gan-equilibria-coincide-original-only

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

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

Sequential (minimax/maximin) and Nash equilibria all coincide for the original GAN game, but this equivalence is not guaranteed for general GAN variants

Dependents

These beliefs depend on this one:

• IN gan-game-theoretic-foundations-fragile-beyond-original — GAN game-theoretic foundations are fragile beyond the original formulation — equilibrium equivalence (minimax, maximin, Nash) holds only for the original game and not its variants, Nash equilibria are not guaranteed to exist in general (Farnia & Ozdaglar 2020), and the two dominant failure modes (mode collapse and vanishing gradients) represent opposed destabilizing forces that the equilibrium theory does not resolve.
• OUT gan-training-stabilizable-given-complete-theory — GAN training would be reliably stabilizable given the complete theoretical characterization (optimal discriminator, JSD minimization, unique equilibrium) and multiple complementary stabilization interventions (non-saturating loss, TTUR, architecture choices) — unless the game-theoretic foundations themselves are limited, with Nash equilibria not guaranteed in general and equilibrium equivalence holding only for the original formulation.