Symmetries in neural networks: a linear group approach.

Journal of Physics A 26 (1993), 3159-3164.

Neural networks storing Hadamard patterns have been completely classified with respect to permutation symmetry. The symmetry group of the Hadamard patterns is found to be isomorphic to $GL(n,{\bf F}_2)$, and the symmetry groups of the networks are explicitly constructed for the most important classes. The volumes of different equivalence classes have been calculated.