  The exact holographic mapping (EHM) provides an explicit duality map between
a conformal field theory (CFT) configuration and a massive field propagating on
an emergent classical geometry. However, designing the optimal holographic
mapping is challenging. Here we introduce the neural network renormalization
group as a universal approach to design generic EHM for interacting field
theories. Given a field theory action, we train a flow-based hierarchical deep
generative neural network to reproduce the boundary field ensemble from
uncorrelated bulk field fluctuations. In this way, the neural network develops
the optimal renormalization group transformations. Using the machine-designed
EHM to map the CFT back to a bulk effective action, we determine the bulk
geodesic distance from the residual mutual information. We apply this approach
to the complex $\phi^4$ theory in two-dimensional Euclidian spacetime in its
critical phase, and show that the emergent bulk geometry matches the
three-dimensional hyperbolic geometry.
