Generative Adversarial Set Transformers

Groups of entities are naturally represented as sets, but generative models usually treat them as independent from each other or as sequences. This either over-simplifies the problem, or imposes an order to the otherwise unordered collections, which has to be accounted for in loss computation. We therefore introduce GAST - a GAN for sets capable of generating variable-sized sets in a permutation-equivariant manner, while accounting for dependencies between set elements. It avoids the problem of formulating a distance metric between sets by using a permutation-invariant discriminator. When evaluated on a dataset of regular polygons and on MNIST point clouds, GAST outperforms graph-convolution-based GANs in sample fidelity, while showing good generalization to novel set sizes.