  The ground-breaking works of Weinberg have opened the way to calculations of
atomic nuclei that are based on systematically improvable Hamiltonians. Solving
the associated many-body Schr\"odinger equation involves non-trivial
difficulties, due to the non-perturbative nature and strong spin-isospin
dependence of nuclear interactions. Artificial neural networks have proven to
be able to compactly represent the wave functions of nuclei with up to $A=4$
nucleons. In this work, we extend this approach to $^6$Li and $^6$He nuclei,
using as input a leading-order pionless effective field theory Hamiltonian. We
successfully benchmark their binding energies, point-nucleon densities, and
radii with the highly accurate hyperspherical harmonics method.
