  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 \textit{concentrated} random vectors. Further exploiting the
fact that Gram matrices, of the type $G = X^T X$ with $X=[x_1,\ldots,x_n]\in
\mathbb{R}^{p\times n}$ and $x_i$ independent concentrated random vectors from
a mixture model, behave asymptotically (as $n,p\to \infty$) 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.
