  Fixed point lattice actions are designed to have continuum classical
properties unaffected by discretization effects and reduced lattice artifacts
at the quantum level. They provide a possible way to extract continuum physics
with coarser lattices, thereby allowing to circumvent problems with critical
slowing down and topological freezing toward the continuum limit. A crucial
ingredient for practical applications is to find an accurate and compact
parametrization of a fixed point action, since many of its properties are only
implicitly defined. Here we use machine learning methods to revisit the
question of how to parametrize fixed point actions. In particular, we obtain a
fixed point action for four-dimensional SU(3) gauge theory using convolutional
neural networks with exact gauge invariance. The large operator space allows us
to find superior parametrizations compared to previous studies, a necessary
first step for future Monte Carlo simulations.
