Encoding unique global minima in nested neural networks

Abstract

Nested neural networks are constructed from outer products of patterns over (-1,0,1)N, whose nonzero bits define subnetworks and the subcodes stored in them. The set of permissible words, which are network-size binary patterns composed of subcode words that agree in their common bits, is characterized, and their number is derived. It is shown that if the bitwise products of the subcode words are linearly independent, the permissible words are the unique global minima of the Hamiltonian associated with the network.