What Can Boolean Networks Learn ?

We study the generalization abilities of networks that are composed of boolean nodes, i.e., nodes that implement only basic boolean functions: and, or and not. The majority of the network learning algorithms proposed so far generate networks where each node implements a threshold function and are inappropriate for the generation of boolean networks from training set data. We propose an algorithm that, given a training set, generates a boolean network of small complexity that is compatible with the training set. The algorithm, inspired in techniques used in the logic synthesis community for the design of VLSI circuits, generates both the connectivity pattern and the architecture of the network. Furthermore, the resulting network can be implemented in silicon in a straightforward way. Experimental results obtained in a set of problems from the machine learning literature show that the generalization performed by boolean networks synthesized with this algorithm compares favorably with the generalization obtained by alternative learning algorithms. Some of these results and examples of the layout of networks obtained using the algorithm are presented and discussed.