Theory of Spike Timing-Based Neural Classifiers

We study the computational capacity of a model neuron, the tempotron, which classifies sequences of spikes by linear-threshold operations. We use statistical mechanics and extreme value theory to derive the capacity of the system in random classification tasks. In contrast with its static analog, the perceptron, the tempotron's solutions space consists of a large number of small clusters of weight vectors. The capacity of the system per synapse is finite in the large size limit and weakly diverges with the stimulus duration relative to the membrane and synaptic time constants.