  We propose the idea of using Kuramoto models (including their
higher-dimensional generalizations) for machine learning over non-Euclidean
data sets. These models are systems of matrix ODE's describing collective
motions (swarming dynamics) of abstract particles (generalized oscillators) on
spheres, homogeneous spaces and Lie groups. Such models have been extensively
studied from the beginning of XXI century both in statistical physics and
control theory. They provide a suitable framework for encoding maps between
various manifolds and are capable of learning over spherical and hyperbolic
geometries. In addition, they can learn coupled actions of transformation
groups (such as special orthogonal, unitary and Lorentz groups). Furthermore,
we overview families of probability distributions that provide appropriate
statistical models for probabilistic modeling and inference in Geometric Deep
Learning. We argue in favor of using statistical models which arise in
different Kuramoto models in the continuum limit of particles. The most
convenient families of probability distributions are those which are invariant
with respect to actions of certain symmetry groups.
