One to Many?

[tap@nmsu.csnet]

It seems that what you want could be supplied by any
associative memory that was capable of pattern completion.
Examples are Hopfield networks, Willshaw networks, and
Anderson's "Brain state in a box" networks.  These networks
are all best used for this purpose as recurrent relaxation
networks, in contrast to the feed-forward networks you seem
to have considered.

To see that these can be used to store a one-to-many
mapping, let A, B, etc. be bit-vectors and then
consider storing the following vectors:

AP
AQ
BR
BS
BT

Now, if A_ (where '_' means zero or random) was used as a
key then there are two patterns which *might* be retrieved;
AP or AQ, but *only one* of these *would* be retreived in a
*particular* relaxation. If B_ was used as a key there are
three patterns which might be retrieved.

Another way of putting this is that there are multiple
attractors which have A as part of their description.  There
might be some problems with trying to make different
attractors out of states which are very close, but there are
ways to cope with this.

Kawamoto (Alan H. Kawamoto, 1986, "Resolution of Lexical
Ambiguity Using a Network that Learns", Dept. of Psychology,
CMU) used a brain state in a box model for associating
spelling, phonetic, part-of-speech, and "semantic"
information about words.  The system coped with ambiguity,
so two different words could have the same spelling, and the
initial perturbations of the system ("context") would
determine which state the system settled to.  If there were
no initial perturbations, then the system would settle to
the state it had been most frequently trained on.

Easier-to-find descriptions of other associative networks
can be found in the PDP books, for example, the
room-"schema" example of Rumelhart, Smolensky, McClelland,
and Hinton in chapter 14.

Tony Plate


-----------------------------
Tony Plate
Computing Research Laboratory
Box 30001
New Mexico State University
Las Cruces, New Mexico 88003
(505) 646-5948
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