Gan: generate adversarial networks

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1 principle

For generating countermeasure networks GAN, A simple understanding is that it can be seen as the process of game , We can regard the generative model and the discriminant model as two sides of the game , For example, in the process of criminals making counterfeit money and police identifying counterfeit money ：

• Generate models G Equivalent to the party making counterfeit money , The purpose is based on the coins seen and the identification technology of the police , Try to generate more real 、 Counterfeit money that the police can't identify .
• Discriminant model D Equivalent to identifying counterfeit money , Its purpose is to identify the counterfeit money made by criminals as much as possible . In this way, through the contest between the counterfeiter and the counterfeiter and the improvement towards the goal , So that the final generation model can be as real as possible 、 Those who can't judge the true and false Nash equilibrium effect ( The probability of true and false currency is 0.5).

2 Training

generator G Our goal is to cheat the discriminator D, The goal is to be able to distinguish between real data and generated data . therefore , When training the generator , We want to maximize the error , At the same time, we want to minimize the error of the discriminator .

2.1 Discriminant model

The objective function is ：

$$ma{x}_D{E}_{x-p_r}[logD(x)]+E_{z-p_g}[log(1-D(x))]$$
among D(x) It is the output of the discrimination model , It's a 0-1 Real values in the range , The probability used to judge whether the picture is a real picture , among Pr and Pg It represents the distribution of the real image and the data distribution of the generated image , It can be seen that the objective function is to find the discriminant model function that maximizes the sum of the following two formulas D(z), The latter two formulas are an addition form , among ：
$$E_{x-p_r}[logD(x)]$$
It refers to putting real data into the discriminant model D(x) The output calculated value and the whole formula value should be as large as possible .
$$E_{z-p_g}[log(1-D(x))]$$
Make the fake data put into the discrimination model D(x) The calculated value of the output is as small as possible and the value of the whole formula is as large as possible .

This integration is to make the objective function as large as possible , Therefore, during training, gradient lifting can be carried out according to the objective function .

2.2 Generate models

The goal is to make the discriminant model unable to distinguish between real pictures and generated pictures , The objective function is ：
$$mi{n}_g(ma{x}_D{E}_{x-p_r}[logD(x)]+E_{z-p_g}[log(1-D(x))])$$
That is, find the generating function g(z) Make the objective function of the generated model as small as possible .

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