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Generative Adversarial Networks : theory and practice

Abstract : Generative Adversarial Networks (GANs) were proposed in 2014 as a new method efficiently producing realistic images. Since their original formulation, GANs have triggered a surge of empirical studies, and have been successfully applied to different domains of machine learning: video, sound generation, and image editing. However, our theoretical understanding of GANs remains limited. This thesis aims to reduce the gap between theory and practice by studying several statistical properties of GANs. After reviewing the main applications of GANs in the introduction, we introduce a mathematical formalism necessary for a better understanding of GANs. This framework is then applied to the analysis of GANs defined by Goodfellow et al. (2014) and Wasserstein GANs, a variant proposed by Arjovsky et al. (2017), well-known in the scientific community for its strong empirical results. The rest of the thesis attempts to solve two practical problems often encountered by researchers: the approximation of Lipschitz functions with constrained neural networks and the learning of non-connected manifolds with GANs.
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Submitted on : Wednesday, December 15, 2021 - 3:41:25 PM
Last modification on : Friday, August 5, 2022 - 3:00:08 PM
Long-term archiving on: : Wednesday, March 16, 2022 - 7:15:11 PM


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  • HAL Id : tel-03481902, version 1


Ugo Tanielian. Generative Adversarial Networks : theory and practice. Statistics [math.ST]. Sorbonne Université, 2021. English. ⟨NNT : 2021SORUS051⟩. ⟨tel-03481902⟩



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