# Convergence Problems with Generative Adversarial Networks (GANs)

arXiv: https://arxiv.org/abs/1806.11382 · HTML: https://mlsanity.com/paper/1806.11382/

## Key facts

- Cited by 14 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jun 2018.

## Built on by (most cited first, 14 of 14)

- [Data Augmentation techniques in time series domain: A survey and taxonomy](https://mlsanity.com/paper/2206.13508/) (2022)
- [A survey on GANs for computer vision: Recent research, analysis and taxonomy](https://mlsanity.com/paper/2203.11242/) (2022)
- [Matching aggregate posteriors in the variational autoencoder](https://mlsanity.com/paper/2311.07693/) (2023)
- [HAD-Net: A Hierarchical Adversarial Knowledge Distillation Network for Improved Enhanced Tumour Segmentation Without Post-Contrast Images](https://mlsanity.com/paper/2103.16617/) (2021)
- [Deep Active Learning in the Presence of Label Noise: A Survey](https://mlsanity.com/paper/2302.11075/) (2023)
- [Semi-Supervised Domain Adaptation with Auto-Encoder via Simultaneous Learning](https://mlsanity.com/paper/2210.09486/) (2022)
- [Generative Adversarial Network: Some Analytical Perspectives](https://mlsanity.com/paper/2104.12210/) (2021)
- [Towards Fine-grained Image Classification with Generative Adversarial Networks and Facial Landmark Detection](https://mlsanity.com/paper/2109.00891/) (2021)
- [MULTI-FLGANs: Multi-Distributed Adversarial Networks for Non-IID distribution](https://mlsanity.com/paper/2206.12178/) (2022)
- [Probabilistic Curriculum Learning for Goal-Based Reinforcement Learning](https://mlsanity.com/paper/2504.01459/) (2025)
- [Adjustable Privacy using Autoencoder-based Learning Structure](https://mlsanity.com/paper/2304.03538/) (2023)
- [3D GANs and Latent Space: A comprehensive survey](https://mlsanity.com/paper/2304.03932/) (2023)
- [Large deviations for interacting particle dynamics for finding mixed equilibria in zero-sum games](https://mlsanity.com/paper/2206.15177/) (2022)
- [ParaGAN: A Scalable Distributed Training Framework for Generative Adversarial Networks](https://mlsanity.com/paper/2411.03999/) (2024)

## Abstract (arXiv)

Generative adversarial networks (GANs) are a novel approach to generative modelling, a task whose goal it is to learn a distribution of real data points. They have often proved difficult to train: GANs are unlike many techniques in machine learning, in that they are best described as a two-player game between a discriminator and generator. This has yielded both unreliability in the training process, and a general lack of understanding as to how GANs converge, and if so, to what. The purpose of this dissertation is to provide an account of the theory of GANs suitable for the mathematician, highlighting both positive and negative results. This involves identifying the problems when training GANs, and how topological and game-theoretic perspectives of GANs have contributed to our understanding and improved our techniques in recent years.