# α-GAN by R'enyi Cross Entropy

arXiv: https://arxiv.org/abs/2505.14190 · HTML: https://mlsanity.com/paper/2505.14190/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 12 of its 29 references that are in the map.
- First posted on arXiv 20 May 2025.

## Builds on (most cited first, 12 of 12)

- [Improved Training of Wasserstein GANs](https://mlsanity.com/paper/1704.00028/) (2017)
- [Generalized Cross Entropy Loss for Training Deep Neural Networks with Noisy Labels](https://mlsanity.com/paper/1805.07836/) (2018)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [StyleSwin: Transformer-based GAN for High-resolution Image Generation](https://mlsanity.com/paper/2112.10762/) (2021)
- [Text to Image Generation with Semantic-Spatial Aware GAN](https://mlsanity.com/paper/2104.00567/) (2021)
- [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)
- [Maximum Causal Tsallis Entropy Imitation Learning](https://mlsanity.com/paper/1805.08336/) (2018)
- [Realizing GANs via a Tunable Loss Function](https://mlsanity.com/paper/2106.05232/) (2021)
- [α-GAN: Convergence and Estimation Guarantees](https://mlsanity.com/paper/2205.06393/) (2022)
- [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)

## Abstract (arXiv)

This paper proposes α-GAN, a generative adversarial network using R'enyi measures. The value function is formulated, by R'enyi cross entropy, as an expected certainty measure incurred by the discriminator's soft decision as to where the sample is from, true population or the generator. The discriminator tries to maximize the R'enyi certainty about sample source, while the generator wants to reduce it by injecting fake samples. This forms a min-max problem with the solution parameterized by the R'enyi order α. This α-GAN reduces to vanilla GAN at α = 1, where the value function is exactly the binary cross entropy. The optimization of α-GAN is over probability (vector) space. It is shown that the gradient is exponentially enlarged when R'enyi order is in the range α ∈ (0,1). This makes convergence faster, which is verified by experimental results. A discussion shows that choosing α ∈ (0,1) may be able to solve some common problems, e.g., vanishing gradient. A following observation reveals that this range has not been fully explored in the existing R'enyi version GANs.