Leveraging phase model reduction and equilibrium propagation for neuromorphic design optimization of oscillatory neural networks

Although neuromorphic computing promises energy-efficient and biologically inspired machine learning architectures, the implementation of neural dynamics into practical hardware design remains a major challenge. This work presents a unified analytical framework that integrates equilibrium propagation (EP) with oscillatory neural networks (ONNs) through a phase-deviation formulation. By exploiting the synchronization properties of oscillatory systems, we establish a mathematical link between circuit dynamics, learning behavior, and the underlying energy landscape derived from the phase-deviation equations. This formulation reveals how ONNs naturally operate as an analog associative memory, where equilibrium points correspond to minima of the energy function governing collective phase dynamics. We derive the full phase-deviation formalism for weakly coupled oscillatory networks and adapt EP to their dynamics. Numerical simulations on pattern-recognition tasks are provided as a supporting example, illustrating how the proposed analytical framework can reproduce learning and retrieval behavior in a phase-based ONN setting. These results support the use of the proposed formalism as a principled framework for analyzing equilibrium structure, learning dynamics, and possible failure modes in oscillatory neuromorphic systems.