Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixtures

01/21/2020 ∙ by Mohamed El Amine Seddik, et al. ∙ 0

This paper shows that deep learning (DL) representations of data produced by generative adversarial nets (GANs) are random vectors which fall within the class of so-called concentrated random vectors. Further exploiting the fact that Gram matrices, of the type G = X^T X with X=[x_1,...,x_n]∈R^p× n and x_i independent concentrated random vectors from a mixture model, behave asymptotically (as n,p→∞) as if the x_i were drawn from a Gaussian mixture, suggests that DL representations of GAN-data can be fully described by their first two statistical moments for a wide range of standard classifiers. Our theoretical findings are validated by generating images with the BigGAN model and across different popular deep representation networks.



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