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Title: Tensor Manipulation Networks: Connectionist and Symbolic Approaches
to Comprehension, Learning, and Planning

Availability: This tech report is available from both the Hughes Research
Laboratories and The UCLA AI Lab.  Request for mailing outside the US
should be sent to UCLA, because Hughes requires some non-trivial paper
work for such mailings.  Otherwise, please flip coin so that we may
stochastically equalize mailing costs.

  From UCLA: valerie at cs.ucla.edu
  From Hughes: tech-reports at aic.hrl.hac.com

Abstract:

It is a controversial issue as to which of the two approaches, the 
Physical Symbol System Hypothesis (PSSH) or Parallel Distributed 
Processing (PDP), is a better characterization of the mind.  At the root 
of this controversy are two questions:  (1) What sort of computer is 
the brain,  and (2) what sort of programs run on that computer?  

What is presented here is a theory which bridges the apparent gap 
between PSSH and PDP approaches.  In particular, a computer is 
presented that adheres to constraints of PDP computation (a network 
of simple processing units), and a program is presented which at first 
glance is only suitable for a PSSH computer but which runs on a PDP 
computer.  The approach presented here, vertical integration, shows 
how to construct PDP computers that can process symbols and how to 
design symbol systems so that they will run on more brain-like 
computers.

The type of computer presented here is called a tensor manipulation 
network.  It is a special type of PDP network where the operation of 
the network is interpreted as manipulations of high rank tensors 
(generalized vector outer products).  The operations on tensors in 
turn are interpreted as operations on symbol structures.  A wide 
range of tensor manipulation architectures are presented with the 
goal of inducing constraints on the symbol structures that it is 
possible for the mind to possess.

As a demonstration of what is possible with constrained symbol 
structures, a program, CRAM, is presented which uses and acquires 
thematic knowledge.  CRAM is able to read, in English, single-
paragraph, fable-like stories and either give a thematically relevant 
summary or generate planning advice for a character in the story.  

CRAM is also able to learn new themes through combination of 
existing, known themes encountered in the fables CRAM reads.
CRAM demonstrates that even the most symbolic cognitive tasks can 
be accomplished with PDP networks, if the networks are designed 
properly.