Positive and negative circuits in discrete neural networks

Julio Aracena; Jacques Demongeot; Eric Goles

doi:10.1109/TNN.2003.821555

Positive and negative circuits in discrete neural networks

Julio Aracena, Jacques Demongeot, Eric Goles

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

64 Scopus citations

Abstract

We study the relationships between the positive and negative circuits of the connection graph and the fixed points of discrete neural networks (DNNs). As main results, we give necessary conditions and sufficient conditions for the existence of fixed points in a DNN. Moreover, we exhibit an upper bound for the number of fixed points in terms of the structure and number of positive circuits in the connection graph. This allows the determination of the maximum capacity for storing vectors in DNNs as fixed points depending on the architecture of the network.

Original language	English
Pages (from-to)	77-83
Number of pages	7
Journal	IEEE Transactions on Neural Networks
Volume	15
Issue number	1
DOIs	https://doi.org/10.1109/TNN.2003.821555
State	Published - Jan 2004
Externally published	Yes

Keywords

Discrete neural networks (DNNs)
Fixed points
Graph
Positive and negative circuits
Positive feedback vertex sets

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10.1109/TNN.2003.821555

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title = "Positive and negative circuits in discrete neural networks",

abstract = "We study the relationships between the positive and negative circuits of the connection graph and the fixed points of discrete neural networks (DNNs). As main results, we give necessary conditions and sufficient conditions for the existence of fixed points in a DNN. Moreover, we exhibit an upper bound for the number of fixed points in terms of the structure and number of positive circuits in the connection graph. This allows the determination of the maximum capacity for storing vectors in DNNs as fixed points depending on the architecture of the network.",

keywords = "Discrete neural networks (DNNs), Fixed points, Graph, Positive and negative circuits, Positive feedback vertex sets",

author = "Julio Aracena and Jacques Demongeot and Eric Goles",

note = "Funding Information: Manuscript received May 30, 2001; revised July 30, 2002 and April 28, 2003. The work of J. Aracena and E. Goles was supported in part by the FONDAP program on Discrete Mathematics and French Cooperation.",

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AU - Demongeot, Jacques

AU - Goles, Eric

N1 - Funding Information: Manuscript received May 30, 2001; revised July 30, 2002 and April 28, 2003. The work of J. Aracena and E. Goles was supported in part by the FONDAP program on Discrete Mathematics and French Cooperation.

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Y1 - 2004/1

N2 - We study the relationships between the positive and negative circuits of the connection graph and the fixed points of discrete neural networks (DNNs). As main results, we give necessary conditions and sufficient conditions for the existence of fixed points in a DNN. Moreover, we exhibit an upper bound for the number of fixed points in terms of the structure and number of positive circuits in the connection graph. This allows the determination of the maximum capacity for storing vectors in DNNs as fixed points depending on the architecture of the network.

AB - We study the relationships between the positive and negative circuits of the connection graph and the fixed points of discrete neural networks (DNNs). As main results, we give necessary conditions and sufficient conditions for the existence of fixed points in a DNN. Moreover, we exhibit an upper bound for the number of fixed points in terms of the structure and number of positive circuits in the connection graph. This allows the determination of the maximum capacity for storing vectors in DNNs as fixed points depending on the architecture of the network.

KW - Discrete neural networks (DNNs)

KW - Fixed points

KW - Graph

KW - Positive and negative circuits

KW - Positive feedback vertex sets

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VL - 15

SP - 77

EP - 83

JO - IEEE Transactions on Neural Networks

JF - IEEE Transactions on Neural Networks

IS - 1

ER -

Positive and negative circuits in discrete neural networks

Abstract

Keywords

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