Lipschitz Continuous

Brief introduction of Lipschitz continuous in machine learning.

Introduction

Lipschitz continuous means that f must be K-Lipschitz continuous. f is called K-Lipschitz continuous if there exists a real constant K≥0 such that, for all x1,x2∈R,

Here K is the Lipschitz constant for function f.

Lipschitz 连续意味着 f 必须是 K-Lipschitz 连续的。 f 被称为 K-Lipschitz 连续，如果存在实常数 K≥0 使得对于所有 x1,x2∈R，

f(x1)−f(x2)

≤K

x1−x2

这里K 是函数f 的Lipschitz 常数。

In Wasserstein GAN, the Lipschitz constraints is enforced in neural network (discriminator), like 1-Lipschitz, for keeping the training stable.

(In our former work, ‘stable’ is something always stand against long-term memory.)

在 Wasserstein GAN 中，Lipschitz 约束在神经网络（鉴别器）中强制执行，如 1-Lipschitz，以保持训练稳定。

（在我们以前的工作中，“稳定”总是与长期记忆背道而驰。）