The N-N-N conjecture in ART1

The authors consider the ART1 neural network architecture introduced by G.A. Carpenter and S. Grossberg (Comput. Vis., Graph., and Image Process. vol.37, 54-115, 1987). In their original paper, Carpenter and Grossberg made the following conjecture. In the fast learning case if the F₂ layer in ART1 has at least N nodes, then each member of a list of N input patterns presented cyclically at the F₁ layer of ART1 will have direct access to an F₂ layer nodes after at most N list representations. It is demonstrated that the conjecture is not valid for certain large L values, where L is a network parameter associated with the adaptation of the bottom-traces in ART1. It is noted that previous work has shown the conjecture to be true for small L values