The R\'{e}nyi 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.

翻译：R\'{{e}nyi 两个分布之间的交叉有机体测量,即香农交叉有机体的概括,最近被用作改进深学习基因对抗网络设计的一种损失函数。在这项工作中,我们检查了这一测量的特性,并在其中一种分布固定时,当两种分布都属于指数式家庭时,为它得出封闭式表达式。我们还分析确定固定高斯进程和有限阿尔法贝特马尔科夫源的交叉有机率公式。