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As the size and ubiquity of artificial intelligence and computational machine learning models grow, the energy required to train and use them is rapidly becoming economically and environmentally unsustainable. Recent laboratory prototypes of self-learning electronic circuits, such as “physical learning machines,” open the door to analog hardware that directly employs physics to learn desired functions from examples at a low energy cost. In this work, we show that this hardware platform allows for an even further reduction in energy consumption by using good initial conditions and a new learning algorithm. Using analytical calculations, simulations, and experiments, we show that a trade-off emerges when learning dynamics attempt to minimize both the error and the power consumption of the solution—greater power reductions can be achieved at the cost of decreasing solution accuracy. Finally, we demonstrate a practical procedure to weigh the relative importance of error and power minimization, improving the power efficiency given a specific tolerance to error. 

Learning is traditionally studied in biological or computational systems. The power of learning frameworks in solving hard inverse problems provides an appealing case for the development of physical learning in which physical systems adopt desirable properties on their own without computational design. It was recently realized that large classes of physical systems can physically learn through local learning rules, autonomously adapting their parameters in response to observed examples of use. We review recent work in the emerging field of physical learning, describing theoretical and experimental advances in areas ranging from molecular self-assembly to flow networks and mechanical materials. Physical learning machines provide multiple practical advantages over computer designed ones, in particular by not requiring an accurate model of the system, and their ability to autonomously adapt to changing needs over time. As theoretical constructs, physical learning machines afford a novel perspective on how physical constraints modify abstract learning theory.