# Generative Adversarial Network: Some Analytical Perspectives

arXiv: https://arxiv.org/abs/2104.12210 · HTML: https://mlsanity.com/paper/2104.12210/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Builds on 33 of its 49 references that are in the map.
- First posted on arXiv 25 Apr 2021.

## Builds on (most cited first, 30 of 33)

- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Generative Adversarial Text to Image Synthesis](https://mlsanity.com/paper/1605.05396/) (2016)
- [Which Training Methods for GANs do actually Converge?](https://mlsanity.com/paper/1801.04406/) (2018)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Generating Videos with Scene Dynamics](https://mlsanity.com/paper/1609.02612/) (2016)
- [Generative Visual Manipulation on the Natural Image Manifold](https://mlsanity.com/paper/1609.03552/) (2016)
- [Deep Generative Image Models using a Laplacian Pyramid of Adversarial Networks](https://mlsanity.com/paper/1506.05751/) (2015)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Improving GANs Using Optimal Transport](https://mlsanity.com/paper/1803.05573/) (2018)
- [Adversarial Uncertainty Quantification in Physics-Informed Neural Networks](https://mlsanity.com/paper/1811.04026/) (2018)
- [Stochastic Modified Equations and Dynamics of Stochastic Gradient Algorithms I: Mathematical Foundations](https://mlsanity.com/paper/1811.01558/) (2018)
- [Quant GANs: Deep Generation of Financial Time Series](https://mlsanity.com/paper/1907.06673/) (2019)
- [Semantic Segmentation using Adversarial Networks](https://mlsanity.com/paper/1611.08408/) (2016)
- [COT-GAN: Generating Sequential Data via Causal Optimal Transport](https://mlsanity.com/paper/2006.08571/) (2020)
- [Stabilizing Generative Adversarial Networks: A Survey](https://mlsanity.com/paper/1910.00927/) (2019)
- [On the Convergence and Robustness of Training GANs with Regularized Optimal Transport](https://mlsanity.com/paper/1802.08249/) (2018)
- [Fluctuation-dissipation relations for stochastic gradient descent](https://mlsanity.com/paper/1810.00004/) (2018)
- [A Geometric View of Optimal Transportation and Generative Model](https://mlsanity.com/paper/1710.05488/) (2017)
- [A generative adversarial network approach to calibration of local stochastic volatility models](https://mlsanity.com/paper/2005.02505/) (2020)
- [A mean-field analysis of two-player zero-sum games](https://mlsanity.com/paper/2002.06277/) (2020)
- [Deep Learning Theory Review: An Optimal Control and Dynamical Systems Perspective](https://mlsanity.com/paper/1908.10920/) (2019)
- [A Closer Look at the Optimization Landscapes of Generative Adversarial Networks](https://mlsanity.com/paper/1906.04848/) (2019)
- [Deep Hedging: Learning to Simulate Equity Option Markets](https://mlsanity.com/paper/1911.01700/) (2019)
- [Deconstructing Generative Adversarial Networks](https://mlsanity.com/paper/1901.09465/) (2019)
- [Convergence Problems with Generative Adversarial Networks (GANs)](https://mlsanity.com/paper/1806.11382/) (2018)
- [f-GANs in an Information Geometric Nutshell](https://mlsanity.com/paper/1707.04385/) (2017)
- [Game on Random Environment, Mean-field Langevin System and Neural Networks](https://mlsanity.com/paper/2004.02457/) (2020)

## Built on by (most cited first, 2 of 2)

- [Convergence of GANs Training: A Game and Stochastic Control Methodology](https://mlsanity.com/paper/2112.00222/) (2021)
- [Meta-learning with GANs for anomaly detection, with deployment in high-speed rail inspection system](https://mlsanity.com/paper/2202.05795/) (2022)

## Abstract (arXiv)

Ever since its debut, generative adversarial networks (GANs) have attracted tremendous amount of attention. Over the past years, different variations of GANs models have been developed and tailored to different applications in practice. Meanwhile, some issues regarding the performance and training of GANs have been noticed and investigated from various theoretical perspectives. This subchapter will start from an introduction of GANs from an analytical perspective, then move on to the training of GANs via SDE approximations and finally discuss some applications of GANs in computing high dimensional MFGs as well as tackling mathematical finance problems.