# On the R'enyi Cross-Entropy

arXiv: https://arxiv.org/abs/2206.14329 · HTML: https://mlsanity.com/paper/2206.14329/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 1 of its 17 references that are in the map.
- First posted on arXiv 28 Jun 2022.

## Builds on (most cited first, 1 of 1)

- [Least kth-Order and R'enyi Generative Adversarial Networks](https://mlsanity.com/paper/2006.02479/) (2020)

## Abstract (arXiv)

The R'enyi cross-entropy measure between two distributions, a generalization of the Shannon cross-entropy, was recently used as a loss function for the improved design of deep learning generative adversarial networks. In this work, we examine the properties of this measure and derive closed-form expressions for it when one of the distributions is fixed and when both distributions belong to the exponential family. We also analytically determine a formula for the cross-entropy rate for stationary Gaussian processes and for finite-alphabet Markov sources.