Effective Covariance Dynamics in Solvable High-Dimensional GANs

We study a solvable high-dimensional model of generative adversarial network (GAN) training in which a linear generator learns a low-dimensional subspace from data with structured latent covariance. Prior solvable GAN analyses assume unconditional signals with diagonal latent covariance; we extend the multi-feature discriminator setting to class-dependent, correlated, and non-zero-mean latent structure. For the quadratic energy discriminator, all such heterogeneity enters the dynamics through a probability-weighted effective second moment. We prove that the stochastic microscopic training proc