Self-Learning Machines Based on Hamiltonian Echo Backpropagation

Abstract

A physical self-learning machine can be defined as a nonlinear dynamical 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, neither external processing and feedback nor knowledge of (and control of) these internal degrees of freedom is required. We introduce a general scheme for self-learning in any time-reversible Hamiltonian system. It relies on implementing a time-reversal operation and injecting a small error signal on top of the echo dynamics. We show how the physical dynamics itself will then lead to the required gradient update of learnable parameters, independent of the details of the Hamiltonian. We illustrate the training of such a self-learning machine numerically for the case of coupled nonlinear wave fields and other examples.