Can Push-forward Generative Models Fit Multimodal Distributions? - MAP5 Accéder directement au contenu
Proceedings/Recueil Des Communications Année : 2022

Can Push-forward Generative Models Fit Multimodal Distributions?

Antoine Salmona
  • Fonction : Auteur
  • PersonId : 1145418
Valentin de Bortoli
  • Fonction : Auteur
  • PersonId : 1084097
  • IdRef : 249460300
Julie Delon
Agnès Desolneux
  • Fonction : Auteur
  • PersonId : 1114785

Résumé

Many generative models synthesize data by transforming a standard Gaussian random variable using a deterministic neural network. Among these models are the Variational Autoencoders and the Generative Adversarial Networks. In this work, we call them "push-forward" models and study their expressivity. We show that the Lipschitz constant of these generative networks has to be large in order to fit multimodal distributions. More precisely, we show that the total variation distance and the Kullback-Leibler divergence between the generated and the data distribution are bounded from below by a constant depending on the mode separation and the Lipschitz constant. Since constraining the Lipschitz constants of neural networks is a common way to stabilize generative models, there is a provable trade-off between the ability of push-forward models to approximate multimodal distributions and the stability of their training. We validate our findings on one-dimensional and image datasets and empirically show that generative models consisting of stacked networks with stochastic input at each step, such as diffusion models do not suffer of such limitations.
Fichier principal
Vignette du fichier
main.pdf (1.4 Mo) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-03708470 , version 1 (18-12-2022)

Identifiants

  • HAL Id : hal-03708470 , version 1

Citer

Antoine Salmona, Valentin de Bortoli, Julie Delon, Agnès Desolneux. Can Push-forward Generative Models Fit Multimodal Distributions?. NeurIPS 2022, The Thirty-sixth Annual Conference on Neural Information Processing Systems, 2022, Advances in Neural Information Processing Systems 35 (NeurIPS 2022). ⟨hal-03708470⟩
68 Consultations
34 Téléchargements

Partager

Gmail Facebook X LinkedIn More