Turing Machines and Connectionist networks

[Jordan B Pollack]

I disagree with Jay, and have disagreed since before I read (and
quoted in my thesis) his bit about paper and pencil which appeared in
chapter 4.  Certainly, while isomorphism to the STRUCTURE to a Turing
machine should not be a concern of connectionist research, the
question of the FUNCTIONAL isomorphism (in idealized models) is a real
concern. Especially in language processing, where fixed-width systems
with non-recursive representations aren't even playing the game!
Humans don't need paper and pencil to understand embedded clauses.  At
CMU Summer School 1986, I pointed out these generative capacity limits
in all known connectionist models, and predicted that "the first such
model to attract the attention of Chomskyists would get the authors
shot out at the knees."

While psychological realism and robustness are not built-in features
of conventional stored program computers, recursive representations and
computations are "of the nature" of cognitive and real-world tasks, and
cannot be wished away simply because we don't YET know how to achieve
them simultaneously with the good qualities of existing connectionist
architectures.

I certainly agree with Jay that recursive-like powers can emerge from
a massively parallel iterative "microstructure". Witness Wolfram's
automata or Mandelbrot's set. Neither are finite OR probabilistic,
however, which may give us a clue...

Jordan Pollack                            Assistant Professor
CIS Dept/OSU                              Laboratory for AI Research
2036 Neil Ave                             Email: pollack at cis.ohio-state.edu
Columbus, OH 43210                        Fax/Phone: (614) 292-4890