We describe a new direct method to estimate bipartite mutual information of a classical spin system based on Monte Carlo sampling enhanced by autoregressive neural networks. It allows studying arbitrary geometries of subsystems and can be generalized to classical field theories. We demonstrate it on the Ising model for four partitionings, including a multiply-connected even-odd division. We show that the area law is satisfied for temperatures away from the critical temperature: the constant term is universal, whereas the proportionality coefficient is different for the even-odd partitioning.

翻译：我们描述了一种基于自回归神经网络增强的蒙特卡洛采样来估计经典自旋系统二分互信息的新直接方法。该方法允许研究子系统的任意几何构型，并可推广至经典场论。我们以伊辛模型为例，对四种分割方式（包括多重连通奇偶划分）进行了演示。研究表明：在远离临界温度时面积律成立——常数项具有普适性，而奇偶划分的比例系数则存在差异。