Optimal discrete perceptrons for graded learning

Perceptrons, the original artificial neural network structure, are finite in number for a given discrete-valued problem, and can be exhaustively enumerated. The great benefit of exhaustive enumeration is that one has a complete distribution of empirical results. Thus, the global optimum is identified, any competitors or multiple solutions are known, and the unusualness of any solution can be assessed. As the complete sample distribution of candidate models is available, model selection, inference, and prediction can be performed with a low level of supervision, that is, by graded learning. The enumeration procedure is described. Although NP-complete, the number of distinct perceptrons is tractable for a low number of inputs. An example application of the method is demonstrated for the task of learning investment rules for the US Treasury Bond market, with encouraging results