The coding of information by spiking neurons: an analytical study.

We analyse analytically the coding of information by a spiking neuron. The emphasis is on the question of how many spikes are necessary for the reliable discrimination of two different input signals. The discrimination ability is measured by the second-order Rényi mutual information between the random variable describing the name of the signal and a sequence of n output spikes. Analysing this measure as a function of n, we study the coding strategy of a single spiking neuron, with the following main results. A small number of output spikes is required for efficient discrimination of input signals, i.e. for encoding them, if the separation is easy; a large number of output spikes is required in the difficult case of separation of very similar input signals. Three different versions of the spike response model of a single neuron are studied. The approach presented can be regarded as a non-parametric version of the reconstruction method of Bialek.