  Quantum-Chromo dynamics (QCD) is a fundamental theory for quarks and gluons,
which describes both the sub-atomic world and the history of our universe. The
simulation for QCD on a lattice (lattice QCD) is one of the most challenging
computational tasks. Recently, machine-learning techniques have been applied to
solve various problems in lattice QCD. We propose gauge covariant neural
networks and their training rule for lattice QCD, which can treat realistic
quarks and gluons in four dimensions. We find that the smearing procedure can
be regarded as extended versions of residual neural networks with fixed
parameters. To show the applicability of our neural networks, we develop the
self-learning hybrid Monte-Carlo for two-color QCD, where results are
consistent with the results of the Hybrid Monte Carlo.
