Turing Machines and Conenctionist networks

[James L. McClelland]

The recent exchanges prompt me to reflect on how much time it's worth
spending on the issue of Turing equivalence.

One of the characteristics of connectionist models is the distinctly
different style of processing and storage that they provide relative
to conventional architectures.  One of the motivations for thinking
that these characteristics might be worth pursuing is that Turing
equivalence is not a guarantee of capturing the kinds of intelligence
that people exhibit but Turing machines do not, such as: Speech
perception, pattern recognition, retrieval of contextually relevant
information from memory, language understanding, and intuitive
thinking.

We need to start thinking about ways of going beyond Turing
equivalence to find tests that can indicate the sufficiency of
mechanisms to exhibit natural cognitive capabilities like those
enumerated above.  Turing equivalence has in my opinion virtually
nothing to do with this matter.  In principle results about what can
be computed using discrete unambiguous sequences of symbols and a
totally infallible, infinite memory will not help us much in
understanding how we cope in real time with mutiple, graded and
uncertain cues.  The need for robustness in performance and learning
in the face of an ambiguous world is not addressed by Turing
equivalence, yet every time we understand a spoken sentence these
issues of robustness arise!

How do humans made of connectoplasm achieve Turing equivalence?  The
equivalence exists at a MACROLEVEL, and should not be sought in the
microstructure (the units and connections).  As whole organisms, we
certainly can compute any computable function.  The procedures that
make up the microstructure of each step in such a computation are, I
would submit, finite and probabilistic.  But we can string sequences
of such steps together, particularly with the aid of real external
memory (pencils and paper, etc), and enough error checking, to compute
anything we want.

More on these and related matters may be found in Chapters 1 and 4 of
Vol 1 and Chapter 14 of Vol 2 of the PDP books.

-- Jay McClelland