  The Ryu-Takayanagi formula directly connects quantum entanglement and
geometry. Yet the assumption of static geometry lead to an exponentially small
mutual information between far-separated disjoint regions, which does not hold
in many systems such as free fermion conformal field theories. In this work, we
proposed a microscopic model by superimposing entanglement features of an
ensemble of random tensor networks of different bond dimensions, which can be
mapped to a statistical gravity model consisting of a massive scalar field on a
fluctuating background geometry. We propose a machine-learning algorithm that
recovers the underlying geometry fluctuation from multi-region entanglement
entropy data by modeling the bulk geometry distribution via a generative neural
network. To demonstrate its effectiveness, we tested the model on a free
fermion system and showed mutual information can be mediated effectively by
geometric fluctuation. Remarkably, locality emerged from the learned
distribution of bulk geometries, pointing to a local statistical gravity theory
in the holographic bulk.
