Gradient descent in materia through homodyne gradient extraction

Parameter optimization is a crucial task for tuneable complex systems, which becomes increasingly time and power consuming as the parameter space scales up. In deep learning, the input-output relation of a deep neural network (DNN) model is given by a differentiable function, where gradient information can be obtained from the partial derivatives of the output with respect to the DNN parameters. Backpropagation is used to efficiently compute the gradient of a loss function with respect to the DNN parameters, allowing for training large and complex DNNs to show unprecedented performance, but often at a high, financial and environmental, cost. This has stimulated the development of specialized hardware, ranging from neuromorphic CMOS integrated circuits to unconventional, material-based computing systems. However, the learning process in these material systems is complicated and time-consuming. Here, we demonstrate a simple yet efficient gradient extraction method, based on the principle of homodyne detection, for performing gradient descent directly in a physical materials system. By perturbing the parameters using sinusoidal waveforms with distinct frequencies, we obtain the gradient information in a robust and scalable manner. We illustrate the method in dopant network processing units, but argue that it is applicable in a wide range of physical systems. Homodyne gradient extraction can in principle be fully implemented in materia, facilitating the development of autonomously learning material systems.