Fibring Neural Networks

Abstract

As we have seen in Chaps. 4 to 7, neural networks can deal with a number of reasoning mechanisms. In many applications these need to be combined (fibred) into a system capable of dealing with the different dimensions of a reasoning agent. In this chapter, we introduce a methodology for combining neural-network architectures based on the idea of fibring logical systems [101]. Fibring allows one to combine different logical systems in a principled way. Fibred neural networks may be composed not only of interconnected neurons but also of other networks, forming a recursive architecture. A fibring function then defines how this recursive architecture behaves by defining how the networks in the ensemble relate to each other, typically by allowing the activation of neurons in one network (A) to influence the change of weights in another network (B). Intuitively, this can be seen as training network B at the same time as network A is running. Although both networks are simple, standard networks, we can show that, in addition to being universal approximators like standard feedforward networks, fibred neural networks can approximate any polynomial function to any desired degree of accuracy, thus being more expressive than standard feedforward networks.