# Realizing GANs via a Tunable Loss Function

arXiv: https://arxiv.org/abs/2106.05232 · HTML: https://mlsanity.com/paper/2106.05232/

## Key facts

- Cited by 10 papers in the map (data through 14 Oct 2026).
- Builds on 18 of its 41 references that are in the map.
- First posted on arXiv 9 Jun 2021.

## Builds on (most cited first, 18 of 18)

- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Towards Principled Methods for Training Generative Adversarial Networks](https://mlsanity.com/paper/1701.04862/) (2017)
- [Geometric GAN](https://mlsanity.com/paper/1705.02894/) (2017)
- [Unrolled Generative Adversarial Networks](https://mlsanity.com/paper/1611.02163/) (2016)
- [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 (not) to Train your Generative Model: Scheduled Sampling, Likelihood, Adversary?](https://mlsanity.com/paper/1511.05101/) (2015)
- [How Well Generative Adversarial Networks Learn Distributions](https://mlsanity.com/paper/1811.03179/) (2018)
- [Stabilizing Generative Adversarial Networks: A Survey](https://mlsanity.com/paper/1910.00927/) (2019)
- [Sobolev GAN](https://mlsanity.com/paper/1711.04894/) (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)
- [Fisher GAN](https://mlsanity.com/paper/1705.09675/) (2017)
- [McGan: Mean and Covariance Feature Matching GAN](https://mlsanity.com/paper/1702.08398/) (2017)
- [A Tunable Loss Function for Binary Classification](https://mlsanity.com/paper/1902.04639/) (2019)
- [On the alpha-loss Landscape in the Logistic Model](https://mlsanity.com/paper/2006.12406/) (2020)

## Built on by (most cited first, 10 of 10)

- [Asymmetry of the Relative Entropy in the Regularization of Empirical Risk Minimization](https://mlsanity.com/paper/2410.02833/) (2024)
- [α-GAN: Convergence and Estimation Guarantees](https://mlsanity.com/paper/2205.06393/) (2022)
- [Analysis of the Relative Entropy Asymmetry in the Regularization of Empirical Risk Minimization](https://mlsanity.com/paper/2306.07123/) (2023)
- [Addressing GAN Training Instabilities via Tunable Classification Losses](https://mlsanity.com/paper/2310.18291/) (2023)
- [Renyi Fair Information Bottleneck for Image Classification](https://mlsanity.com/paper/2203.04950/) (2022)
- [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)
- [Smoothly Giving up: Robustness for Simple Models](https://mlsanity.com/paper/2302.09114/) (2023)
- [α-GAN by R'enyi Cross Entropy](https://mlsanity.com/paper/2505.14190/) (2025)

## Abstract (arXiv)

We introduce a tunable GAN, called α-GAN, parameterized by α ∈ (0,∞], which interpolates between various f-GANs and Integral Probability Metric based GANs (under constrained discriminator set). We construct α-GAN using a supervised loss function, namely, α-loss, which is a tunable loss function capturing several canonical losses. We show that α-GAN is intimately related to the Arimoto divergence, which was first proposed by "Osterriecher (1996), and later studied by Liese and Vajda (2006). We also study the convergence properties of α-GAN. We posit that the holistic understanding that α-GAN introduces will have practical benefits of addressing both the issues of vanishing gradients and mode collapse.