# PolyGAN: High-Order Polynomial Generators

arXiv: https://arxiv.org/abs/1908.06571 · HTML: https://mlsanity.com/paper/1908.06571/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 19 Aug 2019.

## Built on by (most cited first, 10 of 10)

- [Scalable Interpretability via Polynomials](https://mlsanity.com/paper/2205.14108/) (2022)
- [Polynomial Neural Fields for Subband Decomposition and Manipulation](https://mlsanity.com/paper/2302.04862/) (2023)
- [Augmenting Deep Classifiers with Polynomial Neural Networks](https://mlsanity.com/paper/2104.07916/) (2021)
- [CoPE: Conditional image generation using Polynomial Expansions](https://mlsanity.com/paper/2104.05077/) (2021)
- [Hadamard product in deep learning: Introduction, Advances and Challenges](https://mlsanity.com/paper/2504.13112/) (2025)
- [Extrapolation and Spectral Bias of Neural Nets with Hadamard Product: a Polynomial Net Study](https://mlsanity.com/paper/2209.07736/) (2022)
- [NN2Poly: A polynomial representation for deep feed-forward artificial neural networks](https://mlsanity.com/paper/2112.11397/) (2021)
- [Adversarial Audio Synthesis with Complex-valued Polynomial Networks](https://mlsanity.com/paper/2206.06811/) (2022)
- [PNeRV: A Polynomial Neural Representation for Videos](https://mlsanity.com/paper/2406.19299/) (2024)
- [Polynomial-Augmented Neural Networks (PANNs) with Weak Orthogonality Constraints for Enhanced Function and PDE Approximation](https://mlsanity.com/paper/2406.02336/) (2024)

## Abstract (arXiv)

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.