  Understanding how recurrent neural circuits can learn to implement dynamical
systems is a fundamental challenge in neuroscience. The credit assignment
problem, i.e. determining the local contribution of each synapse to the
network's global output error, is a major obstacle in deriving biologically
plausible local learning rules. Moreover, spiking recurrent networks
implementing such tasks should not be hugely costly in terms of number of
neurons and spikes, as they often are when adapted from rate models. Finally,
these networks should be robust to noise and neural deaths in order to sustain
these representations in the face of such naturally occurring perturbation. We
approach this problem by fusing the theory of efficient, balanced spiking
networks (EBN) with nonlinear adaptive control theory. Local learning rules are
ensured by feeding back into the network its own error, resulting in a synaptic
plasticity rule depending solely on presynaptic inputs and post-synaptic
feedback. The spiking efficiency and robustness of the network are guaranteed
by maintaining a tight excitatory/inhibitory balance, ensuring that each spike
represents a local projection of the global output error and minimizes a loss
function. The resulting networks can learn to implement complex dynamics with
very small numbers of neurons and spikes, exhibit the same spike train
variability as observed experimentally, and are extremely robust to noise and
neuronal loss.
