Normalizing flow-based sampling methods have been successful in tackling computational challenges traditionally associated with simulating lattice quantum field theories. Further works have incorporated gauge and translational invariance of the action integral in the underlying neural networks, which have led to efficient training and inference in those models. In this paper, we incorporate locality of the action integral which leads to simplifications to the input domain of conditional normalizing flows that sample constant time sub-lattices in an autoregressive process, dubbed local-Autoregressive Conditional Normalizing Flow (l-ACNF). We find that the autocorrelation times of l-ACNF models outperform an equivalent normalizing flow model on the full lattice by orders of magnitude when sampling $\phi^{4}$ theory on a 2 dimensional lattice.

翻译：[translated abstract in Chinese] 基于归一化流的采样方法已成功应对传统格点量子场论模拟中的计算挑战。后续研究通过将作用量的规范不变性与平移不变性融入底层神经网络，显著提升了模型的训练效率与推理性能。本文进一步引入作用量的局域性，简化了条件归一化流在自回归过程中对恒定时间子格点进行采样的输入域，由此提出局部自回归条件归一化流（l-ACNF）方法。实验表明，在二维格点$\phi^{4}$理论采样中，l-ACNF模型的自相关时间比全格点上的等效归一化流模型低数个数量级。