  Using machine learning techniques, we verify that the emergence of
renormalization group limit cycles beyond the unitary limit is transferred from
the three-boson subsystems to the whole four-boson system. Focussing on four
identical bosons, we first generate populations of synthetic singular
potentials within the latent space of a boosted ensemble of variational
autoencoders. After introducing the limit cycle loss for measuring the
deviation of a given renormalization group flow from limit cycle behavior, we
minimize it by applying an elitist genetic algorithm to the generated
populations. The fittest potentials are observed to accumulate around the
inverse-square potential, which we prove to generate limit cycles for four
bosons and which is already known to produce limit cycles in the three-boson
system. This also indicates that a four-body term does not enter low-energy
observables at leading order, since we do not observe any additional scale to
emerge.
