Geometrical aspects of lattice gauge equivariant convolutional neural networks

Lattice gauge equivariant convolutional neural networks

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 convo…

用规范等变卷积神经网络机器学习 SU(3) 规范理论的固定点作用量

Machine learning a fixed point action for SU(3) gauge theory with a gauge equivariant convolutional neural network

本文利用具有精确规范不变性的卷积神经网络为四维 SU(3) 规范理论构造固定点作用量，通过大算子空间获得优于以往研究的参数化，为未来蒙特卡洛模拟和标度研究奠定基础。

Lattice gauge symmetry in neural networks

We review a novel neural network architecture called lattice gauge equivariant convolutional neural networks (L-CNNs), which can be applied to generic machine learning problems in lattice gauge theory while exactly preserving gauge symmetry. We discuss the concept of gauge equivariance which we use to explicitly construct a gauge equivariant convolutional layer and a bilinear layer. The performance of L-CNNs and non-equivariant CNNs is compared using seemingly simple non-linear regression tasks, where L-CNNs demonstrate generalizability and achieve a high degree of accuracy in their prediction…

Preserving gauge invariance in neural networks

In these proceedings we present lattice gauge equivariant convolutional neural networks (L-CNNs) which are able to process data from lattice gauge theory simulations while exactly preserving gauge symmetry. We review aspects of the architecture and show how L-CNNs can represent a large class of gauge invariant and equivariant functions on the lattice. We compare the performance of L-CNNs and non-equivariant networks using a non-linear regression problem and demonstrate how gauge invariance is broken for non-equivariant models.

Generalization capabilities of translationally equivariant neural networks

The rising adoption of machine learning in high energy physics and lattice field theory necessitates the re-evaluation of common methods that are widely used in computer vision, which, when applied to problems in physics, can lead to significant drawbacks in terms of performance and generalizability. One particular example for this is the use of neural network architectures that do not reflect the underlying symmetries of the given physical problem. In this work, we focus on complex scalar field theory on a two-dimensional lattice and investigate the benefits of using group equivariant convolu…

Applications of Lattice Gauge Equivariant Neural Networks

The introduction of relevant physical information into neural network architectures has become a widely used and successful strategy for improving their performance. In lattice gauge theories, such information can be identified with gauge symmetries, which are incorporated into the network layers of our recently proposed Lattice Gauge Equivariant Convolutional Neural Networks (L-CNNs). L-CNNs can generalize better to differently sized lattices than traditional neural networks and are by construction equivariant under lattice gauge transformations. In these proceedings, we present our progress …