InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets
InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets
Chen, Xi and Chen, Xi and Duan, Yan and Houthooft, Rein and Schulman, John and Sutskever, Ilya and Abbeel, Pieter
2016

Paper summary
aleju
* Usually GANs transform a noise vector `z` into images. `z` might be sampled from a normal or uniform distribution.
* The effect of this is, that the components in `z` are deeply entangled.
* Changing single components has hardly any influence on the generated images. One has to change multiple components to affect the image.
* The components end up not being interpretable. Ideally one would like to have meaningful components, e.g. for human faces one that controls the hair length and a categorical one that controls the eye color.
* They suggest a change to GANs based on Mutual Information, which leads to interpretable components.
* E.g. for MNIST a component that controls the stroke thickness and a categorical component that controls the digit identity (1, 2, 3, ...).
* These components are learned in a (mostly) unsupervised fashion.
### How
* The latent code `c`
* "Normal" GANs parameterize the generator as `G(z)`, i.e. G receives a noise vector and transforms it into an image.
* This is changed to `G(z, c)`, i.e. G now receives a noise vector `z` and a latent code `c` and transforms both into an image.
* `c` can contain multiple variables following different distributions, e.g. in MNIST a categorical variable for the digit identity and a gaussian one for the stroke thickness.
* Mutual Information
* If using a latent code via `G(z, c)`, nothing forces the generator to actually use `c`. It can easily ignore it and just deteriorate to `G(z)`.
* To prevent that, they force G to generate images `x` in a way that `c` must be recoverable. So, if you have an image `x` you must be able to reliable tell which latent code `c` it has, which means that G must use `c` in a meaningful way.
* This relationship can be expressed with mutual information, i.e. the mutual information between `x` and `c` must be high.
* The mutual information between two variables X and Y is defined as `I(X; Y) = entropy(X) - entropy(X|Y) = entropy(Y) - entropy(Y|X)`.
* If the mutual information between X and Y is high, then knowing Y helps you to decently predict the value of X (and the other way round).
* If the mutual information between X and Y is low, then knowing Y doesn't tell you much about the value of X (and the other way round).
* The new GAN loss becomes `old loss - lambda * I(G(z, c); c)`, i.e. the higher the mutual information, the lower the result of the loss function.
* Variational Mutual Information Maximization
* In order to minimize `I(G(z, c); c)`, one has to know the distribution `P(c|x)` (from image to latent code), which however is unknown.
* So instead they create `Q(c|x)`, which is an approximation of `P(c|x)`.
* `I(G(z, c); c)` is then computed using a lower bound maximization, similar to the one in variational autoencoders (called "Variational Information Maximization", hence the name "InfoGAN").
* Basic equation: `LowerBoundOfMutualInformation(G, Q) = E[log Q(c|x)] + H(c) <= I(G(z, c); c)`
* `c` is the latent code.
* `x` is the generated image.
* `H(c)` is the entropy of the latent codes (constant throughout the optimization).
* Optimization w.r.t. Q is done directly.
* Optimization w.r.t. G is done via the reparameterization trick.
* If `Q(c|x)` approximates `P(c|x)` *perfectly*, the lower bound becomes the mutual information ("the lower bound becomes tight").
* In practice, `Q(c|x)` is implemented as a neural network. Both Q and D have to process the generated images, which means that they can share many convolutional layers, significantly reducing the extra cost of training Q.
### Results
* MNIST
* They use for `c` one categorical variable (10 values) and two continuous ones (uniform between -1 and +1).
* InfoGAN learns to associate the categorical one with the digit identity and the continuous ones with rotation and width.
* Applying Q(c|x) to an image and then classifying only on the categorical variable (i.e. fully unsupervised) yields 95% accuracy.
* Sampling new images with exaggerated continuous variables in the range `[-2,+2]` yields sound images (i.e. the network generalizes well).
* ![MNIST examples](https://raw.githubusercontent.com/aleju/papers/master/neural-nets/images/InfoGAN__mnist.png?raw=true "MNIST examples")
* 3D face images
* InfoGAN learns to represent the faces via pose, elevation, lighting.
* They used five uniform variables for `c`. (So two of them apparently weren't associated with anything sensible? They are not mentioned.)
* 3D chair images
* InfoGAN learns to represent the chairs via identity (categorical) and rotation or width (apparently they did two experiments).
* They used one categorical variable (four values) and one continuous variable (uniform `[-1, +1]`).
* SVHN
* InfoGAN learns to represent lighting and to spot the center digit.
* They used four categorical variables (10 values each) and two continuous variables (uniform `[-1, +1]`). (Again, a few variables were apparently not associated with anything sensible?)
* CelebA
* InfoGAN learns to represent pose, presence of sunglasses (not perfectly), hair style and emotion (in the sense of "smiling or not smiling").
* They used 10 categorical variables (10 values each). (Again, a few variables were apparently not associated with anything sensible?)
* ![CelebA examples](https://raw.githubusercontent.com/aleju/papers/master/neural-nets/images/InfoGAN__celeba.png?raw=true "CelebA examples")
InfoGAN: Interpretable Representation Learning by Information Maximizing Generative Adversarial Nets

Chen, Xi and Chen, Xi and Duan, Yan and Houthooft, Rein and Schulman, John and Sutskever, Ilya and Abbeel, Pieter

Neural Information Processing Systems Conference - 2016 via Local Bibsonomy

Keywords: dblp

Chen, Xi and Chen, Xi and Duan, Yan and Houthooft, Rein and Schulman, John and Sutskever, Ilya and Abbeel, Pieter

Neural Information Processing Systems Conference - 2016 via Local Bibsonomy

Keywords: dblp

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