Supervised learning in N-tuple neural networks

An N-tuple Neural Network (NNN) is described in which each node fires selectively to its own table of binary trigger patterns. Each node receives input from k input terminals. Supervised learning is used with specially constructed problems: the system is taught to map specific instances of an input set onto specific instances of an output set. Learning is achieved by: (1) calculating a global error term (how far the set of actual outputs differs from the desired set of outputs); (2) either changing the connections between input terminals and N-tuple nodes, or by changing the trigger patterns that the node fires to; (3) re-calculating the global error term, and retaining the changes to the network if the error is less than in (1). Steepest descent optimisation described in (3), is compared with simulated annealing optimisation. Simulated annealing gives better solutions. Other results are that as connectivity k increases the number of possible solutions increases, but the number of possible non-solutions increases even faster. Simulated annealing is particularly helpful when the relative difficulty (ratio of search to solution) increases. In randomly chosen network configurations there is less entropy in the output than there is in the input to the system. When output is re-cycled as input, NNN either cycles or reaches an end-point. When solving complex I/0 maps the system counteracts this trend by systematically increasing its sensitivity. Predicativity can be improved by combining the results of two or more independent NNN models