  The increasing complexity of neural networks and the energy consumption
associated with training and inference create a need for alternative
neuromorphic approaches, e.g. using optics. Current proposals and
implementations rely on physical non-linearities or opto-electronic conversion
to realise the required non-linear activation function. However, there are
significant challenges with these approaches related to power levels, control,
energy-efficiency, and delays. Here, we present a scheme for a neuromorphic
system that relies on linear wave scattering and yet achieves non-linear
processing with a high expressivity. The key idea is to inject the input via
physical parameters that affect the scattering processes. Moreover, we show
that gradients needed for training can be directly measured in scattering
experiments. We predict classification accuracies on par with results obtained
by standard artificial neural networks. Our proposal can be readily implemented
with existing state-of-the-art, scalable platforms, e.g. in optics, microwave
and electrical circuits, and we propose an integrated-photonics implementation
based on racetrack resonators that achieves high connectivity with a minimal
number of waveguide crossings.
