2 papers on spiking neurons in neuroprose

[Wolfgang Maass]

First paper:
************

FTP-host: archive.cis.ohio-state.edu
FTP-filename: /pub/neuroprose/maass.spiking-details.ps.Z

The file maass.spiking-details.ps.Z is now available for copying
from the Neuroprose repository. This is a 41-page long paper.
Hardcopies are not available.


        LOWER BOUNDS FOR THE COMPUTATIONAL POWER OF 

                NETWORKS OF SPIKING NEURONS

                            by
                       Wolfgang Maass
  
         Institute for Theoretical Computer Science
               Technische Universitaet Graz
                   A-8010 Graz, Austria
              e-mail: maass at igi.tu-graz.ac.at

                         Abstract:

We explore the computational power of formal models for
networks of spiking neurons (often referred to as "integrate-and-fire
neurons"). These neural net models are closer related 
to computations in biological neural systems than the more traditional 
models, since they allow an encoding of information in the timing of 
single spikes (not just in firing rates). 
Our formal model is closely related to the "spike-response model" that
was previously introduced by Gerstner and van Hemmen.

It turns out that the structure of computations in models for 
networks of spiking neurons is quite different from that of
computations in analog (sigmoidal) neural nets. 
In particular it is shown in our paper in a rigorous way 
that simple operations on phase-differences between spike-trains 
provide a very powerful computational tool, that can in principle
be used to carry out highly complex computations 
on a small network of spiking neurons.
We also show in this paper that rather weak assumptions about 
the shape of response-and threshold-functions of spiking neurons
are sufficient in order to employ them for such computations.

An extended abstract of this paper had already been posted in 
November 1994 (it appears in the Proc. of NIPS 94).
In the meantime many have asked me for details
of the constructions, and hence I am now also posting in neuroprose
this detailed version (which appears in Neural Computation). 
A companion paper with detailed proofs for the upper bounds,
will become available in the fall. 
----------------------------------------------------------------------

Second paper:
*************
FTP-host: archive.cis.ohio-state.edu
FTP-filename: /pub/neuroprose/maass.shape.ps.Z

The file maass.shape.ps.Z is now available for copying
from the Neuroprose repository. This is a 6-page long paper.
Hardcopies are not available.


   ON THE RELEVANCE OF THE SHAPE OF POSTSYNAPTIC POTENTIALS 

        FOR THE COMPUTATIONAL POWER OF SPIKING NEURONS

                            by
             Wolfgang Maass  and   Berthold Ruf
  
         Institute for Theoretical Computer Science
               Technische Universitaet Graz
                   A-8010 Graz, Austria
              e-mail: maass at igi.tu-graz.ac.at
                      bruf at igi.tu-graz.ac.at 
                     

                          Abstract:

Recently one has started to explore silicon models for networks
of spiking neurons, where one employs rectangular (i.e.
piecewise constant) pulses instead of the "smooth" excitatory
postsynaptic potentials (EPSP's) that are employed by biological neurons. 
We show in this paper that models of spiking neurons that employ
rectangular pulses (EPSP's)  have substantial computational
power, and we give a precise characterization of their
computational power in terms of a common benchmark model
from computer science (random access machine). 

This characterization allows us to prove the following somewhat 
surprising result:
Models of networks of spiking neurons with rectangular 
pulses are from the computational point of view 
STRICTLY WEAKER 
than models with "smooth" EPSP's of the type as they are 
observed in biological neurons. 




************ How to obtain a copy of the first paper *************

Via Anonymous FTP:

unix> ftp archive.cis.ohio-state.edu
Name: anonymous
Password: (type your email address)
ftp> cd pub/neuroprose
ftp> binary
ftp> get maass.spiking-details.ps.Z
ftp> quit
unix> uncompress maass.spiking-details.ps.Z
unix> lpr  maass.spiking-details.ps (or what you normally do to print PostScript)


For the second paper proceed analogously 
(but with filename  maass.shape.ps.Z).