Gradient descent in materia through homodyne gradient extraction.

Deep learning, a multilayered neural-network approach inspired by the brain, has revolutionized machine learning. Its success relies on backpropagation, which computes gradients of a loss function for use in gradient descent. However, digital implementations are energy hungry, with power demands limiting many applications. This has motivated specialized hardware, from neuromorphic CMOS and photonic tensor cores to unconventional material-based systems. Learning in such systems, for example via artificial evolution, equilibrium propagation, or surrogate modelling, is typically complicated and slow. Here, we demonstrate a simple gradient-extraction method based on homodyne detection, enabling gradient descent directly in physical systems without the need for an analytical description. By perturbing parameters with sinusoidal waveforms at distinct frequencies, we robustly obtain gradient information in a scalable manner. We illustrate the method in reconfigurable nonlinear-processing units and argue for broad applicability. Homodyne gradient extraction can in principle be fully implemented in materia, facilitating autonomously learning material systems.