  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.

Statistical Mechanics;Disordered Systems and Neural Networks;High Energy Physics - Lattice;Machine Learning