论文标题
重新归一化组作为最佳运输
Renormalization Group Flow as Optimal Transport
论文作者
论文摘要
我们确定Polchinski的精确重新规范化组流量方程等于田间理论相对熵的最佳传输梯度流。这提供了以最佳运输语言表达的精确重新归一化组的引人入胜的信息理论。一个惊人的结果是，相对熵的正则化实际上是RG单调。我们在几个示例中计算了这个单调。我们的结果更广泛地适用于其他精确的重新归一化组流程方程，包括广泛使用的Wegner-Morris流量。此外，我们对RG的最佳运输框架使我们能够将RG流动作为变异问题。这实现了新的数值技术，并在神经网络方法和常规场理论的RG流之间建立了系统的联系。
We establish that Polchinski's equation for exact renormalization group flow is equivalent to the optimal transport gradient flow of a field-theoretic relative entropy. This provides a compelling information-theoretic formulation of the exact renormalization group, expressed in the language of optimal transport. A striking consequence is that a regularization of the relative entropy is in fact an RG monotone. We compute this monotone in several examples. Our results apply more broadly to other exact renormalization group flow equations, including widely used specializations of Wegner-Morris flow. Moreover, our optimal transport framework for RG allows us to reformulate RG flow as a variational problem. This enables new numerical techniques and establishes a systematic connection between neural network methods and RG flows of conventional field theories.
