year: 2014
paper: https://arxiv.org/pdf/1406.2661.pdf
website:
code:
status: reference
type: revolutionary
Takeaways
Minmax loss 1
In the paper that introduced GANs, the generator tries to minimize the following function while the discriminator tries to maximize it:
In this function:
D(x)is the discriminator’s estimate of the probability that real data instance x is real.- Ex is the expected value over all real data instances.
G(z)is the generator’s output when given noise z.D(G(z))is the discriminator’s estimate of the probability that a fake instance is real.- Ez is the expected value over all random inputs to the generator (in effect, the expected value over all generated fake instances G(z)).
- The formula derives from the cross-entropy between the real and generated distributions. 2
The generator can’t directly affect the log(D(x)) term in the function, so, for the generator, minimizing the loss is equivalent to minimizing log(1 - D(G(z))).