Design of Self-Learning Machines using Hamiltonian Echo Backpropagation

A self-learning machine can be defined as a physical system that can be trained on data (similar to artificial neural networks), but where the update of the internal degrees of freedom that serve as learnable parameters happens autonomously. We introduce Hamiltonian Echo Backpropagation, a general scheme to use any time-reversible Hamiltonian system as a self-learning machine. A particularly appealing feature of our scheme is that it does not require any knowledge of the internal dynamics of the Hamiltonian system, which can be operated as a black box. We show how this scheme can be applied to some promising physical platforms.