Algebriac rules

[Lokendra Shastri]

Dear Connectionists:

The following technical report may be of interest to some of you.
Best wishes.

Lokendra Shastri
-------

	A Spatiotemporal Connectionist Model of Algebraic Rule-Learning

		Lokendra Shastri and Shawn Chang
			 TR-99-011
			July, 1999
	         Interntational Computer Science Institute
	           Berkeley, CA 94707

        Recent experiments by Marcus, Vijaya, Rao, and Vishton suggest that
        infants are capable of extracting and using abstract algebraic rules
        such as ``the first item X is the same as the third item Y''. Such 
        an algebraic rule represents a relationship between placeholders or
        variables for which one can substitute arbitrary values. As Marcus 
        et al. point out, while most neural network models excel at capturing
        statistical patterns and regularities in data, they have difficulty
        in extracting algebraic rules that generalize to new items. We
        describe a connectionist network architecture that can readily
        acquire algebraic rules. The extracted rules are not tied to features
        of words used during habituation, and generalize to new words.
        Furthermore, the network acquires rules from a small number of
        examples, without using negative evidence, and without pretraining.
        A significant aspect of the proposed model is that it identifies a 
        sufficient set of architectural and representational conditions that
        transform the problem of learning algebraic rules to the much simpler
        problem of learning to detect coincidences within a spatiotemporal
        pattern. Two key representational conditions are (i) the existence of
        nodes that encode serial position within a sequence and (ii) the use
        of temporal synchrony for expressing bindings between a positional
        role node and the item that occupies this position in a given
        sequence. This work suggests that even abstract algebraic rules can
        be grounded in concrete and basic notions such as spatial and temporal
        location, and coincidence.

Available at:

http://www.icsi.berkeley.edu/~shastri/psfiles/tr-99-011.ps.gz
OR
http://www.icsi.berkeley.edu/~shastri/psfiles/tr-99-011.pdf




Lokendra Shastri
International Computer Science Institute
1947 Center Street, Suite 600
Berkeley, CA 94704

shastri at icsi.berkeley.edu
http://www.icsi.berkeley.edu/~shastri

Phone:	(510) 642-4274 ext 310
FAX:	(510) 643-7684