Fully Non-Linear Neuromorphic Computing with Linear Wave Scattering

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.