Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixtures - Archive ouverte HAL Accéder directement au contenu
Communication Dans Un Congrès Année : 2020

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

Résumé

This paper shows that deep learning (DL) representations of data produced by generative ad-versarial 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.
Fichier principal
Vignette du fichier
rmt4gan.pdf (4.65 Mo) Télécharger le fichier
Origine : Fichiers éditeurs autorisés sur une archive ouverte
Loading...

Dates et versions

hal-02971185 , version 1 (19-10-2020)

Identifiants

  • HAL Id : hal-02971185 , version 1

Citer

Mohamed El Amine Seddik, Cosme Louart, Mohamed Tamaazousti, Romain Couillet. Random Matrix Theory Proves that Deep Learning Representations of GAN-data Behave as Gaussian Mixtures. ICML 2020 : Thirty-seventh International Conference on Machine Learning, 2020, Online, France. ⟨hal-02971185⟩
68 Consultations
155 Téléchargements

Partager

Gmail Facebook X LinkedIn More