Physical learning of energy-efficient solutions

Unlike an artificial neural network, the brain does not need an accompanying processor in order to learn. The ability to learn via local rules instead of a processor endows the brain with a vast power efficiency advantage compared to artificial neural networks, whose high power consumption constitutes a large economic and environmental burden. Physical learning systems that use physics-enabled local rules to replace processors have a similar power advantage. Here we show that power consumption can be lowered even further in physical learning networks. We train both experimental and computational physical networks not only for good performance on desired tasks, but also for energy-efficient solutions. This goal is achieved through explicit regularization of the local learning rules, promoting the optimization of the dissipated power together with performance. We describe the regularized learning dynamics and discuss how regularization leads to a trade-off between task performance and energy efficiency. In realistic noisy situations, regularization may improve energy efficiency at no penalty to performance. Finally, we propose a simple and practical training method that yields energy-efficient solutions in systems ranging from electronic circuits to mechanical spring networks.