Coulomb GANs: Provably Optimal Nash Equilibria via Potential Fields

By Thomas Unterthiner, Bernhard Nessler, Günter Klambauer, Martin Heusel, Hubert Ramsauer, Sepp Hochreiter. 2017

81 citations recorded by the source corpus.

Generative adversarial networks (GANs) evolved into one of the most successful unsupervised techniques for generating realistic images. Even though it has recently been shown that GAN training converges, GAN models often end up in local Nash equilibria that are associated with mode collapse or otherwise fail to model the target distribution. We introduce Coulomb GANs, which pose the GAN learning problem as a potential field of charged particles, where generated samples are attracted to training set samples but repel each other. The discriminator learns a potential field while the generator decreases the energy by moving its samples along the vector (force) field determined by the gradient of the potential field. Through decreasing the energy, the GAN model learns to generate samples according to the whole target distribution and does not only cover some of its modes. We prove that Coulomb GANs possess only one Nash equilibrium which is optimal in the sense that the model distribution equals the target distribution. We show the efficacy of Coulomb GANs on a variety of image datasets. On LSUN and celebA, Coulomb GANs set a new state of the art and produce a previously unseen variety of different samples.

Subfields: Computer Vision and Pattern Recognition, Generative Models

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Citations in the corpus

The GAN Landscape: Losses, Architectures, Regularization, and Normalization (2018, background): “[29] Thomas Unterthiner, Bernhard Nessler, Calvin Seward, Günter Klambauer, Martin Heusel, Hubert Ramsauer, and Sepp Hochreiter.”
Improving MMD-GAN Training with Repulsive Loss Function (2018, methodology): “Thus, MMD has been applied to compare the generated samples to real ones directly (Li et al. (2015); Dziugaite et al. (2015)) and extended as the loss function to the GAN framework recently (Unterthiner et al. (2018); Li et al. (2017a); Bińkowski et al. (2018)).”
Fréchet ChemNet Distance: A Metric for Generative Models for Molecules in Drug Discovery (2018, background): “However, generative models might suffer from mode collapse [16, 23], such that they produce only molecules with a low diversity.”
Learning Implicit Generative Models with the Method of Learned Moments (2018, methodology): “In Coulomb GAN (Unterthiner et al., 2017), the discriminator and generator steps are: The authors deﬁne the empirical estimate of the potential function Φ (not to be confused with feature functions in the main text) as: To demonstrate that the loss is a distance, it remains to show that the…”
A Large-Scale Study on Regularization and Normalization in GANs (2018, unknown): “Metrics There already seems to be a divergence in how the FID score is computed: (1) Some authors report the score on training data, yielding a FID between 50K training and 50K generated samples (Unterthiner et al., 2018).”
Dropout-GAN: Learning from a Dynamic Ensemble of Discriminators (2018, background): “On the other hand, [36, 38] reformulated the original GANs problem using an energy-based objective to promote sample variability.”
Discriminator optimal transport (2019, background): “Since from the first successful implementation by convolutional neural nets [2], most literatures concentrate on how to improve the unstable optimization procedures including changing objective functions [3, 4, 5, 6, 7, 8], adding penalty terms [9, 10, 11], techniques on optimization precesses thems”
Sphere Generative Adversarial Network Based on Geometric Moment Matching (2019, unknown): “05 Coulomb GAN [32] 27.”
Towards Accurate Generative Models of Video: A New Metric & Challenges (2018, background): “6This has lead to confusion regarding FID in the past, when researchers used different sample sizes in their comparisons [28, 42, 14].”
Understanding the Effectiveness of Lipschitz Constraint in Training of GANs via Gradient Analysis (2018, background): “Coulomb GAN [25] poses the GAN learning problem as a potential field of charged particles, where the discriminator learns a potential field while the generator decreases the energy by moving its samples along the vector field determined by the gradient of the potential field.”
Generative Adversarial Network Training is a Continual Learning Problem (2018, background): “GAN convergence While GAN convergence is not the focus of this paper, convergence does similarly avoid mode collapse, and there are a number of works on the topic (Heusel et al., 2017; Unterthiner et al., 2018; Nagarajan & Kolter, 2017; Mescheder et al., 2017).”