Connectionist symbol processing & work by Baxter

[Danny L. Silver]

Along the lines of Dr. Zhu, I would like to point out the 
important work of Jon Baxter concerning the "learning of internal
represenations" in which he develops a "canonical distortion measure"
The CDM is in fact a metric over the input space defined by the 
probability distribution over a domain of tasks (e.g. character recognition)
each of which shares the input space.  The metric can be used to measure 
the similarity of input vectors.

The important aspect of Baxter's work  is that he shows formally and 
demonstrates imperically that the CDM for a particular task (or environmental)
domain can be LEARNED to the desired level of accuracy 
if the learner samples sufficiently from the domain of tasks.
i.e if the learner "experiences" the environment long enough and well enough.
Once learned  this CDM metric can be used to facilitate learning 
any new task from the domain - thus it can be consider a process of
"learning to learn".
Baxter, in fact demonstrates how the CDM metric can be  
learned within the hidden node representations of a neural network
for a simple task domain. 

Based on this .. I would conclude that the facility of symbolic representation
and logical metrics is largely a function of the domain of tasks
under consideration and not necessarily THE best representation or  metric.

For details please refer to:
Jonathan Baxter. Learning Internal Representations. PhD Thesis, 
Dept. Mathematics and Statss, The Flinders University of South Australia, 1995.
Draft copy available in Neuroprose Archive -
/pub/neuroprose/Thesis/baxter.thesis.ps.Z

Jonathan Baxter. The Canonical Distortion Measure for Vector Quantization
and Function Approximation. Learning to Learn, edited by Sebastian Thrun and
Lorien Pratt, 1998, Kluwer Academic Publishers, p.159-179


Cheers  .. Danny Silver
-- 


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=  Daniel L. Silver    University of Western Ontario, London, Canada    =
=                      N6A 3K7 - Dept. of Comp. Sci.                    =
=  dsilver at csd.uwo.ca  H: (902)582-7558   O: (902)494-1813              =
=  WWW home page ....  http://www.csd.uwo.ca/~dsilver                   =
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