GAN史上最全基础入门总结

阅读提醒：中英文混杂

1. Introduction to GAN

1.1 Motivation

Generative models:

• explicit models: Likelihood-based models ( autoregressive and flows/VAE)

• implicit models: sample z → sample x, learning the deep neural network without explicit density estimation

1.2 GAN (original GAN) [Goodfellow, NIPS, 2014]

G captures the data distribution, D estimates the divergence between $p_{data}$ and $p_G$.
$$\begin{gathered} mi{n}_{G}ma{x}_{D}V(G,D) \\ V(G,D)={\mathbb{E}}_{x\sim p_{data}}[\log D(x)]+{\mathbb{E}}_{z\sim p_z}[\log (1-D(G(z)))] \end{gathered}$$
D尽力区别原始数据与生成数据的区别，形成一个二分类器；G给D提供负样本，并且尽力期骗D使D犯错。

# last layer of D is nn.Sigmoid()
criterion=nn.BCELoss()
# Discriminator
f_loss = criterion(netD(fake_img.detach()), f_l)
r_loss = criterion(netD(real_img.detach()), r_l)
D_loss = (f_loss+r_loss)/2
# Generator
G_loss = criterion(netD(fake_img), r_l)  # 注意用的是real的label

Limitations:

• unstable convergence
• vanishing gradient
• more collapse

1.3 Evaluation

Parzen-Window density estimator (Kernel density estimator)

• 只适用于低维
• could be unreliable

Inception Score (IS)

$$IS(x)=\exp (H(y)-H(y|x))$$

• IS 越大越好：希望$H(y)$越大越好，表明生成图片的种类越多；希望$H(y|x)$越小越好，表明生成图片$x$后其类别确定，即能够产生被分类的real image.
• IS 没有充分度量diversity

Frechet Inception Distance (FID)

• FID 越小越好

1.4 GAN theory

1.4.1 Bayes-Optimal Discriminator

用D衡量divergence，小的divergence是使discriminator很难分辨的东西，这个divergence不必显示表达，而是用一个NN来实现，这个NN就是D。
$$D^{\ast }=ar$$