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In this paper, the auto-association problem is discussed using group theoreticalmethods. Considering the symmetry group of a given set of test sequences, itis shown to be possible to construct a class of neural networks acting asauto-associators on this set. It turnsout that the symmetry of the network structure is already determined by thesymmetries 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 asolution found by a particular learning algorithm is optimal or not.