  Both the three-body system and the inverse square potential carry a special
significance in the study of renormalization group limit cycles. In this work,
we pursue an exploratory approach and address the question which two-body
interactions lead to limit cycles in the three-body system at low energies,
without imposing any restrictions upon the scattering length. For this, we
train a boosted ensemble of variational autoencoders, that not only provide a
severe dimensionality reduction, but also allow to generate further synthetic
potentials, which is an important prerequisite in order to efficiently search
for limit cycles in low-dimensional latent space. We do so by applying an
elitist genetic algorithm to a population of synthetic potentials that
minimizes a specially defined limit-cycle-loss. The resulting fittest
individuals suggest that the inverse square potential is the only two-body
potential that minimizes this limit cycle loss independent of the hyperangle.
