# Understanding and Stabilizing GANs' Training Dynamics with Control Theory

arXiv: https://arxiv.org/abs/1909.13188 · HTML: https://mlsanity.com/paper/1909.13188/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Sep 2019.

## Built on by (most cited first, 5 of 5)

- [Understanding Overparameterization in Generative Adversarial Networks](https://mlsanity.com/paper/2104.05605/) (2021)
- [SAN: Inducing Metrizability of GAN with Discriminative Normalized Linear Layer](https://mlsanity.com/paper/2301.12811/) (2023)
- [Instability and Local Minima in GAN Training with Kernel Discriminators](https://mlsanity.com/paper/2208.09938/) (2022)
- [Stabilizing GANs' Training with Brownian Motion Controller](https://mlsanity.com/paper/2306.10468/) (2023)
- [Generalization of GANs and overparameterized models under Lipschitz continuity](https://mlsanity.com/paper/2104.02388/) (2021)

## Abstract (arXiv)

Generative adversarial networks (GANs) are effective in generating realistic images but the training is often unstable. There are existing efforts that model the training dynamics of GANs in the parameter space but the analysis cannot directly motivate practically effective stabilizing methods. To this end, we present a conceptually novel perspective from control theory to directly model the dynamics of GANs in the function space and provide simple yet effective methods to stabilize GANs' training. We first analyze the training dynamic of a prototypical Dirac GAN and adopt the widely-used closed-loop control (CLC) to improve its stability. We then extend CLC to stabilize the training dynamic of normal GANs, where CLC is implemented as a squared L2 regularizer on the output of the discriminator. Empirical results show that our method can effectively stabilize the training and obtain state-of-the-art performance on data generation tasks.