The N-N-N conjecture in ART1

Michael Georgiopoulos; Gregory L. Heileman; Juxin Huang

doi:10.1016/S0893-6080(05)80135-2

The N-N-N conjecture in ART1

Michael Georgiopoulos, Gregory L. Heileman, Juxin Huang

Research output: Contribution to journal › Article › peer-review

9 Scopus citations

Abstract

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 language	English (US)
Pages (from-to)	745-753
Number of pages	9
Journal	Neural Networks
Volume	5
Issue number	5
DOIs	https://doi.org/10.1016/S0893-6080(05)80135-2
State	Published - 1992
Externally published	Yes

Keywords

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

ASJC Scopus subject areas

Cognitive Neuroscience
Artificial Intelligence

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10.1016/S0893-6080(05)80135-2

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@article{0bfeb2a746814d4ba12f279987501331,

title = "The N-N-N conjecture in ART1",

abstract = "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.",

keywords = "ART1, Adaptive resonance theory, Learning, Neural network, Pattern recognition, Self-organization",

author = "Michael Georgiopoulos and Heileman, {Gregory L.} and Juxin Huang",

note = "Funding Information: We assume that the reader is familiar with the ART 1 architecture introduced by Carpenter and Grossberg (1987), as well as the terminology and theorems contained therein. However, it is worth mentioning certain results regarding ART1 that are closely related to the work presented in this paper. These results appear as Theorems 5 and 6 in Carpenter and Grossberg (1987), Acknowledgments: This research was supported in part by a grant from the Florida High Technology and Industry Council, and in part by a grant from Sandia National Laboratoriesu nder Contract 3-24026.",

year = "1992",

doi = "10.1016/S0893-6080(05)80135-2",

language = "English (US)",

volume = "5",

pages = "745--753",

journal = "Neural Networks",

issn = "0893-6080",

publisher = "Elsevier Ltd",

number = "5",

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TY - JOUR

T1 - The N-N-N conjecture in ART1

AU - Georgiopoulos, Michael

AU - Heileman, Gregory L.

AU - Huang, Juxin

N1 - Funding Information: We assume that the reader is familiar with the ART 1 architecture introduced by Carpenter and Grossberg (1987), as well as the terminology and theorems contained therein. However, it is worth mentioning certain results regarding ART1 that are closely related to the work presented in this paper. These results appear as Theorems 5 and 6 in Carpenter and Grossberg (1987), Acknowledgments: This research was supported in part by a grant from the Florida High Technology and Industry Council, and in part by a grant from Sandia National Laboratoriesu nder Contract 3-24026.

PY - 1992

Y1 - 1992

N2 - 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.

AB - 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.

KW - ART1

KW - Adaptive resonance theory

KW - Learning

KW - Neural network

KW - Pattern recognition

KW - Self-organization

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UR - http://www.scopus.com/inward/citedby.url?scp=0026923906&partnerID=8YFLogxK

U2 - 10.1016/S0893-6080(05)80135-2

DO - 10.1016/S0893-6080(05)80135-2

M3 - Article

AN - SCOPUS:0026923906

SN - 0893-6080

VL - 5

SP - 745

EP - 753

JO - Neural Networks

JF - Neural Networks

IS - 5

ER -

The N-N-N conjecture in ART1

Abstract

Keywords

ASJC Scopus subject areas

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