# α-GAN: Convergence and Estimation Guarantees

arXiv: https://arxiv.org/abs/2205.06393 · HTML: https://mlsanity.com/paper/2205.06393/

## Key facts

- Cited by 5 papers in the map (data through 14 Oct 2026).
- Builds on 16 of its 34 references that are in the map.
- First posted on arXiv 12 May 2022.

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

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [Weight Normalization: A Simple Reparameterization to Accelerate Training of Deep Neural Networks](https://mlsanity.com/paper/1602.07868/) (2016)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Norm-Based Capacity Control in Neural Networks](https://mlsanity.com/paper/1503.00036/) (2015)
- [Size-Independent Sample Complexity of Neural Networks](https://mlsanity.com/paper/1712.06541/) (2017)
- [Generalization and Equilibrium in Generative Adversarial Nets (GANs)](https://mlsanity.com/paper/1703.00573/) (2017)
- [Training generative neural networks via Maximum Mean Discrepancy optimization](https://mlsanity.com/paper/1505.03906/) (2015)
- [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)
- [A Tunable Loss Function for Robust Classification: Calibration, Landscape, and Generalization](https://mlsanity.com/paper/1906.02314/) (2019)
- [A Tunable Loss Function for Binary Classification](https://mlsanity.com/paper/1902.04639/) (2019)
- [Realizing GANs via a Tunable Loss Function](https://mlsanity.com/paper/2106.05232/) (2021)
- [Cumulant GAN](https://mlsanity.com/paper/2006.06625/) (2020)
- [Minimax Estimation of Neural Net Distance](https://mlsanity.com/paper/1811.01054/) (2018)
- [Least kth-Order and R'enyi Generative Adversarial Networks](https://mlsanity.com/paper/2006.02479/) (2020)

## Built on by (most cited first, 5 of 5)

- [Addressing GAN Training Instabilities via Tunable Classification Losses](https://mlsanity.com/paper/2310.18291/) (2023)
- [A Unifying Generator Loss Function for Generative Adversarial Networks](https://mlsanity.com/paper/2308.07233/) (2023)
- [(αD,αG)-GANs: Addressing GAN Training Instabilities via Dual Objectives](https://mlsanity.com/paper/2302.14320/) (2023)
- [Classification Utility, Fairness, and Compactness via Tunable Information Bottleneck and R'enyi Measures](https://mlsanity.com/paper/2206.10043/) (2022)
- [α-GAN by R'enyi Cross Entropy](https://mlsanity.com/paper/2505.14190/) (2025)

## Abstract (arXiv)

We prove a two-way correspondence between the min-max optimization of general CPE loss function GANs and the minimization of associated f-divergences. We then focus on α-GAN, defined via the α-loss, which interpolates several GANs (Hellinger, vanilla, Total Variation) and corresponds to the minimization of the Arimoto divergence. We show that the Arimoto divergences induced by α-GAN equivalently converge, for all α∈ ℝ>0cup∞. However, under restricted learning models and finite samples, we provide estimation bounds which indicate diverse GAN behavior as a function of α. Finally, we present empirical results on a toy dataset that highlight the practical utility of tuning the α hyperparameter.