**Generative Adversarial Networks (GAN)** is a framework for estimating generative models via an adversarial process by training two models simultaneously.
A generative model *G* that captures the data distribution, and a discriminative model *D* that estimates the probability that a sample came from the training data rather than G.
It was proposed and presented in Advances in Neural Information Processing Systems (NIPS) 2014.

# Introduction

- Taxonomy of
**Machine Learning****Supervised learning**: The discriminative model learns how to classify input to its class.**Unsupervised learning**: The generative model learns the distribution of training data.- More challenging than supervised learning because there is no label or curriculum which leads self learning
- NN solutions: Boltzmann machine, Auto-encoder, Variation Inference, GAN

- The goal of the generative model is to find a \(p_{model}(x)\) that approximates \(p_{data}(x)\) well.

# Generative Adversarial Nets (GAN)

## Intuition of GAN

- The
**discriminator***D*should classify a real image as real (\(D(x)\) close to 1) and a fake image as fake (\(D(G(z))\) close to 0). - The
**generator***G*should create an image that is indistinguishable from real to deceive the discriminator (\(D(G(z))\) close to 1).

## Objective Function

**Objective function**of GAN is minimax game of two-player*G*and*D*.

- For the
**discriminator***D*should maximize \(V(D,G)\)- Sample \(x\) from real data distribution for \(p_{data}(x)\)
- Sample latent code \(z\) from Gaussian distribution for \(p_z(z)\)
- \(V(D,G)\) is maximum when \(D(x)=1\) and \(D(G(z))=0\)

- For the
**generator***G*should minimize \(V(D,G)\)*G*is independent of \(\mathbb{E}_{x\sim p_{data}~(x)}[log D(x)]\)- \(V(D,G)\) is minimum when \(D(G(z))=1\)

**Saturating problem**- In practice, early in learning, when
*G*is poor,*D*can reject samples with high confidence because they are clearly different from the training data. - In this case, the gradient is relatively small at \(D(G(z))=0\) which makes \(\log (1-D(G(z)))\) saturates.
- Rather than training
*G*to minimize \(\log (1-D(G(z)))\), we can train*G*to maximize \(\log D(G(z))\). - This objective function results in the same fixed point of the dynamics of
*G*and*D*but provides much stronger gradients early in learning.

- In practice, early in learning, when
**Why does GANs work?**- Because it actually minimizes the distance between the real data distribution \(p_{data}\) and the model distribution \(p_g\).
**Jensen-Shannon divergence (JSD)**is a method of measuring the similarity between two probability distributions based on the**Kullback-Leibler divergence (KL)**.

- Because it actually minimizes the distance between the real data distribution \(p_{data}\) and the model distribution \(p_g\).

# Variants of GAN

## Deep Convolutional GAN (DCGAN), 2015

**DCGAN**used convolution for discriminator and deconvolution for generator.- It is stable to train in most settings compared to GANs.
- DCGAN used the trained discriminators for image classification tasks, showing competitive performance with other unsupervised algorithms.
- Specific filters of DCGAN have learned to draw specific objects.
- The generators have interesting vector arithmetic properties allowing for easy manipulation of many semantic qualities of generated samples.

**Latent vector arithmetic**- They showed consistent and stable generations that semantically obeyed the linear arithmetic including object manipulation and face pose.

## Least Squares GAN (LSGAN), 2016

**LSGAN**adopt the**least squares loss function**for the discriminator instead of cross entropy loss function of GAN.- Since, cross entropy loss function may lead to the
**vanishing gradient problem**. - LSGANs are able to generate higher quality images than regular GANs.
- LSGANs performs more stable during the learning process.

- Since, cross entropy loss function may lead to the

## Semi-Supervised GAN (SGAN), 2016

**SGAN**extend GANs that allows them to learn a generative model and a classifier simultaneously.- SGAN improves classification performance on restricted data sets over a baseline classifier with no generative component.
- SGAN can significantly improve the quality of the generated samples and reduce training times for the generator.

## Auxiliary Classifier GAN (ACGAN), 2016

**ACGAN**is added more structure to the GAN latent space along with a specialized cost function results in higher quality samples.

# Extensions of GAN

## CycleGAN: Unpaired Image-to-Image Translation

**CycleGAN**presents a GAN model that transfer an image from a source domain A to a target domain B in the absence of paired examples.- The generator \(G_{AB}\) should generates a horse from the zebra to deceive the discriminator \(D_B\).
- \(G_{BA}\) generates a reconstructed image of domain A which makes the shape to be maintained when \(G_{AB}\) generates a horse image from the zebra.

**Result**

## StackGAN: Text to Photo-realistic Image Synthesis

**StackGAN**generate \(256 \times 256\) photo-realistic images conditioned on text descriptions.

**Result**

## Latest work

**Visual Attribute Transfer**- Jing Liao et al. Visual Attribute Transfer through Deep Image Analogy, 2017

**User-Interactive Image Colorization**- Richard Zhang et al. Real-Time User-Guided Image Colorization with Learned Deep Prioirs, 2017

# References

- Paper: Generative Adversarial Nets [Link]
- Paper: Unsupervised representation learning with deep convolutional generative adversarial networks [Link]
- Paper: Least Squares Generative Adversarial Networks [Link]
- Paper: Semi-Supervised Learning with Generative Adversarial Networks [Link]
- Paper: Conditional Image Synthesis With Auxiliary Classifier GANs [Link]
- Paper: Unpaired Image-to-Image Translation using Cycle-Consistent Adversarial Networks [Link]
- Paper: StackGAN: Text to Photo-realistic Image Synthesis with Stacked Generative Adversarial Networks [Link]
- PPT: Generative Adversarial Nets by Yunjey Choi [Link]