Fibring Neural Networks

Artur S. d’Avila Garcez and Dov M. Gabbay

Neural-symbolic systems are hybrid systems that integrate symbolic logic and neural networks. The goal of neural-symbolic integration is to benefit from the combination of features of the symbolic and connectionist paradigms of artificial intelligence. This paper introduces a new neural network architecture based on the idea of fibring logical systems. 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 must behave 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 that one runs network A. We 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. Keywords: Neural-Symbolic Integration, Fibring Systems, Recursion.

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