  Photonic brain-inspired platforms are emerging as novel analog computing
devices, enabling fast and energy-efficient operations for machine learning.
These artificial neural networks generally require tailored optical elements,
such as integrated photonic circuits, engineered diffractive layers,
nanophotonic materials, or time-delay schemes, which are challenging to train
or stabilize. Here we present a neuromorphic photonic scheme - photonic extreme
learning machines - that can be implemented simply by using an optical encoder
and coherent wave propagation in free space. We realize the concept through
spatial light modulation of a laser beam, with the far field that acts as
feature mapping space. We experimentally demonstrated learning from data on
various classification and regression tasks, achieving accuracies comparable to
digital extreme learning machines. Our findings point out an optical machine
learning device that is easy-to-train, energetically efficient, scalable and
fabrication-constraint free. The scheme can be generalized to a plethora of
photonic systems, opening the route to real-time neuromorphic processing of
optical data.
