# Stability Analysis Framework for Particle-based Distance GANs with Wasserstein Gradient Flow

arXiv: https://arxiv.org/abs/2307.01879 · HTML: https://mlsanity.com/paper/2307.01879/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 29 references that are in the map.
- First posted on arXiv 4 Jul 2023.

## Builds on (most cited first, 21 of 21)

- [Generative Adversarial Networks](https://mlsanity.com/paper/2203.00667/) (2022)
- [Image-to-Image Translation with Conditional Adversarial Networks](https://mlsanity.com/paper/1611.07004/) (2016)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Photo-Realistic Single Image Super-Resolution Using a Generative Adversarial Network](https://mlsanity.com/paper/1609.04802/) (2016)
- [Spectral Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/1802.05957/) (2018)
- [Demystifying MMD GANs](https://mlsanity.com/paper/1801.01401/) (2018)
- [Learning a Probabilistic Latent Space of Object Shapes via 3D Generative-Adversarial Modeling](https://mlsanity.com/paper/1610.07584/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [MMD GAN: Towards Deeper Understanding of Moment Matching Network](https://mlsanity.com/paper/1705.08584/) (2017)
- [A Note on the Inception Score](https://mlsanity.com/paper/1801.01973/) (2018)
- [Consistency Regularization for Generative Adversarial Networks](https://mlsanity.com/paper/1910.12027/) (2019)
- [The Cramer Distance as a Solution to Biased Wasserstein Gradients](https://mlsanity.com/paper/1705.10743/) (2017)
- [Stabilizing Training of Generative Adversarial Networks through Regularization](https://mlsanity.com/paper/1705.09367/) (2017)
- [Spectral Regularization for Combating Mode Collapse in GANs](https://mlsanity.com/paper/1908.10999/) (2019)
- [Adversarial Lipschitz Regularization](https://mlsanity.com/paper/1907.05681/) (2019)
- [On gradient regularizers for MMD GANs](https://mlsanity.com/paper/1805.11565/) (2018)
- [Gradient Normalization for Generative Adversarial Networks](https://mlsanity.com/paper/2109.02235/) (2021)
- [Improving MMD-GAN Training with Repulsive Loss Function](https://mlsanity.com/paper/1812.09916/) (2018)
- [On the Convergence of Gradient Descent in GANs: MMD GAN As a Gradient Flow](https://mlsanity.com/paper/2011.02402/) (2020)
- [Elastic Interaction Energy-Based Generative Model: Approximation in Feature Space](https://mlsanity.com/paper/2303.10553/) (2023)

## Abstract (arXiv)

In this paper, we investigate the training process of generative networks that use a type of probability density distance named particle-based distance as the objective function, e.g. MMD GAN, Cram'er GAN, EIEG GAN. However, these GANs often suffer from the problem of unstable training. In this paper, we analyze the stability of the training process of these GANs from the perspective of probability density dynamics. In our framework, we regard the discriminator D in these GANs as a feature transformation mapping that maps high dimensional data into a feature space, while the generator G maps random variables to samples that resemble real data in terms of feature space. This perspective enables us to perform stability analysis for the training of GANs using the Wasserstein gradient flow of the probability density function. We find that the training process of the discriminator is usually unstable due to the formulation of minG maxD E(G, D) in GANs. To address this issue, we add a stabilizing term in the discriminator loss function. We conduct experiments to validate our stability analysis and stabilizing method.