Building a Family of Neural Networks using Symmetry as a Foundation

Abstract

In order to perform a function mapping task, a neural network needs two supporting mechanisms: an input and an output training vector, and a training regime. A new approach is proposed to generating a family of neural networks for performing a set of related functions. Within a family, only one network needs to be trained to perform an input-output function mapping task and other networks can be derived from this trained base network without training. The base net thus acts as a generator of the derived nets. The proposed approach builds on three mathematical foundations: (1) symmetry for defining the relationship between functions; (2) weight transformations for generating a family of networks; (3) Euclidian distance function for measuring the symmetric relationships between the related functions. The proposed approach provides a formal foundation for systemic information reuse in ANNs.