Computing functions with spiking neurons in temporal coding

Abstract

For fast neural computations within the brain it is very likely that the timing of single firing events is relevant. Recently Maass has shown that under certain weak assumptions functions can be computed in temporal coding by leaky integrate-and-fire neurons. Here we demonstrate with the help of computer simulations using GENESIS that biologically more realistic neurons can compute linear functions in a natural and straightforward way based on the basic principles of the construction given by Maass. One only has to assume that a neuron receives all its inputs in a time intervall of approximately the length of the rising segment of its excitatory postsynaptic potentials. We also show that under certain assumptions there exists within this construction some type of activation function being computed by such neurons, which allows the fast computation of arbitrary continuous bounded functions.