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NeuroCOLT
Technical Report NC-TR-96-016
On
the Computational Power of Noisy Spiking Neurons
Wolfgang
Maass
Institute for Theoretical Computer Science
Technische Universitaet Graz
Austria
Abstract
This article provides some first results about the computational power
of neural networks that are based on a neuron model which is acceptable
to many neurobiologists as being reasonably realistic for a biological
neuron. Biological neurons communicate via spike-trains, i.e.
via sequences of stereotyped pulses (``spikes'') that encode information
in their time-differences (``temporal coding''). In addition it is
wellknown that biological neurons are quite ``noisy'', i.e. the precise
times when they ``fire'' (and thereby issue a spike) depend not only
on the incoming spike-trains, but also on various types of ``noise''.
It has remained unknown whether one can in principle carry out reliable
digital computations with noisy spiking neurons. This article presents
rigorous constructions for simulating in real-time arbitrary given
boolean circuits and finite automata with arbitrarily high reliability
by networks of noisy spiking neurons. In addition we show that
with the help of ``shunting inhibition'' such networks can simulate
in real-time any McCulloch-Pitts neuron (or ``threshold gate''), and
therefore any multilayer perceptron (or ``threshold circuit'') in
a reliable manner. These constructions provide a possible explanation
for the fact that biological neural systems can carry out quite complex
computations within 100 msec. It turns out that the assumption
that these constructions require about the shape of the EPSP's and
the behaviour of the noise are surprisingly weak.
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