Contrastive learning through non-equilibrium memory

Learning algorithms based on backpropagation have been very powerful in silico but alternatives based on local rules offer potential benefits for learning in physical systems. A broad class of such local learning rules - contrastive learning rules - require comparing the spontaneous behavior of the system with the behavior of the system when driven to a desired state. We do not understand the fundamental physical requirements on memory needed for such contrastive learning. Here, we show how the simplest form of non-equilibrium memory in each `synapse' of a network allows for contrastive rules such as equilibrium propagation. In this framework, the free and clamped states are seen in sequence over time as part of a sawtooth-like protocol which breaks the symmetry in time. We identify principles for optimal protocols and determine the fundamental Landauer energy cost of supervised learning through physical dynamics. These principles are also applicable to mechanical, chemical or other physical systems where non-equilibrium synaptic memory can naturally arise through ubiquitous feedback circuits.