论文标题
学习晶格量规理论的微不足道梯度流
Learning Trivializing Gradient Flows for Lattice Gauge Theories
论文作者
论文摘要
我们提出了一种统一的方法，该方法是从吕瑟尔（Lüscher）的微不足道地图的扰动构造开始，然后通过学习来改进它。可以使用晶格场理论的通用工具来实现所得的连续归一化流模型，并且比任何现有的机器学习方法都需要几个数量级的参数。具体而言，我们的模型可以实现竞争性能，只有14个参数，而现有的深入学习模型的$ SU（3）$ YANG-MILLS理论约为16^2 $ lattice。这对训练速度和解释性产生了明显的后果。它还为缩放机器学习方法的方法提供了一条合理的路径。
We propose a unifying approach that starts from the perturbative construction of trivializing maps by Lüscher and then improves on it by learning. The resulting continuous normalizing flow model can be implemented using common tools of lattice field theory and requires several orders of magnitude fewer parameters than any existing machine learning approach. Specifically, our model can achieve competitive performance with as few as 14 parameters while existing deep-learning models have around 1 million parameters for $SU(3)$ Yang--Mills theory on a $16^2$ lattice. This has obvious consequences for training speed and interpretability. It also provides a plausible path for scaling machine-learning approaches toward realistic theories.
