Two-State Dynamical Synapses as a Physical Substrate for Equilibrium Propagation
Abstract
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 ± 0.09% test error versus 2.00 ± 0.13% for standard EqProp, and the continual model reaches 2.24 ± 0.11% versus 2.28 ± 0.16% for continual EqProp. The framework further specifies the dynamical requirements that a volatile--non-volatile synaptic device must satisfy to implement this learning mechanism.
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BibTeX
@misc{liu2026twostate,
title = {{Two-State Dynamical Synapses as a Physical Substrate for Equilibrium Propagation}},
author = {Dongshu Liu and Julie Grollier},
howpublished = {arXiv},
year = {2026},
month = oct,
doi = {10.48550/arxiv.2610.18058},
eprint = {2610.18058},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2610.18058},
}
RIS
TY - UNPB
TI - Two-State Dynamical Synapses as a Physical Substrate for Equilibrium Propagation
AU - Dongshu Liu
AU - Julie Grollier
PY - 2026
DA - 2026/10/13
PB - arXiv
DO - 10.48550/arxiv.2610.18058
UR - https://arxiv.org/abs/2610.18058
AB - 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 ± 0.09% test error versus 2.00 ± 0.13% for standard EqProp, and the continual model reaches 2.24 ± 0.11% versus 2.28 ± 0.16% for continual EqProp. The framework further specifies the dynamical requirements that a volatile--non-volatile synaptic device must satisfy to implement this learning mechanism.
ER -