# Measure-conditional Discriminator with Stationary Optimum for GANs and Statistical Distance Surrogates

arXiv: https://arxiv.org/abs/2101.06802 · HTML: https://mlsanity.com/paper/2101.06802/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 25 references that are in the map.
- First posted on arXiv 17 Jan 2021.

## Builds on (most cited first, 16 of 16)

- [Deep Learning Face Attributes in the Wild](https://mlsanity.com/paper/1411.7766/) (2014)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Conditional Generative Adversarial Nets](https://mlsanity.com/paper/1411.1784/) (2014)
- [Deep Sets](https://mlsanity.com/paper/1703.06114/) (2017)
- [Training GANs with Optimism](https://mlsanity.com/paper/1711.00141/) (2017)
- [Universal Approximation with Deep Narrow Networks](https://mlsanity.com/paper/1905.08539/) (2019)
- [Physics-Informed Generative Adversarial Networks for Stochastic Differential Equations](https://mlsanity.com/paper/1811.02033/) (2018)
- [Large-Scale Optimal Transport and Mapping Estimation](https://mlsanity.com/paper/1711.02283/) (2017)
- [Adversarial Uncertainty Quantification in Physics-Informed Neural Networks](https://mlsanity.com/paper/1811.04026/) (2018)
- [MaskGAN: Better Text Generation via Filling in the______](https://mlsanity.com/paper/1801.07736/) (2018)
- [Point Cloud GAN](https://mlsanity.com/paper/1810.05795/) (2018)
- [Adversarial Feature Matching for Text Generation](https://mlsanity.com/paper/1706.03850/) (2017)
- [Approximation capability of neural networks on spaces of probability measures and tree-structured domains](https://mlsanity.com/paper/1906.00764/) (2019)
- [Mixed batches and symmetric discriminators for GAN training](https://mlsanity.com/paper/1806.07185/) (2018)
- [Generative Ensemble Regression: Learning Particle Dynamics from Observations of Ensembles with Physics-Informed Deep Generative Models](https://mlsanity.com/paper/2008.01915/) (2020)

## Built on by (most cited first, 1 of 1)

- [Ten Years of Generative Adversarial Nets (GANs): A survey of the state-of-the-art](https://mlsanity.com/paper/2308.16316/) (2023)

## Abstract (arXiv)

We propose a simple but effective modification of the discriminators, namely measure-conditional discriminators, as a plug-and-play module for different GANs. By taking the generated distributions as part of input so that the target optimum for the discriminator is stationary, the proposed discriminator is more robust than the vanilla one. A variant of the measure-conditional discriminator can also handle multiple target distributions, or act as a surrogate model of statistical distances such as KL divergence with applications to transfer learning.