PERBOOL: Learning Boolean Functions with Back-Propagation

Abstract

This program illustrates the function of a feed-forward layered neural network as described in Chapts. 5–7. Its task is to learn an arbitrary Boolean function of a small number of Boolean variables. This is achieved by a three-layer feed-forward network which is trained by a gradient-descent method, i.e. by the rule of error back-propagation. The network consists of an input layer σ _k , 1 ≤ k ≤ n _in, a hidden layer s _j , 1 ≤ j ≤ n _hid, and an output layer S _i , 1 ≤ i ≤ n _out. The synaptic connections are ${\bar w_{jk}}$ from the input to the hidden layer, and w _ij from the hidden to the output layer. In addition there are activation thresholds ${\bar \vartheta _j}$ and ϑ _i . The neurons have two activation values chosen as −1 and +1 (the transformation to the values 0 and 1 commonly used to represent binary numbers is trivial).