Generative models
One of our core aspirations at OpenAI is to develop algorithms and techniques that endow computers with an understanding of our world.
It’s easy to forget just how much you know about the world: you understand that it is made up of 3D environments, objects that move, collide, interact; people who walk, talk, and think; animals who graze, fly, run, or bark; monitors that display information encoded in language about the weather, who won a basketball game, or what happened in 1970.
This tremendous amount of information is out there and to a large extent easily accessible—either in the physical world of atoms or the digital world of bits. The only tricky part is to develop models and algorithms that can analyze and understand this treasure trove of data.
Generative models are one of the most promising approaches towards this goal. To train a generative model we first collect a large amount of data in some domain (e.g., think millions of images, sentences, or sounds, etc.) and then train a model to generate data like it. The intuition behind this approach follows a famous quote from Richard Feynman(opens in a new window):
DCGAN is initialized with random weights, so a random code plugged into the network would generate a completely random image. However, as you might imagine, the network has millions of parameters that we can tweak, and the goal is to find a setting of these parameters that makes samples generated from random codes look like the training data. Or to put it another way, we want the model distribution to match the true data distribution in the space of images.
This is exciting—these neural networks are learning what the visual world looks like! These models usually have only about 100 million parameters, so a network trained on ImageNet has to (lossily) compress(opens in a new window) 200GB of pixel data into 100MB of weights. This incentivizes it to discover the most salient features of the data: for example, it will likely learn that pixels nearby are likely to have the same color, or that the world is made up of horizontal or vertical edges, or blobs of different colors. Eventually, the model may discover many more complex regularities: that there are certain types of backgrounds, objects, textures, that they occur in certain likely arrangements, or that they transform in certain ways over time in videos, etc.
Mathematically, we think about a dataset of examples x1,…,xn x_1, \ldots, x_n as samples from a true data distribution p(x) p(x) . In the example image below, the blue region shows the part of the image space that, with a high probability (over some threshold) contains real images, and black dots indicate our data points (each is one image in our dataset). Now, our model also describes a distribution p^θ(x) \hat{p}_{\theta}(x) (green) that is defined implicitly by taking points from a unit Gaussian distribution(opens in a new window) (red) and mapping them through a (deterministic) neural network—our generative model (yellow). Our network is a function with parameters θ \theta , and tweaking these parameters will tweak the generated distribution of images. Our goal then is to find parameters θ \theta that produce a distribution that closely matches the true data distribution (for example, by having a small KL divergence(opens in a new window) loss(opens in a new window)). Therefore, you can imagine the green distribution starting out random and then the training process iteratively changing the parameters θ \theta to stretch and squeeze it to better match the blue distribution.
InfoGAN(opens in a new window) (code(opens in a new window)). Peter Chen and colleagues introduce InfoGAN—an extension of GAN that learns disentangled and interpretable representations for images. A regular GAN achieves the objective of reproducing the data distribution in the model, but the layout and organization of the code space is underspecified—there are many possible solutions to mapping the unit Gaussian to images and the one we end up with might be intricate and highly entangled. The InfoGAN imposes additional structure on this space by adding new objectives that involve maximizing the mutual information(opens in a new window) between small subsets of the representation variables and the observation. This approach provides quite remarkable results. For example, in the images of 3D faces below we vary one continuous dimension of the code, keeping all others fixed. It’s clear from the five provided examples (along each row) that the resulting dimensions in the code capture interpretable dimensions, and that the model has perhaps understood that there are camera angles, facial variations, etc., without having been told that these features exist and are important: