Hidden Convexity of Wasserstein GANs: Interpretable Generative Models with Closed-Form Solutions

• URL: http://arxiv.org/abs/2107.05680v1
• Date: Mon, 12 Jul 2021 18:33:49 GMT
• Title: Hidden Convexity of Wasserstein GANs: Interpretable Generative Models with Closed-Form Solutions
• Authors: Arda Sahiner, Tolga Ergen, Batu Ozturkler, Burak Bartan, John Pauly, Morteza Mardani, Mert Pilanci
• Abstract summary: We analyze the impact of Wasserstein GANs with two-layer neural network discriminators through the lens of convex duality. We further demonstrate the power of different activation functions of discriminator.
• Score: 31.952858521063277
• License: http://creativecommons.org/licenses/by/4.0/
• Abstract: Generative Adversarial Networks (GANs) are commonly used for modeling complex distributions of data. Both the generators and discriminators of GANs are often modeled by neural networks, posing a non-transparent optimization problem which is non-convex and non-concave over the generator and discriminator, respectively. Such networks are often heuristically optimized with gradient descent-ascent (GDA), but it is unclear whether the optimization problem contains any saddle points, or whether heuristic methods can find them in practice. In this work, we analyze the training of Wasserstein GANs with two-layer neural network discriminators through the lens of convex duality, and for a variety of generators expose the conditions under which Wasserstein GANs can be solved exactly with convex optimization approaches, or can be represented as convex-concave games. Using this convex duality interpretation, we further demonstrate the impact of different activation functions of the discriminator. Our observations are verified with numerical results demonstrating the power of the convex interpretation, with applications in progressive training of convex architectures corresponding to linear generators and quadratic-activation discriminators for CelebA image generation. The code for our experiments is available at https://github.com/ardasahiner/ProCoGAN.

Related papers

• Straightness of Rectified Flow: A Theoretical Insight into Wasserstein Convergence [54.580605276017096]
  Rectified Flow (RF) aims to learn straight flow trajectories from noise to data using a sequence of convex optimization problems. RF theoretically straightens the trajectory through successive rectifications, reducing the number of evaluations function (NFEs) while sampling. We provide the first theoretical analysis of the Wasserstein distance between the sampling distribution of RF and the target distribution.
  arXiv  Detail & Related papers  (2024-10-19T02:36:11Z)
• Diffusion models for Gaussian distributions: Exact solutions and Wasserstein errors [0.0]
  Diffusion or score-based models recently showed high performance in image generation. We study theoretically the behavior of diffusion models and their numerical implementation when the data distribution is Gaussian.
  arXiv  Detail & Related papers  (2024-05-23T07:28:56Z)
• The Convex Landscape of Neural Networks: Characterizing Global Optima and Stationary Points via Lasso Models [75.33431791218302]
  Deep Neural Network Network (DNN) models are used for programming purposes. In this paper we examine the use of convex neural recovery models. We show that all the stationary non-dimensional objective objective can be characterized as the standard a global subsampled convex solvers program. We also show that all the stationary non-dimensional objective objective can be characterized as the standard a global subsampled convex solvers program.
  arXiv  Detail & Related papers  (2023-12-19T23:04:56Z)
• Data Interpolants -- That's What Discriminators in Higher-order Gradient-regularized GANs Are [20.03447539784024]
  We show analytically, via the least-squares gradient (LSGAN) and Wasserstein (WGAN) GAN variants, that the discriminator optimization problem is one of $n$-dimensions. The optimal discriminator, using variational Calculus, turns out to be the solution to a partial differential equation involving the iterated Laplacian or the polyharmonic operator. We employ the Poly-WGAN discriminator to model the latent space distribution of the data with encoder-decoder-based GAN flavors such as Wasserstein autoencoders.
  arXiv  Detail & Related papers  (2023-06-01T15:16:36Z)
• Score-based Diffusion Models in Function Space [140.792362459734]
  Diffusion models have recently emerged as a powerful framework for generative modeling. We introduce a mathematically rigorous framework called Denoising Diffusion Operators (DDOs) for training diffusion models in function space. We show that the corresponding discretized algorithm generates accurate samples at a fixed cost independent of the data resolution.
  arXiv  Detail & Related papers  (2023-02-14T23:50:53Z)
• Instability and Local Minima in GAN Training with Kernel Discriminators [20.362912591032636]
  Generative Adversarial Networks (GANs) are a widely-used tool for generative modeling of complex data. Despite their empirical success, the training of GANs is not fully understood due to the min-max optimization of the generator and discriminator. This paper analyzes these joint dynamics when the true samples, as well as the generated samples, are discrete, finite sets, and the discriminator is kernel-based.
  arXiv  Detail & Related papers  (2022-08-21T18:03:06Z)
• Inferential Wasserstein Generative Adversarial Networks [9.859829604054127]
  We introduce a novel inferential Wasserstein GAN (iWGAN) model, which is a principled framework to fuse auto-encoders and WGANs. The iWGAN greatly mitigates the symptom of mode collapse, speeds up the convergence, and is able to provide a measurement of quality check for each individual sample.
  arXiv  Detail & Related papers  (2021-09-13T00:43:21Z)
• Discriminator Contrastive Divergence: Semi-Amortized Generative Modeling by Exploring Energy of the Discriminator [85.68825725223873]
  Generative Adversarial Networks (GANs) have shown great promise in modeling high dimensional data. We introduce the Discriminator Contrastive Divergence, which is well motivated by the property of WGAN's discriminator. We demonstrate the benefits of significant improved generation on both synthetic data and several real-world image generation benchmarks.
  arXiv  Detail & Related papers  (2020-04-05T01:50:16Z)
• Your GAN is Secretly an Energy-based Model and You Should use Discriminator Driven Latent Sampling [106.68533003806276]
  We show that sampling in latent space can be achieved by sampling in latent space according to an energy-based model induced by the sum of the latent prior log-density and the discriminator output score. We show that Discriminator Driven Latent Sampling(DDLS) is highly efficient compared to previous methods which work in the high-dimensional pixel space.
  arXiv  Detail & Related papers  (2020-03-12T23:33:50Z)
• Convex Geometry and Duality of Over-parameterized Neural Networks [70.15611146583068]
  We develop a convex analytic approach to analyze finite width two-layer ReLU networks. We show that an optimal solution to the regularized training problem can be characterized as extreme points of a convex set. In higher dimensions, we show that the training problem can be cast as a finite dimensional convex problem with infinitely many constraints.
  arXiv  Detail & Related papers  (2020-02-25T23:05:33Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.