Two-State Dynamical Synapses as a Physical Substrate for Equilibrium Propagation

Equilibrium Propagation (EqProp) updates each synapse by comparing a local term at the free and nudged equilibria. Because these two values occur at different times, a physical implementation requires temporary local memory. We show that this memory can emerge from a two-timescale synaptic model in which neural and volatile synaptic dynamics are jointly derived from a single energy function. A volatile state $w$ relaxes toward the product of the pre- and postsynaptic activities, while a non-volatile state $M$ stores the learned parameter. At equilibrium, $w$ equals the local term entering the EqProp update. Using its net change between phases implements phase-based EqProp, while transferring its successive changes during nudging yields continual EqProp, in which the temporal comparison is carried by the synaptic dynamics themselves. On MNIST with a single-hidden-layer network, the phase-based model reaches $2.01\pm 0.09\mathrm{\%}$ test error versus $2.00\pm 0.13\mathrm{\%}$ for standard EqProp, and the continual model reaches $2.24\pm 0.11\mathrm{\%}$ versus $2.28\pm 0.16\mathrm{\%}$ for continual EqProp. The framework further specifies the dynamical requirements that a volatile–non-volatile synaptic device must satisfy to implement this learning mechanism.