IEICE TRANSACTIONS on Fundamentals
Some Characteristics of Higher Order Neural Networks with Decreasing Energy Functions
Summary :
This paper describes some dynamical properties of higher order neural networks with decreasing energy functions. First, we will show that for any symmetric higher order neural network which permits only one element to transit at each step, there are only periodic sequences with the length 1. Further, it will be shown that for any higher order neural network, with decreasing energy functions, which permits all elements to transit at each step, there does not exist any periodic sequence with the length being over k + 1, where k is the order of the network. Lastly, we will give a characterization for higher order neural networks, with the order 2 and a decreasing energy function each, which permit plural elements to transit at each step and have periodic sequences only with the lengh 1.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E79-A No.10 pp.1624-1629
- Publication Date
- 1996/10/25
- Publicized
- Online ISSN
- DOI
- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and its Applications (NOLTA))
- Category
- Neural Nets and Human Being
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Hiromi MIYAJIMA, Shuji YATSUKI, Michiharu MAEDA, "Some Characteristics of Higher Order Neural Networks with Decreasing Energy Functions" in IEICE TRANSACTIONS on Fundamentals,
vol. E79-A, no. 10, pp. 1624-1629, October 1996, doi: .
Abstract: This paper describes some dynamical properties of higher order neural networks with decreasing energy functions. First, we will show that for any symmetric higher order neural network which permits only one element to transit at each step, there are only periodic sequences with the length 1. Further, it will be shown that for any higher order neural network, with decreasing energy functions, which permits all elements to transit at each step, there does not exist any periodic sequence with the length being over k + 1, where k is the order of the network. Lastly, we will give a characterization for higher order neural networks, with the order 2 and a decreasing energy function each, which permit plural elements to transit at each step and have periodic sequences only with the lengh 1.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1587/e79-a_10_1624/_p
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@ARTICLE{e79-a_10_1624,
author={Hiromi MIYAJIMA, Shuji YATSUKI, Michiharu MAEDA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Some Characteristics of Higher Order Neural Networks with Decreasing Energy Functions},
year={1996},
volume={E79-A},
number={10},
pages={1624-1629},
abstract={This paper describes some dynamical properties of higher order neural networks with decreasing energy functions. First, we will show that for any symmetric higher order neural network which permits only one element to transit at each step, there are only periodic sequences with the length 1. Further, it will be shown that for any higher order neural network, with decreasing energy functions, which permits all elements to transit at each step, there does not exist any periodic sequence with the length being over k + 1, where k is the order of the network. Lastly, we will give a characterization for higher order neural networks, with the order 2 and a decreasing energy function each, which permit plural elements to transit at each step and have periodic sequences only with the lengh 1.},
keywords={},
doi={},
ISSN={},
month={October},}
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TY - JOUR
TI - Some Characteristics of Higher Order Neural Networks with Decreasing Energy Functions
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 1624
EP - 1629
AU - Hiromi MIYAJIMA
AU - Shuji YATSUKI
AU - Michiharu MAEDA
PY - 1996
DO -
JO - IEICE TRANSACTIONS on Fundamentals
SN -
VL - E79-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 1996
AB - This paper describes some dynamical properties of higher order neural networks with decreasing energy functions. First, we will show that for any symmetric higher order neural network which permits only one element to transit at each step, there are only periodic sequences with the length 1. Further, it will be shown that for any higher order neural network, with decreasing energy functions, which permits all elements to transit at each step, there does not exist any periodic sequence with the length being over k + 1, where k is the order of the network. Lastly, we will give a characterization for higher order neural networks, with the order 2 and a decreasing energy function each, which permit plural elements to transit at each step and have periodic sequences only with the lengh 1.
ER -
English
