论文标题
晶格量规卷积神经网络
Lattice gauge equivariant convolutional neural networks
论文作者
论文摘要
我们提出了晶格量规卷积神经网络（L-CNNS），以用于晶格规定问题的通用机器学习应用。该网络结构的核心是一个新颖的卷积层，可以保留仪表的量规，同时在连续的双线性层中形成任意形状的威尔逊环。与拓扑信息（例如，从Polyakov循环中），这样的网络原则上可以近似于晶格上的任何量规协方差函数。我们证明，L-CNN可以学习和概括不变的数量，传统的卷积神经网络无法找到。
We propose Lattice gauge equivariant Convolutional Neural Networks (L-CNNs) for generic machine learning applications on lattice gauge theoretical problems. At the heart of this network structure is a novel convolutional layer that preserves gauge equivariance while forming arbitrarily shaped Wilson loops in successive bilinear layers. Together with topological information, for example from Polyakov loops, such a network can in principle approximate any gauge covariant function on the lattice. We demonstrate that L-CNNs can learn and generalize gauge invariant quantities that traditional convolutional neural networks are incapable of finding.
