# Fast sigmoidal networks via spiking neurons

### Abstract:

We show that networks of relatively realistic mathematical models for
biological neurons can in principle simulate arbitrary feedforward sigmoidal
neural nets in a way which 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 via temporal coding points to possible new ways of implementing
feedforward and recurrent sigmoidal neural nets with pulse stream VLSI.

**Reference:** W. Maass.
Fast sigmoidal networks via spiking neurons.
*Neural Computation*, 9:279-304, 1997.