  Generative adversarial networks (GANs) are pow- erful generative models based
on providing feed- back to a generative network via a discriminator network.
However, the discriminator usually as- sesses individual samples. This prevents
the dis- criminator from accessing global distributional statistics of
generated samples, and often leads to mode dropping: the generator models only
part of the target distribution. We propose to feed the discriminator with
mixed batches of true and fake samples, and train it to predict the ratio of
true samples in the batch. The latter score does not depend on the order of
samples in a batch. Rather than learning this invariance, we introduce a
generic permutation-invariant discriminator ar- chitecture. This architecture
is provably a uni- versal approximator of all symmetric functions.
Experimentally, our approach reduces mode col- lapse in GANs on two synthetic
datasets, and obtains good results on the CIFAR10 and CelebA datasets, both
qualitatively and quantitatively.
