Generalized Inverse Gaussian (GIG) Models for Energy-Efficient Neurons

We extend to the GIG case the Schrödinger-WienerGerstein-Mandelbrot real neuron model of the conditional probability density function (pdf) for the random time, T , that it takes the neuron’s post-synaptic potential to reach the spiking threshold when the realization of the random afferent excitation rate, Λ, assumes the value λ. Then we analyze how to maximize I(Λ;T ) per joule of energy the neuron expends when the energy cost function belongs to the family apropos of the GIG model. Our investigations suggest that neurons anticipated mathematical statistics and information theory eons before there were mathematical statisticians and information theorists.