The XY-model as a Neuromorphic System, trained via Equilibrium Propagation

The recent explosion of resources needed to train and run deep neural networks provides an urgent motivation for novel hardware designs which allow us to efficiently implement the functionality of neural networks in physical systems. One of the greatest challenges for such neuromorphic systems is efficient training, preferably based on physical interactions.

In our work, we demonstrate that the XY model can be used as an energy-based neuromorphic system and that it can be trained using the recently introduced technique of equilibrium propagation, which is a local, physical algorithm for efficient gradient extraction. The trainability of the network and the validity of the algorithm are tested on the benchmark scenarios of XOR and handwritten digits recognition. Our results illustrate a new class of neuromorphic platforms for artificial intelligence, including systems like coupled laser arrays, coupled synchronizing mechanical oscillators, or magnetic systems.