The N-N-N conjecture in ART1

Michael Georgiopoulos, Gregory L. Heileman, Juxin Huang

Research output: Contribution to journalArticlepeer-review

9 Scopus citations


In this paper we consider the ART1 neural network architecture introduced by Carpenter and Grossberg. 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 node after at most N list presentations. In this paper, we demonstrate that the conjecture is not valid for certain large L values, where L is a network parameter associated with the adaptation of the bottom-up traces in ART1. It is worth noting that previous work has shown the conjecture to be true for small L values.

Original languageEnglish (US)
Pages (from-to)745-753
Number of pages9
JournalNeural Networks
Issue number5
StatePublished - 1992
Externally publishedYes


  • ART1
  • Adaptive resonance theory
  • Learning
  • Neural network
  • Pattern recognition
  • Self-organization

ASJC Scopus subject areas

  • Cognitive Neuroscience
  • Artificial Intelligence


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