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About this Article

  • Authors: Ian J. Goodfellow, Jean Pouget-Abadie, Mehdi Mirza, Bing Xu, David Warde-Farley, Sherjil Ozair, Aaron Courville, Yoshua Bengio
  • Journals: arXiv (later, Advances in neural information processing systems)
  • Year: 2014
  • Citation: Goodfellow, Ian J., et al. “Generative adversarial nets.” Advances in neural information processing systems 27 (2014).


Accomplishments

  • Developed Generative Adversarial Nets (GAN), an architecture for generating data.


Key Points

1. Idea

The basic idea of GAN is to compete two distinct models(networks), one is a Generator(G) and the other is a Discriminator(D). The purpose of two networks are as follows.

  • G: Make data which is difficult to discriminate from the real data.
  • D: Distinguish whether given data is fake or real.

G and D will progressively compete like a police(D) and a fraud(G). The final goal is to make G perfect that D prints 1/2 for any input data.

2. Value Function

1. Basic Notations

  • $p_g$: generator’s distribution.
  • $G(z)$: data produced by generator G from noise z.
  • $D(x)$: the probability that data x came from the data rather than $p_g$. (In other words, from actual data.)
  • $D(G(z)))$: the probability that D determines fake data $G(z)$ as an actual data.
  • $(1-D(G(z)))$: the probability that D determines a fake data as a fake data.

2. Basic sketch We train D and G:

  • D to maximize the probability of assigning correct label to both training examples and samples from G.
  • G to minimize $log(1-D(G(z)))$.

3. Value function The value(objective) function $V(D,G)$ is \(\min_{G} \max_{D} V(D,G) = \mathbb{E}_{x \sim p_{\text{data}}(x)}[\log D(x)] + \mathbb{E}_{z \sim p_{z}(z)}[\log(1-D(G(z)))]\)

4. In the viewpoint of D D should discriminate real data as real data. Therefore, D has to maximize the probability $D(x)$ close to 1.

5. In the viewpoint of G The goal of G is to cheat D. Therefore, G has to minimize $log(1-D(G(z)))$.

6. In early training In early training, $log(1-D(G(z)))$ saturates (vanishing gradient). To solve this problem, authors used maximizing $log(D(G(z)))$ instead.

3. Algorithm



Authors alternatively trained D (k steps) and G (1 step).

  1. Training D: Extract m noise data and m real data. Update D by using a gradient of value function. Add (ascending) the gradient because the purpose of D is maximization.
  2. Training G: Extract m noise data. Update G by using a gradient of value function. Subtract (descending) the gradient because the purpose of G is minimization.

4. Theoretical Guarantees

There are two mathematical theorems that guarantee the validity of GAN.

  • Global Optimality of $p_g = p_{\text{data}}$: This shows that GAN works as we intended. Authors also suggest that the global optimum of value function is $-log~4$.
  • Convergence of Algorithm: This shows that GAN training algorithm works.

5. Advantages and Disadvantages

1. Advantages

  • Markov chains are never needed, only backprop is needed.
  • No inference is needed.
  • A wide variety of functions can be incorporated into the model.
  • Components of inputs are not copied directly into the generator’s parameters.

2. Disadvantages

  • No explicit representation of $p_g(x)$.
  • Training speed of G and D should be well-synchronized.
  • The Helvetica scenario: Mode collapse can happen. If G is trained too much without updating D, G can find and make only one perfect sample that can deceive D, for any input noise distribution z.


Further Research

  1. Conditional Generative Model: By conditioning input, we can control a model to generate certain types of data. (This idea leads to cGAN.)
  2. Learned Approximate Inference: GAN in this article learned ‘input noise z -> output x’ direction. We can introduce another auxiliary network to infer the reverse direction, from output to input noise. (This idea leads to BiGAN, ALI.)
  3. Modeling Conditionals: By training conditional models that share the same parameters, we can make a model to predict the rest part of data when only part of it is given. (Think image refining tools, ‘AI eraser’ of Galaxy or ‘Clean up’ of iOS.)
  4. Semi-supervised Learning: If labeled data is limited, features from the discriminator D can be used to improve performance of classifiers.
  5. Efficiency improvements: Training can be accelerated by devising better methods for coordinating G and D. It can also be improved by a better noise distribution z.


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