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

Sep 25, 2019 Blind Submission readers: everyone Show Bibtex
• Keywords: Random Matrix Theory, Deep Learning Representations, GANs
• Abstract: 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'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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