An invariance principle for maintaining the operating point of a neuron

Abstract

Sensory neurons adapt to changes in the natural statistics of their environments through processes such as gain control and firing threshold adjustment. It has been argued that neurons early in sensory pathways adapt according to information-theoretic criteria, perhaps maximising their coding efficiency or information rate. Here, we draw a distinction between how a neuron's preferred operating point is determined and how its preferred operating point is maintained through adaptation. We propose that a neuron's preferred operating point can be characterised by the probability density function (PDF) of its output spike rate, and that adaptation maintains an invariant output PDF, regardless of how this output PDF is initially set. Considering a sigmoidal transfer function for simplicity, we derive simple adaptation rules for a neuron with one sensory input that permit adaptation to the lower-order statistics of the input, independent of how the preferred operating point of the neuron is set. Thus, if the preferred operating point is, in fact, set according to information-theoretic criteria, then these rules nonetheless maintain a neuron at that point. Our approach generalises from the unimodal case to the multimodal case, for a neuron with inputs from distinct sensory channels, and we briefly consider this case too.

• Neuronal adaptation
• operating point
• gain control
• multisensory integration

Notes

Notes

[1] Carleman's condition on the moments is sufficient to ensure uniqueness (Feller 1967). The classic counter-examples to this condition are the Cauchy distribution, which has no moments, and the log-normal distribution, for which M_X(t) does not exist despite all the moments existing.