  Generative Adversarial Networks (GANs) have become the gold standard when it
comes to learning generative models for high-dimensional distributions. Since
their advent, numerous variations of GANs have been introduced in the
literature, primarily focusing on utilization of novel loss functions,
optimization/regularization strategies and network architectures. In this
paper, we turn our attention to the generator and investigate the use of
high-order polynomials as an alternative class of universal function
approximators. Concretely, we propose PolyGAN, where we model the data
generator by means of a high-order polynomial whose unknown parameters are
naturally represented by high-order tensors. We introduce two tensor
decompositions that significantly reduce the number of parameters and show how
they can be efficiently implemented by hierarchical neural networks that only
employ linear/convolutional blocks. We exhibit for the first time that by using
our approach a GAN generator can approximate the data distribution without
using any activation functions. Thorough experimental evaluation on both
synthetic and real data (images and 3D point clouds) demonstrates the merits of
PolyGAN against the state of the art.
