Self-learning machines based on time reversal

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. In this way, no knowledge of (and control of) these internal degrees of freedom is required. We introduce a general scheme to use any time-reversible Hamiltonian system as a self-learning machine. In particular, we show how this scheme can be applied to coupled nonlinear wave fields. We illustrate the training of such a self-learning machine numerically for the case of image recognition.