Equilibrium Propagation and (Memristor-based) Oscillatory Neural Networks

Weakly Connected Oscillatory Networks (WCONs) are bio-inspired models which exhibit associative memory properties and can be exploited for information processing. It has been shown that the nonlinear dynamics of WCONs can be reduced to equations for the phase variable if oscillators admit stable limit cycles with nearly identical periods. Moreover, if connections are symmetric, the phase deviation equation admits a gradient formulation establishing a one-to-one correspondence between phase equilibria, limit cycle of the WCON and minima of the system's potential function. The overall objective of this work is to provide a simulated WCON based on memristive connections and Van der Pol oscillators that exploits the device mem-conductance programmability to implement a novel local supervised learning algorithm for gradient models: Equilibrium Propagation (EP). Simulations of the phase dynamics of the WCON system trained with EP show that the retrieval accuracy of the proposed novel design outperforms the current state-of-the-art performance obtained with the Hebbian learning.