Egri, L., & Shultz, T. R.
(2006). A compositional neural-network solution to prime-number testing. *Proceedings of the Twenty-eighth Annual
Conference of the Cognitive Science Society* (pp. 1263-1268).

A long-standing difficulty for connectionism has been to
implement compositionality, the idea of building a knowledge representation out
of components such that the meaning arises from the meanings of the individual
components and how they are combined. Here we show how a neural-learning
algorithm, knowledge-based cascade-correlation (KBCC), creates a compositional
representation of the prime-number concept and uses this representation to
decide whether its input *n* is a prime
number or not. KBCC conformed to a basic prime-number testing algorithm by
recruiting source networks representing division by prime numbers in order from
smallest to largest prime divisor up to √*n*. KBCC learned how to test prime numbers faster and generalized
better to untrained numbers than did similar knowledge-free neural learners.
The results demonstrate that neural networks can learn to perform in a
compositional manner and underscore the importance of basing learning on
existing knowledge.

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