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Understanding how recurrent neural circuits can learn to implement dynamicalsystems is a fundamental challenge in neuroscience. The credit assignmentproblem, i.e. determining the local contribution of each synapse to thenetwork's global output error, is a major obstacle in deriving biologicallyplausible local learning rules. Moreover, spiking recurrent networksimplementing such tasks should not be hugely costly in terms of number ofneurons 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 sustainthese representations in the face of such naturally occurring perturbation. Weapproach this problem by fusing the theory of efficient, balanced spikingnetworks (EBN) with nonlinear adaptive control theory. Local learning rules areensured by feeding back into the network its own error, resulting in a synapticplasticity rule depending solely on presynaptic inputs and post-synapticfeedback. The spiking efficiency and robustness of the network are guaranteedby maintaining a tight excitatory/inhibitory balance, ensuring that each spikerepresents a local projection of the global output error and minimizes a lossfunction. The resulting networks can learn to implement complex dynamics withvery small numbers of neurons and spikes, exhibit the same spike trainvariability as observed experimentally, and are extremely robust to noise andneuronal loss.

Learning arbitrary dynamics in efficient, balanced spiking networks using local plasticity rules