  Finding spike-based learning algorithms that can be implemented within the
local constraints of neuromorphic systems, while achieving high accuracy,
remains a formidable challenge. Equilibrium Propagation is a promising
alternative to backpropagation as it only involves local computations, but
hardware-oriented studies have so far focused on rate-based networks. In this
work, we develop a spiking neural network algorithm called EqSpike, compatible
with neuromorphic systems, which learns by Equilibrium Propagation. Through
simulations, we obtain a test recognition accuracy of 97.6% on MNIST, similar
to rate-based Equilibrium Propagation, and comparing favourably to alternative
learning techniques for spiking neural networks. We show that EqSpike
implemented in silicon neuromorphic technology could reduce the energy
consumption of inference and training respectively by three orders and two
orders of magnitude compared to GPUs. Finally, we also show that during
learning, EqSpike weight updates exhibit a form of Spike Timing Dependent
Plasticity, highlighting a possible connection with biology.
