IN premise — entries/2026/06/21/wiki-Generative_adversarial_network-chunk-2.md

Created 2026-06-21T09:55:49+00:00

At the unique GAN equilibrium, the generator matches the data distribution exactly (μ̂_G = μ_ref), the discriminator outputs 1/2 everywhere, and the objective value is −2 ln 2

Dependents

These beliefs depend on this one:

• IN gan-complete-theoretical-characterization — GAN theory provides a complete analytical characterization of optimal behavior: the optimal discriminator has a closed-form solution (Radon-Nikodym derivative), the objective implicitly minimizes Jensen-Shannon divergence, and at the unique equilibrium the generator exactly recovers the data distribution.
• OUT gan-stable-convergence-guaranteed — GAN training reliably converges to the unique equilibrium where the generator matches the data distribution, given TTUR and asymptotic consistency guarantees.