Machine learning techniques, in particular the so-called normalizing flows, are becoming increasingly popular in the context of Monte Carlo simulations as they can effectively approximate target probability distributions. In the case of lattice field theories (LFT) the target distribution is given by the exponential of the action. The common loss function's gradient estimator based on the "reparametrization trick" requires the calculation of the derivative of the action with respect to the fields. This can present a significant computational cost for complicated, non-local actions like e.g. fermionic action in QCD. In this contribution, we propose an estimator for normalizing flows based on the REINFORCE algorithm that avoids this issue. We apply it to two dimensional Schwinger model with Wilson fermions at criticality and show that it is up to ten times faster in terms of the wall-clock time as well as requiring up to $30\%$ less memory than the reparameterization trick estimator. It is also more numerically stable allowing for single precision calculations and the use of half-float tensor cores. We present an in-depth analysis of the origins of those improvements. We believe that these benefits will appear also outside the realm of the LFT, in each case where the target probability distribution is computationally intensive.

翻译：机器学习技术，特别是所谓的归一化流，在蒙特卡洛模拟中日益流行，因为它们能够有效逼近目标概率分布。在格点场论（LFT）中，目标分布由作用量的指数给出。基于“重参数化技巧”的常见损失函数梯度估计器需要计算作用量相对于场的导数。对于复杂、非局域的作用量（如量子色动力学中的费米子作用量），这可能会带来显著的计算成本。在本文中，我们提出了一种基于REINFORCE算法的归一化流估计器，避免了这一问题。我们将其应用于临界状态下包含Wilson费米子的二维Schwinger模型，并表明该估计器在墙钟时间上快至十倍，同时内存需求比重参数化技巧估计器最多减少$30\%$。此外，它在数值上更稳定，支持单精度计算和半浮点张量核心的使用。我们深入分析了这些改进的根源。我们相信这些优势将不仅限于格点场论领域，而会出现在任何目标概率分布计算密集的场景中。