  Understanding how the brain learns to compute functions reliably, efficiently
and robustly with noisy spiking activity is a fundamental challenge in
neuroscience. Most sensory and motor tasks can be described as dynamical
systems and could presumably be learned by adjusting connection weights in a
recurrent biological neural network. However, this is greatly complicated by
the credit assignment problem for learning in recurrent network, e.g. the
contribution of each connection to the global output error cannot be determined
based only on locally accessible quantities to the synapse. Combining tools
from adaptive control theory and efficient coding theories, we propose that
neural circuits can indeed learn complex dynamic tasks with local synaptic
plasticity rules as long as they associate two experimentally established
neural mechanisms. First, they should receive top-down feedbacks driving both
their activity and their synaptic plasticity. Second, inhibitory interneurons
should maintain a tight balance between excitation and inhibition in the
circuit. The resulting networks could learn arbitrary dynamical systems and
produce irregular spike trains as variable as those observed experimentally.
Yet, this variability in single neurons may hide an extremely efficient and
robust computation at the population level.
