# Conditional Generative Adversarial Nets

- Category: Article
- Created: January 25, 2022 10:27 AM
- Status: Open
- URL: https://arxiv.org/pdf/1411.1784.pdf
- Updated: February 15, 2022 6:53 PM

# Background

In this work we introduce the conditional version of generative adversarial nets, which can be constructed by simply feeding the data, \(y\), we wish to condition on to both the generator and discriminator.

# Highlights

- By conditioning the model on additional information it is possible to direct the data generation process.
- Many interesting problems are more naturally thought of as a probabilistic one-to-many mapping. One way to address the problem is to use a conditional probabilistic generative model, the input is taken to be the conditioning variable and the one-to-many mapping is instantiated as a conditional predictive distribution.

# Methods

Generative adversarial nets can be extended to a conditional model if both the generator and discriminator are conditioned on some extra information \(y\). \(y\) could be any kind of auxiliary information, such as class labels or data from other modalities. We can perform the conditioning by feeding \(y\) into the both the discriminator and generator as additional input layer.

### Generator

In the generator the prior input noise \(p_z(z)\), and \(y\) are combined in joint hidden representation, and the adversarial training framework allows for considerable flexibility in how this hidden representation is composed.

### Discriminator

In the discriminator \(x\) and \(y\) are presented as inputs and to a discriminative function (embodied again by a MLP in this case).

### Objective function

\[ \min _{G} \max _{D} V(D, G)=\mathbb{E}_{\boldsymbol{x} \sim p_{\mathrm{d}} \boldsymbol{d a}(\boldsymbol{x})}[\log D(\boldsymbol{x} \mid \boldsymbol{y})]+\mathbb{E}_{\boldsymbol{z} \sim p_{\boldsymbol{z}}(\boldsymbol{z})}[\log (1-D(G(\boldsymbol{z} \mid \boldsymbol{y})))] \]