Fisher vs Shannon information in Populations of Neurons

The accuracy of the neural code is commonly investigated using two different measures: (i) Shannon mutual information and derived quantities when investigating very small populations of neurons and (ii) Fisher information when studying large populations. How these measures compare in finite size populations has not been systematically explored. We here aim at filling this gap. We are particularly interested in understanding which stimuli are best encoded by a given neuron in a population and how this depends on the chosen measure. In models of independent neurons, we find that the predictions of Fisher information and of a stimulus-specific decomposition of Shannon information (the SSI) agree very well, even for relatively small population sizes. According to both measures, the stimuli that are best encoded are then those falling at the flanks of the neuron’s tuning curve.

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