Gauge covariant neural network for quarks and gluons

We propose gauge-covariant neural networks along with a specialized training algorithm for lattice QCD, designed to handle realistic quarks and gluons in four-dimensional space-time. We show that the smearing procedure can be interpreted as an extended version of residual neural networks with fixed parameters. To demonstrate the applicability of our neural networks, we develop a self-learning hybrid Monte Carlo algorithm in the context of two-color QCD, yielding outcomes consistent with those from the conventional Hybrid Monte Carlo approach.