An experimental comparison of some algorithms for self-organizing systems

Several alternative systems of "adjustable logic" are available for use in a self-organizing system having discrete channels as inputs and outputs. For example, a device might consist of a network of McCulloch-Pitts neurons with variable thresholds, or use "summation logic" (refs. 1, 2) with variable weights attached to the input signals. A further possibility is described by Kochen (ref, 3). The system of "adjustable logic" used in the present study depends on the evaluation of a polynomial function of the input signals, with a facility for adjustment of the coefficients of the polynomial terms. The output is a single binary signal of value 0 or 1 depending on whether the polynomial sum is negative or positive. Means are provided for introducing new terms if certain criteria show them to be advantageous, and of eliminating terms which are redundant. It is trivial to show that any logical function whatever can be represented by a polynomial in this way. This system of logic was originally selected because polynomial functions can also be employed in self-organizing systems for continuous variables. (refs. 4, 5, 6, 7). The system with discrete signals was intended to illustrate certain strategies which are applicable to the continuous case. Important differences, however, do exist between the discrete and continuous cases, and further work on continuous systems is in progress. Nevertheless, the work on discrete systems has produced a number of interesting conclusions. The facility whereby extra terms can be added to the polynomial function is similar to the capacity for amoebalike growth shown by the "Janet" program due to Foulkes (ref. 8).