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). Mahwah, NJ: Erlbaum.



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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