Learning phase relationships through circuits of Kuramoto oscillators

Coupled Learning is a local learning framework for implementing machine learning in physical systems through contrastive local adaptation rules rather than global optimization. Recent studies have applied the Coupled Learning framework to construct physical analogue networks that autonomously train themselves to perform nonlinear tasks with low power dissipation and strong robustness when compared to digital network architectures. However, most laboratory realizations are for electrical networks, for which the average voltage drop per edge could become comparable to noise for large networks. Motivated by these challenges, we explore a novel experimental implementation of Coupled Learning using a network of coupled phase oscillators. In these networks, information is encoded in the oscillator phases, and training occurs through adjustments of coupling strengths. Because the oscillator signals are digital and self-reinforcing, this phase-based design naturally suppresses noise accumulation and mitigates signal degradation while maintaining the distributed nature of learning, providing a step toward fully scalable, low-loss, energy-efficient physical learning systems.