New file in neuroprose

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New file in neuroprose:

          FTP-host: archive.cis.ohio-state.edu
          FTP-filename: /pub/neuroprose/wolpert.field-comp.ps.Z




A Computationally Universal Field Computer That is Purely Linear


	by D. H. Wolpert and B. J. Maclennan


Abastract: As defined in MacLennan (1987), a "field computer" is a
(spatial) continuum-limit neural net.  This paper investigates field
computers whose dynamics is also continuum-limit, being governed by a
purely linear integro-differential equation. Such systems are
motivated both as a means of studying neural nets and as a model for
cognitive processing. As this paper proves, such systems are
computationally universal. The ``trick'' used to get such universal
nonlinear behavior from a purely linear system is quite similar to the
way nonlinear macroscopic physics arises from the purely linear
microscopic physics of Schrodinger's equation. More precisely, the
``trick'' involves two parts. First, the kind of field computer
studied in this paper is a continuum-limit threshold neural net. That
is, the meaning of the system's output is determined by which neurons
have an activation exceeding a threshold (which in this paper is taken
to be 0), rather than by the actual activation values of the neurons.
Second, the occurrence of output is determined in the same
thresholding fashion; output is available only when certain "
output-flagging" neurons exceed the threshold, rather than after a
certain fixed number of iterations of the system. In addition to
proving and discussing their computational universality, this paper
cursorily investigates the dynamics of these kinds of systems.




INDEX:  wolpert.field-comp.ps.Z
	28 pages
	A computationally universal continuum-limit neural net which
is purely linear.


Instructions for retrieval: Log on to the FTP-host as anonymous, type
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Thanks to Jordan Pollack for maintaining this archive.


David Wolpert
The Santa Fe Institute
1660 Old Pecos Trail, Suite A 
Santa Fe, NM, 87501, USA

dhw at santafe.edu
(505) 988-8814 (voice)
(505) 982-0565 (fax)