computing with noisy spiking neurons: paper in neuroprose

[Wolfgang Maass]

The file maass.noisy-spiking.ps.Z is now available for copying
from the Neuroprose repository. This is a 9-page long paper.
Hardcopies are not available.

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



          On the Computational Power of Noisy Spiking Neurons

                            Wolfgang Maass
              Institute for Theoretical Computer Science
                     Technische Universitaet Graz
                         Klosterwiesgasse 32/2
                         A-8010 Graz, Austria
                    e-mail: maass at igi.tu-graz.ac.at


                               Abstract

This article provides positive results about the computational power
of neural networks that are based on a neuron model ("noisy spiking
neuron") which is acceptable to most neurobiologists as being  
reasonably realistic for a biological neuron. In fact:
this model tends to underestimate the computational capabilities
of a biological neuron, since it simplifies dendritic integration.
 
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". There is some "jitter" in their
firing times, and neurons (as well as synapses) my fail to fire with 
a certain probability.

It has remained unknown whether one can in principle carry out reliable
computation in networks of noisy spiking neurons. This article presents
rigorous  constructions  for simulating  in real-time  arbitrary  given
boolean circuits and finite automata on such networks.

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.  In view of the tremendous
computational power of threshold circuits (even with few layers),
this construction provides a possible explanation for the fact 
that biological neural systems can carry out quite complex 
computations within 100 msec.

It turns out that the assumptions that these constructions require about
the shape of the EPSP's and the behaviour of the noise are surprisingly
weak.

This article continues the related work from NIPS '94, where we had
considered computations on networks of spiking neurons without noise.
The current paper will appear in 
Advances in Neural Information Processing Systems,  vol. 8  
(=  Proc. of NIPS '95) .


************ How to obtain a copy  *****************

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.noisy-spiking.ps.Z
ftp> quit
unix> uncompress maass.noisy-spiking.ps.Z
unix> lpr  maass.noisy-spiking.ps (or what you normally do to print PostScript)