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NeuroCOLT
Technical Report NC-TR-99-040
On the Complexity of Learning for Spiking
Neurons with Temporal Coding
Wolfgang Maass
Institute for Theoretical Computer Science
Technische Universität Graz
Michael Schmitt
Lehrstuhl Mathematik und Informatik
Fakultät für Mathematik
Ruhr-Universität
Bochum
Received:
22-MAR-1999
Abstract
Spiking neurons are models for the
computational units in biological neural systems where information
is considered to be encoded mainly in the temporal patterns of their
activity. In a network of spiking neurons a new set of parameters
becomes relevant which has no counterpart in traditional neural network
models: the time that a pulse needs to travel through a connection
between two neurons (also known as delay of a connection). It is known
that these delays are tuned in biological neural systems through a
variety of mechanisms. In this article we consider the arguable most
simple model for a spiking neuron, which can also easily be implemented
in pulsed VLSI. We investigate the VC dimension of networks of
spiking neurons where the delays are viewed as programmable parameters
and we prove tight bounds for this VC dimension. Thus we get quantitative
estimates for the diversity of functions that a network with fixed
architecture can compute with different settings of its delays. In
particular, it turns out that a network of spiking neurons with $k$
adjustable delays is able to compute a much richer class of functions
than a threshold circuit with $k$ adjustable weights. The results
also yield bounds for the number of training examples that an algorithm
needs for tuning the delays of a network of spiking neurons. Results
about the computational complexity of such algorithms are also given.
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