  Fracton models host unconventional topological orders in three and higher
dimensions and provide promising candidates for quantum memory platforms.
Understanding their robustness against quantum fluctuations is an important
task but also poses great challenges due to the lack of efficient numerical
tools. In this work, we establish neural quantum states (NQS) as new tools to
study phase transitions in these models. Exact and efficient parametrizations
are derived for three prototypical fracton codes - the checkerboard and X-cube
model, as well as Haah's code - both in terms of a restricted Boltzmann machine
(RBM) and a correlation-enhanced RBM. We then adapt the correlation-enhanced
RBM architecture to a perturbed checkerboard model and reveal its strong
first-order phase transition between the fracton phase and a trivial
field-polarizing phase. To this end, we simulate this highly entangled system
on lattices of up to 512 qubits with high accuracy, representing a cutting-edge
application of variational neural-network methods. Our work demonstrates the
remarkable potential of NQS in studying complicated three-dimensional problems
and highlights physics-oriented constructions of NQS architectures.
