gan-architectural-asymmetry-mirrors-game-theory

IN derived (depth 1)

Created 2026-06-21T13:38:09+00:00 · Reviewed 2026-06-21T15:37:01+00:00

GAN architectural asymmetry (deconvolutional generator vs convolutional discriminator in image tasks) parallels its game-theoretic asymmetry — the discriminator has a closed-form optimal solution while the generator does not, and these two asymmetries coexist in the minimax game structure, though the antecedents do not establish that the architectural choices were designed to instantiate the mathematical asymmetry.

Justifications

SL — Architectural and game-theoretic asymmetries are structurally parallel

Antecedents (all must be IN):

IN gan-generator-deconv-discriminator-conv — For image tasks, the GAN generator is typically a deconvolutional neural network and the discriminator is typically a convolutional neural network
IN gan-optimal-discriminator-formula — The optimal discriminator for a fixed generator is D*(x) = μ_ref(x) / (μ_ref(x) + μ_G(x)), which is the Radon-Nikodym derivative dμ_ref/d(μ_ref + μ_G)
IN gan-two-network-minimax-game — A GAN consists of exactly two neural networks (generator and discriminator) trained as a minimax zero-sum game where the generator minimizes and the discriminator maximizes the same objective function