Symmetry and Network Structure

摘要

In this paper, the auto-association problem is discussed using group theoretical methods. Considering the symmetry group of a given set of test sequences, it is shown to be possible to construct a class of neural networks acting as auto-associators on this set. It turns out that the symmetry of the network structure is already determined by the symmetries of the set of test sequences, indicating that learning a set of elements applied is concerned with finding invariant relations inherent in this set. Moreover, the main result offers the possibility, to construct all optimal network structures and, hence, to decide whether a solution found by a particular learning algorithm is optimal or not.