### ASA 124th Meeting New Orleans 1992 October

## 3aSP8. Iterative algebraic learning for language acquisition.

**K. Farrell
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R. J. Mammone
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*Rutgers Univ., CAIP Ctr., Core Bldg., Frelinghuysen Rd., Piscataway, NJ
08855
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**A. L. Gorin
**

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*AT&T Bell Labs., Murray Hill, NJ 07974
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A new iterative approach to adaptive language acquisition is presented.
Prior methods for adaptive language acquisition have used statistical
associations to determine the connection between words and actions. However,
the performance of these methods degrades when dealing with small-sample
statistics. An alternative approach for language acquisition has been recently
developed, which circumvents the problems of small-sample statistics. This
alternative approach consists of modeling the language acquisition problem as a
linear system of equations (i.e., algebraic learning), where each equation
represents a sentence. The pseudoinverse solution for this linear system of
equations, as obtained by a singular value decomposition (SVD), has been found
to provide connection weights that are less subject to the effects of
small-sample statistics. However, the batch-mode form and computational
requirements of the SVD make it unsuitable for adaptive on-line language
acquisition. A logical method for overcoming this limitation is to iteratively
solve the linear system of equations. An iterative approach based on this
concept is now presented. The iterative approach consists of solving for the
connection weights on a ``sentence-by-sentence'' basis as opposed to requiring
a block of sentences as in the SVD approach. The iterative approach is shown to
converge to a pseudoinverse solution. The iterative approach provides
significant improvement over the SVD approach due to the availability of
on-line training and in addition provides improved generalization. Techniques
for iterative training and simulation results are discussed.