  We study whether neural quantum states based on multi-layer feed-forward
networks can find ground states which exhibit volume-law entanglement entropy.
As a testbed, we employ the paradigmatic Sachdev-Ye-Kitaev model. We find that
both shallow and deep feed-forward networks require an exponential number of
parameters in order to represent the ground state of this model. This
demonstrates that sufficiently complicated quantum states, although being
physical solutions to relevant models and not pathological cases, can still be
difficult to learn to the point of intractability at larger system sizes. This
highlights the importance of further investigations into the physical
properties of quantum states amenable to an efficient neural representation.
