Wasserstein GAN

Abstract: We introduce a new algorithm named WGAN, an alternative to traditional GAN training. In this new model, we show that we can improve the stability of learning, get rid of problems like mode collapse, and provide meaningful learning curves useful for debugging and hyperparameter searches. Furthermore, we show that the corresponding optimization problem is sound, and provide extensive theoretical work highlighting the deep connections to other distances between distributions.

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Synopsis

Overview

  • Keywords: Wasserstein GAN, Generative Adversarial Networks, Earth Mover's Distance, Optimization, Mode Collapse
  • Objective: Introduce the Wasserstein GAN (WGAN) framework to improve the training stability and performance of GANs.
  • Hypothesis: The use of the Earth Mover's (EM) distance as a loss function will enhance the convergence properties of GANs compared to traditional methods.

Background

  • Preliminary Theories:

    • Generative Adversarial Networks (GANs): A framework where two neural networks, a generator and a discriminator, are trained simultaneously to generate realistic data.
    • Earth Mover's Distance (EM): A measure of the distance between two probability distributions, representing the minimum cost of transforming one distribution into another.
    • Kantorovich-Rubinstein Duality: A mathematical principle that connects the EM distance to the optimization of Lipschitz functions, providing a foundation for WGAN.
    • Mode Collapse: A common issue in GANs where the generator produces a limited variety of outputs, failing to capture the diversity of the training data.
  • Prior Research:

    • 2014: Introduction of GANs by Ian Goodfellow et al., establishing the framework for adversarial training.
    • 2015: Development of various GAN architectures, including DCGAN, which improved image generation quality.
    • 2016: Identification of training instabilities and mode collapse in GANs, leading to further exploration of alternative loss functions.
    • 2017: Proposal of WGAN, addressing the limitations of traditional GANs by utilizing the EM distance for more stable training.

Methodology

  • Key Ideas:

    • EM Distance as Loss Function: WGAN employs the EM distance to provide a more stable and meaningful loss metric that correlates with the quality of generated samples.
    • Lipschitz Constraint: The critic (discriminator) is constrained to be 1-Lipschitz, ensuring that the gradients are well-behaved during training.
    • Weight Clipping: A technique used to enforce the Lipschitz constraint by restricting the weights of the critic to a compact space.
  • Experiments:

    • Image Generation: Experiments conducted on the LSUN-Bedrooms dataset to evaluate the performance of WGAN against traditional GANs.
    • Architectural Variations: Testing various generator architectures, including DCGAN and MLP, to assess the robustness of WGAN.
    • Metrics: Evaluation based on the convergence of the loss function and the visual quality of generated samples.
  • Implications: The design of WGAN allows for continuous training of the critic, leading to improved gradient estimates and reduced mode collapse.

Findings

  • Outcomes:

    • WGAN significantly improves training stability compared to traditional GANs, with no observed mode collapse across various architectures.
    • The loss function derived from the EM distance provides a meaningful metric that correlates well with the quality of generated samples.
    • The ability to train the critic to optimality results in better gradients for the generator, enhancing overall performance.
  • Significance: WGAN demonstrates that using the EM distance as a loss function addresses critical issues in GAN training, such as mode collapse and unstable convergence, which were prevalent in earlier models.

  • Future Work: Exploration of alternative methods for enforcing Lipschitz constraints and further refinement of the WGAN framework to enhance performance across diverse applications.

  • Potential Impact: Advancements in WGAN could lead to more reliable generative models applicable in various fields, including image synthesis, data augmentation, and unsupervised learning tasks.

Notes

Meta

Published: 2017-01-26

Updated: 2025-08-27

URL: https://arxiv.org/abs/1701.07875v3

Authors: Martin Arjovsky, Soumith Chintala, Léon Bottou

Citations: 4549

H Index: 3

Categories: stat.ML, cs.LG

Model: gpt-4o-mini