# A Mathematical Introduction to Generative Adversarial Nets (GAN)

arXiv: https://arxiv.org/abs/2009.00169 · HTML: https://mlsanity.com/paper/2009.00169/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 1 Sep 2020.

## Built on by (most cited first, 8 of 8)

- [Regularising Inverse Problems with Generative Machine Learning Models](https://mlsanity.com/paper/2107.11191/) (2021)
- [Imitation Learning-based Implicit Semantic-aware Communication Networks: Multi-layer Representation and Collaborative Reasoning](https://mlsanity.com/paper/2210.16118/) (2022)
- [Convergence of Deep ReLU Networks](https://mlsanity.com/paper/2107.12530/) (2021)
- [Convergence of Deep Convolutional Neural Networks](https://mlsanity.com/paper/2109.13542/) (2021)
- [Uniform Convergence of Deep Neural Networks with Lipschitz Continuous Activation Functions and Variable Widths](https://mlsanity.com/paper/2306.01692/) (2023)
- [Training Generative Adversarial Networks with Adaptive Composite Gradient](https://mlsanity.com/paper/2111.05508/) (2021)
- [Convergence Analysis of Deep Residual Networks](https://mlsanity.com/paper/2205.06571/) (2022)
- [Convergence of Deep Neural Networks with General Activation Functions and Pooling](https://mlsanity.com/paper/2205.06570/) (2022)

## Abstract (arXiv)

Generative Adversarial Nets (GAN) have received considerable attention since the 2014 groundbreaking work by Goodfellow et al. Such attention has led to an explosion in new ideas, techniques and applications of GANs. To better understand GANs we need to understand the mathematical foundation behind them. This paper attempts to provide an overview of GANs from a mathematical point of view. Many students in mathematics may find the papers on GANs more difficulty to fully understand because most of them are written from computer science and engineer point of view. The aim of this paper is to give more mathematically oriented students an introduction to GANs in a language that is more familiar to them.