4 research outputs found
On the estimation of the Wasserstein distance in generative models
Generative Adversarial Networks (GANs) have been used to model the underlying
probability distribution of sample based datasets. GANs are notoriuos for
training difficulties and their dependence on arbitrary hyperparameters. One
recent improvement in GAN literature is to use the Wasserstein distance as loss
function leading to Wasserstein Generative Adversarial Networks (WGANs). Using
this as a basis, we show various ways in which the Wasserstein distance is
estimated for the task of generative modelling. Additionally, the secrets in
training such models are shown and summarized at the end of this work. Where
applicable, we extend current works to different algorithms, different cost
functions, and different regularization schemes to improve generative models.Comment: Accepted and presented at GCPR 2019 (http://gcpr2019.tu-dortmund.de/
Encoding Invariances in Deep Generative Models
Reliable training of generative adversarial networks (GANs) typically require massive datasets in order to model complicated distributions. However, in several applications, training samples obey invariances that are \textit{a priori} known; for example, in complex physics simulations, the training data obey universal laws encoded as well-defined mathematical equations. In this paper, we propose a new generative modeling approach, InvNet, that can efficiently model data spaces with known invariances. We devise an adversarial training algorithm to encode them into data distribution. We validate our framework in three experimental settings: generating images with fixed motifs; solving nonlinear partial differential equations (PDEs); and reconstructing two-phase microstructures with desired statistical properties. We complement our experiments with several theoretical results