论文标题
精确翻新群的倒数作为统计推断
The Inverse of Exact Renormalization Group Flows as Statistical Inference
论文作者
论文摘要
我们基于确切的重新归一化组（ERG）的视图，作为功能对流扩散方程描述的最佳运输的实例化。我们提供了一种新的信息理论观点，可以通过贝叶斯统计推断的中介理解ERG。动力学贝叶斯推理方案促进了这种联系，该方案以一个概率分布的一个参数族的形式编码贝叶斯推断，该概率分布求解了从贝叶斯定律得出的全差异方程。在本说明中，我们演示了动态贝叶斯推理方程本身是如何等同于扩散方程的，我们将贝叶斯扩散列为贝叶斯扩散。确定定义贝叶斯扩散的特征，并将它们映射到定义ERG的特征上，我们获得了一个字典，概述了如何将重新归一化的理解为统计推断的倒数。
We build on the view of the Exact Renormalization Group (ERG) as an instantiation of Optimal Transport described by a functional convection-diffusion equation. We provide a new information theoretic perspective for understanding the ERG through the intermediary of Bayesian Statistical Inference. This connection is facilitated by the Dynamical Bayesian Inference scheme, which encodes Bayesian inference in the form of a one parameter family of probability distributions solving an integro-differential equation derived from Bayes' law. In this note, we demonstrate how the Dynamical Bayesian Inference equation is, itself, equivalent to a diffusion equation which we dub Bayesian Diffusion. Identifying the features that define Bayesian Diffusion, and mapping them onto the features that define the ERG, we obtain a dictionary outlining how renormalization can be understood as the inverse of statistical inference.
