A Compositional Neural-network Solution to Prime-number Testing

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.