# Non-Asymptotic Error Bounds for Bidirectional GANs

arXiv: https://arxiv.org/abs/2110.12319 · HTML: https://mlsanity.com/paper/2110.12319/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 19 of its 36 references that are in the map.
- First posted on arXiv 24 Oct 2021.

## Builds on (most cited first, 19 of 19)

- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Progressive Growing of GANs for Improved Quality, Stability, and Variation](https://mlsanity.com/paper/1710.10196/) (2017)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Generative Adversarial Text to Image Synthesis](https://mlsanity.com/paper/1605.05396/) (2016)
- [Adversarial Autoencoders](https://mlsanity.com/paper/1511.05644/) (2015)
- [Adversarial Feature Learning](https://mlsanity.com/paper/1605.09782/) (2016)
- [Adversarially Learned Inference](https://mlsanity.com/paper/1606.00704/) (2016)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [Deep Network Approximation Characterized by Number of Neurons](https://mlsanity.com/paper/1906.05497/) (2019)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [On the Discrimination-Generalization Tradeoff in GANs](https://mlsanity.com/paper/1711.02771/) (2017)
- [Approximation and Convergence Properties of Generative Adversarial Learning](https://mlsanity.com/paper/1705.08991/) (2017)
- [Approximability of Discriminators Implies Diversity in GANs](https://mlsanity.com/paper/1806.10586/) (2018)
- [Nonparametric Density Estimation & Convergence Rates for GANs under Besov IPM Losses](https://mlsanity.com/paper/1902.03511/) (2019)
- [On the capacity of deep generative networks for approximating distributions](https://mlsanity.com/paper/2101.12353/) (2021)
- [Bounding the expectation of the supremum of empirical processes indexed by H"older classes](https://mlsanity.com/paper/2003.13530/) (2020)
- [A Universal Approximation Theorem of Deep Neural Networks for Expressing Probability Distributions](https://mlsanity.com/paper/2004.08867/) (2020)
- [Bidirectional Generative Modeling Using Adversarial Gradient Estimation](https://mlsanity.com/paper/2002.09161/) (2020)

## Built on by (most cited first, 3 of 3)

- [A Statistical Analysis of Wasserstein Autoencoders for Intrinsically Low-dimensional Data](https://mlsanity.com/paper/2402.15710/) (2024)
- [A Statistical Learning Perspective on Semi-dual Adversarial Neural Optimal Transport Solvers](https://mlsanity.com/paper/2502.01310/) (2025)
- [Distribution estimation and change-point estimation for time series via DNN-based GANs](https://mlsanity.com/paper/2211.14577/) (2022)

## Abstract (arXiv)

We derive nearly sharp bounds for the bidirectional GAN (BiGAN) estimation error under the Dudley distance between the latent joint distribution and the data joint distribution with appropriately specified architecture of the neural networks used in the model. To the best of our knowledge, this is the first theoretical guarantee for the bidirectional GAN learning approach. An appealing feature of our results is that they do not assume the reference and the data distributions to have the same dimensions or these distributions to have bounded support. These assumptions are commonly assumed in the existing convergence analysis of the unidirectional GANs but may not be satisfied in practice. Our results are also applicable to the Wasserstein bidirectional GAN if the target distribution is assumed to have a bounded support. To prove these results, we construct neural network functions that push forward an empirical distribution to another arbitrary empirical distribution on a possibly different-dimensional space. We also develop a novel decomposition of the integral probability metric for the error analysis of bidirectional GANs. These basic theoretical results are of independent interest and can be applied to other related learning problems.