# A Unifying Generator Loss Function for Generative Adversarial Networks

arXiv: https://arxiv.org/abs/2308.07233 · HTML: https://mlsanity.com/paper/2308.07233/

## Key facts

- Cited by 3 papers in the map (data through 14 Oct 2026).
- Builds on 14 of its 37 references that are in the map.
- First posted on arXiv 14 Aug 2023.

## Builds on (most cited first, 14 of 14)

- [Adam: A Method for Stochastic Optimization](https://mlsanity.com/paper/1412.6980/) (2014)
- [A Style-Based Generator Architecture for Generative Adversarial Networks](https://mlsanity.com/paper/1812.04948/) (2018)
- [Large Scale GAN Training for High Fidelity Natural Image Synthesis](https://mlsanity.com/paper/1809.11096/) (2018)
- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Unsupervised Representation Learning with Deep Convolutional Generative Adversarial Networks](https://mlsanity.com/paper/1511.06434/) (2015)
- [Least Squares Generative Adversarial Networks](https://mlsanity.com/paper/1611.04076/) (2016)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Exploiting Deep Generative Prior for Versatile Image Restoration and Manipulation](https://mlsanity.com/paper/2003.13659/) (2020)
- [PacGAN: The power of two samples in generative adversarial networks](https://mlsanity.com/paper/1712.04086/) (2017)
- [Augmented CycleGAN: Learning Many-to-Many Mappings from Unpaired Data](https://mlsanity.com/paper/1802.10151/) (2018)
- [Realizing GANs via a Tunable Loss Function](https://mlsanity.com/paper/2106.05232/) (2021)
- [Least kth-Order and R'enyi Generative Adversarial Networks](https://mlsanity.com/paper/2006.02479/) (2020)
- [α-GAN: Convergence and Estimation Guarantees](https://mlsanity.com/paper/2205.06393/) (2022)
- [(αD,αG)-GANs: Addressing GAN Training Instabilities via Dual Objectives](https://mlsanity.com/paper/2302.14320/) (2023)

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

- [Addressing GAN Training Instabilities via Tunable Classification Losses](https://mlsanity.com/paper/2310.18291/) (2023)
- [Generalized Dual Discriminator GANs](https://mlsanity.com/paper/2507.17684/) (2025)
- [α-GAN by R'enyi Cross Entropy](https://mlsanity.com/paper/2505.14190/) (2025)

## Abstract (arXiv)

A unifying α-parametrized generator loss function is introduced for a dual-objective generative adversarial network (GAN), which uses a canonical (or classical) discriminator loss function such as the one in the original GAN (VanillaGAN) system. The generator loss function is based on a symmetric class probability estimation type function, Lα, and the resulting GAN system is termed Lα-GAN. Under an optimal discriminator, it is shown that the generator's optimization problem consists of minimizing a Jensen-fα-divergence, a natural generalization of the Jensen-Shannon divergence, where fα is a convex function expressed in terms of the loss function Lα. It is also demonstrated that this Lα-GAN problem recovers as special cases a number of GAN problems in the literature, including VanillaGAN, Least Squares GAN (LSGAN), Least kth order GAN (LkGAN) and the recently introduced (αD,αG)-GAN with αD=1. Finally, experimental results are conducted on three datasets, MNIST, CIFAR-10, and Stacked MNIST to illustrate the performance of various examples of the Lα-GAN system.