  Given the rapidly growing scale and resource requirements of machine learning
applications, the idea of building more efficient learning machines much closer
to the laws of physics is an attractive proposition. One central question for
identifying promising candidates for such neuromorphic platforms is whether not
only inference but also training can exploit the physical dynamics. In this
work, we show that it is possible to successfully train a system of coupled
phase oscillators - one of the most widely investigated nonlinear dynamical
systems with a multitude of physical implementations, comprising laser arrays,
coupled mechanical limit cycles, superfluids, and exciton-polaritons. To this
end, we apply the approach of equilibrium propagation, which permits to extract
training gradients via a physical realization of backpropagation, based only on
local interactions. The complex energy landscape of the XY/ Kuramoto model
leads to multistability, and we show how to address this challenge. Our study
identifies coupled phase oscillators as a new general-purpose neuromorphic
platform and opens the door towards future experimental implementations.
