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Conditional GANs |
/cgans/ |
7 |
In traditional GANs the data is unconditionally generated but we can condition the model on additional information which can direct the data generation process.
For GANs we have the value function:
$$\min\limits_G\max\limits_D V(G, D)={\mathbb E}{x\sim p{\rm data}}[\log D(x)]+{\mathbb E}_{x\sim p_z}[\log(1-D(G(z)))]$$
We can extend GANs to include some extra information
- In generator the prior input noise
$p_z(z)$ and$y$ are combined in joint hidden representation. - In the discriminator
$x$ and$y$ are presented as inputs.
The objective function becomes:
$$\min\limits_G\max\limits_DV(G, D)={\mathbb E}{x\sim p{\rm data}}[\log D(x\mid y)]+{\mathbb E}_{x\sim p_z(z)}[\log(1-D(G(z\mid y)))]$$
This is illustrated in the below figure:
-
Generator: (From paper) We trained a conditional adversarial net on MNIST images conditioned on their class labels encoded as one-hot vectors. Noise prior
$z$ with dimensionality$100$ was drawn from a normal distribution. Both$z$ and$y$ are mapped to hidden layers with ReLu activation with layer sizes$200$ and$1000$ respectively, before both being mapped to second, combined hidden ReLu layer of dimensionality$1200$ . We have a final tanh unit layer as our output for generating the$784$ -dimensional MNIST samples. -
Discriminator: (From paper) The discriminator maps
$x$ to a max-out layer with$240$ units and$5$ pieces, and$y$ to a max-out layer with$50$ units and$5$ pieces. Both the hidden layers are mapped to joint max-out layer with$240$ units and$4$ pieces before being fed to a sigmoid layer. -
Model: (From code) The model was trained using Adam with learning rate
$\eta=0.0002$ and$\beta_1=0.5$ - (From code) We experimented on the MNIST dataset for handwritten digits. We observed the results as shown in figure. The code can be found in the Code folder.
