*** Please note that the location of the files was changed at the beginning of
** the year, so that any copies you have of the previous instructions should be
* discarded. The new location and instructions are given at the end of the list.
[This posting has been edited to list only those reports relating to
computational neuroscience]
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NeuroCOLT Technical Report NC-TR-96-040:
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The Computational Power of Spiking Neurons Depends on the Shape of
the Postsynaptic Potentials
by Wolfgang Maass, Technische Universitaet Graz, Austria
Berthold Ruf, Technische Universitaet Graz, Austria
Abstract:
Recently one has started to investigate the computational power of
spiking neurons (also called ``integrate and fire neurons''). These are
neuron models that are substantially more realistic from the biological
point of view than the ones which are traditionally employed in
artificial neural nets. It has turned out that the computational power
of networks of spiking neurons is quite large. In particular they have
the ability to communicate and manipulate analog variables in
spatio-temporal coding, i.e.~encoded in the time points when specific
neurons ``fire'' (and thus send a ``spike'' to other neurons).
These preceding results have motivated the question which details of
the firing mechanism of spiking neurons are essential for their
computational power, and which details are ``accidental'' aspects of
their realization in biological ``wetware''. Obviously this question
becomes important if one wants to capture some of the advantages of
computing and learning with spatio-temporal coding in a new generation
of artificial neural nets, such as for example pulse stream VLSI.
The firing mechanism of spiking neurons is defined in terms of their
postsynaptic potentials or ``response functions'', which describe the
change in their electric membrane potential as a result of the firing
of another neuron. We consider in this article the case where the
response functions of spiking neurons are assumed to be of the
mathematically most elementary type: they are assumed to be
step-functions (i.e. piecewise constant functions). This happens to be
the functional form which has so far been adapted most frequently in
pulse stream VLSI as the form of potential changes (``pulses'') that
mimic the role of postsynaptic potentials in biological neural
systems. We prove the rather surprising result that in models without
noise the computational power of networks of spiking neurons with
arbitrary piecewise constant response functions is strictly weaker than
that of networks where the response functions of neurons also contain
short segments where they increase respectively decrease in a linear
fashion (which is in fact biologically more realistic). More precisely
we show for example that an addition of analog numbers is impossible
for a network of spiking neurons with piecewise constant response
functions (with any bounded number of computation steps, i.e. spikes),
whereas addition of analog numbers is easy if the response functions
have linearly increasing segments.
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***************** ACCESS INSTRUCTIONS ******************
The Report NC-TR-96-001 can be accessed and printed as follows
% ftp ftp.dcs.rhbnc.ac.uk (134.219.96.1)
Name: anonymous
password: your full email address
ftp> cd pub/neurocolt/tech_reports
ftp> binary
ftp> get nc-tr-96-001.ps.Z
ftp> bye
% zcat nc-tr-96-001.ps.Z | lpr -l
Similarly for the other technical reports.
Uncompressed versions of the postscript files have also been
left for anyone not having an uncompress facility.
In some cases there are two files available, for example,
nc-tr-96-002-title.ps.Z
nc-tr-96-002-body.ps.Z
The first contains the title page while the second contains the body
of the report. The single command,
ftp> mget nc-tr-96-002*
will prompt you for the files you require.
A full list of the currently available Technical Reports in the
Series is held in a file `abstracts' in the same directory.
The files may also be accessed via WWW starting from the NeuroCOLT
homepage (note that this is undergoing some corrections and may be
temporarily inaccessible):
http://www.dcs.rhbnc.ac.uk/neural/neurocolt.html
Best wishes
John Shawe-Taylor
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