Evolving A-Type Artificial Neural Networks

We investigate Turing's notion of an A-type artificial neural network. We study a refinement of Turing's original idea, motivated by work of Teuscher, Bull, Preen and Copeland. Our A-types can process binary data by accepting and outputting sequences of binary vectors; hence we can associate a function to an A-type, and we say the A-type {\em represents} the function. There are two modes of data processing: clamped and sequential. We describe an evolutionary algorithm, involving graph-theoretic manipulations of A-types, which searches for A-types representing a given function. The algorithm uses both mutation and crossover operators. We implemented the algorithm and applied it to three benchmark tasks. We found that the algorithm performed much better than a random search. For two out of the three tasks, the algorithm with crossover performed better than a mutation-only version.