gan-training-stabilizable-given-complete-theory
OUT derived (depth 2)
Created 2026-06-21T11:59:56+00:00
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.
Justifications
SL — complete theory plus interventions would suffice for stability but game-theoretic foundations break beyond original formulation
Antecedents (all must be IN):
- 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.
- IN gan-training-stability-requires-multiple-interventions — GAN training stability benefits from several complementary design choices — non-saturating loss to address vanishing gradients when the generator is poor, two-timescale update rule for provable convergence to a stationary local Nash equilibrium (though not mode collapse prevention), and deterministic discriminators for optimality of the discriminator — each addressing a distinct failure mode, but none individually sufficient for overall stability.
Unless (any of these IN defeats this justification):
- IN gans-no-guaranteed-nash-equilibrium — Farnia & Ozdaglar (ICML 2020) proved that GANs do not always have Nash equilibria, establishing a theoretical limitation of adversarial training
- IN gan-equilibria-coincide-original-only — Sequential (minimax/maximin) and Nash equilibria all coincide for the original GAN game, but this equivalence is not guaranteed for general GAN variants