  Representing surfaces as zero level sets of neural networks recently emerged
as a powerful modeling paradigm, named Implicit Neural Representations (INRs),
serving numerous downstream applications in geometric deep learning and 3D
vision. Training INRs previously required choosing between occupancy and
distance function representation and different losses with unknown limit
behavior and/or bias. In this paper we draw inspiration from the theory of
phase transitions of fluids and suggest a loss for training INRs that learns a
density function that converges to a proper occupancy function, while its log
transform converges to a distance function. Furthermore, we analyze the limit
minimizer of this loss showing it satisfies the reconstruction constraints and
has minimal surface perimeter, a desirable inductive bias for surface
reconstruction. Training INRs with this new loss leads to state-of-the-art
reconstructions on a standard benchmark.
