Normalizing flows are machine-learned maps between different lattice theories
which can be used as components in exact sampling and inference schemes.
Ongoing work yields increasingly expressive flows on gauge fields, but it
remains an open question how flows can improve lattice QCD at state-of-the-art
scales. We discuss and demonstrate two applications of flows in replica
exchange (parallel tempering) sampling, aimed at improving topological mixing,
which are viable with iterative improvements upon presently available flows.

通过归一化流在格点理论之间建立机器学习映射，可以作为精确采样和推理方案的组成部分。我们讨论并演示了在复制交换（并行加热）采样中应用流的两个应用，旨在改善拓扑混合，这些应用在当前可用的流的迭代改进基础上是可行的。

规范场上机器学习流的实际应用

Practical applications of machine-learned flows on gauge fields

A central task in many applications is reasoning about processes that change
over continuous time. Continuous-Time Bayesian Networks is a general compact
representation language for multi-component continuous-time processes. However,
exact inference in such processes is exponential in the number of components,
and thus infeasible for most models of interest. Here we develop a novel Gibbs
sampling procedure for multi-component processes. This procedure iteratively
samples a trajectory for one of the components given the remaining ones. We
show how to perform exact sampling that adapts to the natural time scale of the
sampled process. Moreover, we show that this sampling procedure naturally
exploits the structure of the network to reduce the computational cost of each
step. This procedure is the first that can provide asymptotically unbiased
approximation in such processes.

该研究论文介绍了连续时间贝叶斯网络的一种新的采样方法 ——Gibbs 采样，以解决对多组件过程进行精确推理的困难。该方法可以适应进程的自然时间尺度，减少计算成本，并提供渐近无偏的近似。

因式化连续时间马尔可夫过程中的吉布斯采样

Gibbs Sampling in Factorized Continuous-Time Markov Processes

We generalize the Metropolis et al. random walk algorithm to the situation
where the energy is noisy and can only be estimated. Two possible applications
are for long range potentials and for mixed quantum-classical simulations. If
the noise is normally distributed we are able to modify the acceptance
probability by applying a penalty to the energy difference and thereby achieve
exact sampling even with very strong noise. When one has to estimate the
variance we have an approximate formula, good in the limit of large number of
independent estimates. We argue that the penalty method is nearly optimal. We
also adapt an existing method by Kennedy and Kuti and compare to the penalty
method on a one dimensional double well.

本文推广了 Metropolis 算法，使其适用于能量受噪声干扰且只能估计的情况，并提出了基于惩罚方法改进接受概率的方案，实现了对强噪声进行准确采样。该方法在了解方差只能近似估计的情况下通过近似公式，在独立估计数量大的情况下取得了良好效果。此外，文章将现有 Kennedy 和 Kuti 方法进行改进，并在一维双井比较了不同方法的性能表现。