We describe a direct approach 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：我们提出了一种基于自回归神经网络增强的蒙特卡洛采样，直接估计经典自旋系统二分互信息的方法。该方法能够研究子系统的任意几何结构，并可推广至经典场论。我们以伊辛模型为例，对包括多连通奇偶划分在内的四种分割方式进行了验证。结果表明：在远离临界温度的区域，面积律始终成立——常数项具有普适性，而奇偶划分的比例系数则存在差异。