# Generalization and Equilibrium in Generative Adversarial Nets (GANs)

arXiv: https://arxiv.org/abs/1703.00573 · HTML: https://mlsanity.com/paper/1703.00573/

## Key facts

- Cited by 166 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 2 Mar 2017.

## Built on by (most cited first, 30 of 166)

- [Inversion by Direct Iteration: An Alternative to Denoising Diffusion for Image Restoration](https://mlsanity.com/paper/2303.11435/) (2023)
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- [Provably Efficient Imitation Learning from Observation Alone](https://mlsanity.com/paper/1905.10948/) (2019)
- [Membership Inference Attacks against Synthetic Data through Overfitting Detection](https://mlsanity.com/paper/2302.12580/) (2023)
- [Verifying the Union of Manifolds Hypothesis for Image Data](https://mlsanity.com/paper/2207.02862/) (2022)
- [MG-GAN: A Multi-Generator Model Preventing Out-of-Distribution Samples in Pedestrian Trajectory Prediction](https://mlsanity.com/paper/2108.09274/) (2021)
- [Transferability in Deep Learning: A Survey](https://mlsanity.com/paper/2201.05867/) (2022)
- [Variational Wasserstein gradient flow](https://mlsanity.com/paper/2112.02424/) (2021)
- [Breaking the Curse of Dimensionality: Diffusion Models Efficiently Learn Low-Dimensional Distributions](https://mlsanity.com/paper/2409.02426/) (2024)
- [Deep Generative Models through the Lens of the Manifold Hypothesis: A Survey and New Connections](https://mlsanity.com/paper/2404.02954/) (2024)
- [An error analysis of generative adversarial networks for learning distributions](https://mlsanity.com/paper/2105.13010/) (2021)
- [Quantifying and Improving Transferability in Domain Generalization](https://mlsanity.com/paper/2106.03632/) (2021)
- [AI and the Problem of Knowledge Collapse](https://mlsanity.com/paper/2404.03502/) (2024)
- [Property Inference Attacks Against GANs](https://mlsanity.com/paper/2111.07608/) (2021)
- [Free Lunch for Domain Adversarial Training: Environment Label Smoothing](https://mlsanity.com/paper/2302.00194/) (2023)
- [Tractable Density Estimation on Learned Manifolds with Conformal Embedding Flows](https://mlsanity.com/paper/2106.05275/) (2021)
- [On the Generalization of Diffusion Model](https://mlsanity.com/paper/2305.14712/) (2023)
- [Beyond Privacy: Navigating the Opportunities and Challenges of Synthetic Data](https://mlsanity.com/paper/2304.03722/) (2023)
- [On Computation and Generalization of Generative Adversarial Imitation Learning](https://mlsanity.com/paper/2001.02792/) (2020)
- [Multi-Source Unsupervised Domain Adaptation via Pseudo Target Domain](https://mlsanity.com/paper/2202.10725/) (2022)
- [Diagnosing and Fixing Manifold Overfitting in Deep Generative Models](https://mlsanity.com/paper/2204.07172/) (2022)
- [Outlier-Robust Optimal Transport: Duality, Structure, and Statistical Analysis](https://mlsanity.com/paper/2111.01361/) (2021)
- [Conditional Image Generation by Conditioning Variational Auto-Encoders](https://mlsanity.com/paper/2102.12037/) (2021)
- [This Person (Probably) Exists. Identity Membership Attacks Against GAN Generated Faces](https://mlsanity.com/paper/2107.06018/) (2021)
- [Difficulty-Aware Simulator for Open Set Recognition](https://mlsanity.com/paper/2207.10024/) (2022)
- [A Neural Tangent Kernel Perspective of GANs](https://mlsanity.com/paper/2106.05566/) (2021)
- [A Survey on Statistical Theory of Deep Learning: Approximation, Training Dynamics, and Generative Models](https://mlsanity.com/paper/2401.07187/) (2024)
- [Deep MMD Gradient Flow without adversarial training](https://mlsanity.com/paper/2405.06780/) (2024)
- [Deep Extrapolation for Attribute-Enhanced Generation](https://mlsanity.com/paper/2107.02968/) (2021)

## Abstract (arXiv)

We show that training of generative adversarial network (GAN) may not have good generalization properties; e.g., training may appear successful but the trained distribution may be far from target distribution in standard metrics. However, generalization does occur for a weaker metric called neural net distance. It is also shown that an approximate pure equilibrium exists in the discriminator/generator game for a special class of generators with natural training objectives when generator capacity and training set sizes are moderate. This existence of equilibrium inspires MIX+GAN protocol, which can be combined with any existing GAN training, and empirically shown to improve some of them.