Fast Sigmoidal Networks via Spiking Neurons

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Abstract
We show that networks of relatively realistic mathematical models for biological neurons in principle can simulate arbitrary feedforward sigmoidal neural nets in a way that has previously not been considered. This new approach is based on temporal coding by single spikes (respectively by the timing of synchronous firing in pools of neurons) rather than on the traditional interpretation of analog variables in terms of firing rates. The resulting new simulation is substantially faster and hence more consistent with experimental results about the maximal speed of information processing in cortical neural systems. As a consequence we can show that networks of noisy spiking neurons are "universal approximators" in the sense that they can approximate with regard to temporal coding any given continuous function of several variables. This result holds for a fairly large class of schemes for coding analog variables by firing times of spiking neurons. This new proposal for the possible organization of computations in networks of spiking neurons systems has some interesting consequences for the type of learning rules that would be needed to explain the self-organization of such networks. Finally, the fast and noise-robust implementation of sigmoidal neural nets by temporal coding points to possible new ways of implementing feedforward and recurrent sigmoidal neural nets with pulse stream VLSI.