mlsanityData to 7 Oct 2026

A Wasserstein perspective of Vanilla GANs

arXiv 2403.15312 ↗First posted 22 Mar 2024math.ST cs.LG stat.MLcited by 3

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Abstract (arXiv)

The empirical success of Generative Adversarial Networks (GANs) caused an increasing interest in theoretical research. The statistical literature is mainly focused on Wasserstein GANs and generalizations thereof, which especially allow for good dimension reduction properties. Statistical results for Vanilla GANs, the original optimization problem, are still rather limited and require assumptions such as smooth activation functions and equal dimensions of the latent space and the ambient space. To bridge this gap, we draw a connection from Vanilla GANs to the Wasserstein distance. By doing so, existing results for Wasserstein GANs can be extended to Vanilla GANs. In particular, we obtain an oracle inequality for Vanilla GANs in Wasserstein distance. The assumptions of this oracle inequality are designed to be satisfied by network architectures commonly used in practice, such as feedforward ReLU networks. By providing a quantitative result for the approximation of a Lipschitz function by a feedforward ReLU network with bounded H"older norm, we conclude a rate of convergence for Vanilla GANs as well as Wasserstein GANs as estimators of the unknown probability distribution.

Key facts. Cited by 3 papers in the map (data through 7 Oct 2026). Builds on 33 of its 54 references that are in the map. First posted on arXiv 22 Mar 2024.

Builds on

33 of 54 references.

References · 33

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21 more
  1. 2018Improving the Improved Training of Wasserstein GANs: A Consistency Term and Its Dual Effectcited by 49
  2. 2018Limitations of the Lipschitz constant as a defense against adversarial examplescited by 48
  3. 2017Many Paths to Equilibrium: GANs Do Not Need to Decrease a Divergence At Every Stepcited by 45
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Cited by year (2026 to 7 Oct)

Citing papers per year: 2025: 2; 2026: 1.

3 papers.

  1. 2025On the minimax optimality of Flow Matching through the connection to kernel density estimationcited by 9
  2. 2025Distribution estimation via Flow Matching with Lipschitz guaranteescited by 5
  3. 2026HP-GAN: Harnessing pretrained networks for GAN improvement with FakeTwins and discriminator consistencycited by 0