What is a Lipschitz constraint?

What is a Lipschitz constraint?

“hard” 1-Lipschitz constraint: forcing the gradient to be lower or equal to one at every point of the input domain. The gradient can be lower than one at some points. This is used when dealing with adversarial robustness.

What is Wasserstein Gan?

The Wasserstein Generative Adversarial Network, or Wasserstein GAN, is an extension to the generative adversarial network that both improves the stability when training the model and provides a loss function that correlates with the quality of generated images.

Does f satisfy a Lipschitz condition on D?

Theorem 1 Suppose f(t,y) is defined on a convex set D in R2. If a constant L  0 exists with ∂f ∂y t, y ≤ L, for all t, y in D, then f satisfies a Lipschitz condition on D in the variable y with Lipschitz constant L. So, f satisfies a Lipschitz condition with a constant 4.

What does the name Lipschitz mean?

The name is derived from the Slavic “lipa,” meaning “linden tree” or “lime tree.” The name may relate to a number of different place names: “Liebeschitz,” the name of a town in Bohemia, “Leipzig,” the name of a famous German city, or “Leobschutz,” the name of a town in Upper Silesia.

How do you train GANs?

Steps to train a GAN

  1. Step 1: Define the problem.
  2. Step 2: Define architecture of GAN.
  3. Step 3: Train Discriminator on real data for n epochs.
  4. Step 4: Generate fake inputs for generator and train discriminator on fake data.
  5. Step 5: Train generator with the output of discriminator.

Is Wgan better than GAN?

WGAN-GP Experiments As shown below, when the model design is less optimal, WGAN-GP can still create good results while the original GAN cost function fails. Below is the inception score using different methods. The experiment from the WGAN-GP paper demonstrates better image quality and convergence comparing with WGAN.

Why does gradient penalty help?

The simplest way to achieve this is to penalize the gradient on real data alone: when the generator distribution produces the true data distribution and the discriminator is equal to 0 on the data manifold, the gradient penalty ensures that the discriminator cannot create a non-zero gradient orthogonal to the data …

How do you prove Lipschitz?

We prove that uniformly continuous functions on convex sets are almost Lipschitz continuous in the sense that f is uniformly continuous if and only if, for every ϵ > 0, there exists a K < ∞, such that f(y) − f(x) ≤ Ky − x + ϵ. functions and Lipschitz-continuous functions.

What kind of name is Lipschitz?

Lipschitz, Lipshitz, or Lipchitz is an Ashkenazi Jewish surname. The surname has many variants, including: Lifshitz (Lifschitz), Lifshits, Lifshuts, Lefschetz; Lipschitz, Lipshitz, Lipshits, Lopshits, Lipschutz (Lipschütz), Lipshutz, Lüpschütz; Libschitz; Livshits; Lifszyc, Lipszyc.