Accuracy and learning in neuronal populations.

The information about various sensory and motor variables contained in neuronal spike trains may be quantified by either Shannon mutual information or Fisher information. Although they are related, the Fisher information measure is more convenient for dealing with continuous variables which are more common in lower level sensory and motor representations. The accuracy of encoding and decoding by a population of neurons as described by Fisher information has some general properties, including a universal scaling law with respect to the width of the tuning functions. The theoretical accuracy for reading out information from population activity can be reached, in principle, by Bayesian reconstruction method, which can be simplified by exploiting Poisson spike statistics. The Bayesian method can be implemented by a feedforward network, where the desired synaptic strength can be established by a Hebbian learning rule that is proportional to the logarithm of the presynaptic firing rate, suggesting that the method might be potentially relevant to biological systems.