Signal transcoding by nonlinear sensory neurons: information-entropy maximization, optimal transfer function, and anti-Hebbian adaptation.

A principle of information-entropy maximization is introduced in order to characterize the optimal representation of an arbitrarily varying quantity by a neural output confined to a finite interval. We then study the conditions under which a neuron can effectively fulfil the requirements imposed by this information-theoretic optimal principle. We show that this can be achieved with the natural properties available to the neuron. Specifically, we first deduce that neural (monotonically increasing and saturating) nonlinearities are potentially efficient for achieving the entropy maximization, for any given input signal. Secondly, we derive simple laws which adaptively adjust modifiable parameters of a neuron toward maximum entropy. Remarkably, the adaptation laws that realize entropy maximization are found to belong to the class of anti-Hebbian laws (a class having experimental groundings), with a special, yet simple, nonlinear form. The present results highlight the usefulness of general information-theoretic principles in contributing to the understanding of neural systems and their remarkable performances for information processing.