---
# System prepended metadata

title: Generative Adversarial Nets
tags: [paper]

---

{%hackmd SybccZ6XD %}
###### tags: `paper`

# Generative Adversarial Nets

Goal
> Estimating generative models

Two parts of this framework (example)
> Generator: produce fake currency
> Discriminator: determine whether a sample is from the model distribution or the data distribution. detect the counterfeit currency.

Generator
> ![](https://hackmd.io/_uploads/ryyaq8Grn.png)

Discriminator
> ![](https://hackmd.io/_uploads/Sy6msLzH3.png)

## Algorithm
> ![](https://hackmd.io/_uploads/SybQ2LfHn.png)

Discriminator
> ![](https://hackmd.io/_uploads/H1QA3IMH2.png)
> 清楚分辨真假
> real x -> D -> 越大越好，代表Discriminator判定為真圖片
> fake G(z) -> D -> 越小越好，代表Discriminator判定為假圖片

Generator
> ![](https://hackmd.io/_uploads/rywx08GH2.png)
> z -> G -> fake G(z) -> D -> 越大越好，代表Discriminator判定為真圖片

Global Optimality of $p_g = p_{data}$
> For discriminator
> ![](https://hackmd.io/_uploads/HyEYALMr3.png)
> the function y → a log(y) + b log(1 − y) achieves its maximum in [0, 1] at $\frac{a}{a + b}$