  We present a bit encoding scheme for a highly efficient and scalable
representation of bosonic Fock number states in the restricted Boltzmann
machine neural network architecture. In contrast to common density matrix
implementations, the complexity of the neural network scales only with the
number of bit-encoded neurons rather than the maximum boson number. Crucially,
in the high occupation regime its information compression efficiency is shown
to surpass even maximally optimized density matrix implementations, where a
projector method is used to access the sparsest Hilbert space representation
available.
