IEICE TRANSACTIONS on Fundamentals
Avoidance of the Permanent Oscillating State in the Inverse Function Delayed Neural Network
Summary :
Many researchers have attempted to solve the combinatorial optimization problems, that are NP-hard or NP-complete problems, by using neural networks. Though the method used in a neural network has some advantages, the local minimum problem is not solved yet. It has been shown that the Inverse Function Delayed (ID) model, which is a neuron model with a negative resistance on its dynamics and can destabilize an intended region, can be used as the powerful tool to avoid the local minima. In our previous paper, we have shown that the ID network can separate local minimum states from global minimum states in case that the energy function of the embed problem is zero. It can achieve 100% success rate in the N-Queen problem with the certain parameter region. However, for a wider parameter region, the ID network cannot reach a global minimum state while all of local minimum states are unstable. In this paper, we show that the ID network falls into a particular permanent oscillating state in this situation. Several neurons in the network keep spiking in the particular permanent oscillating state, and hence the state transition never proceed for global minima. However, we can also clarify that the oscillating state is controlled by the parameter α which affects the negative resistance region and the hysteresis property of the ID model. In consequence, there is a parameter region where combinatorial optimization problems are solved at the 100% success rate.
- Publication
- IEICE TRANSACTIONS on Fundamentals Vol.E90-A No.10 pp.2101-2107
- Publication Date
- 2007/10/01
- Publicized
- Online ISSN
- 1745-1337
- DOI
- 10.1093/ietfec/e90-a.10.2101
- Type of Manuscript
- Special Section PAPER (Special Section on Nonlinear Theory and its Applications)
- Category
- Neuron and Neural Networks
Authors
Keyword
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Akari SATO, Yoshihiro HAYAKAWA, Koji NAKAJIMA, "Avoidance of the Permanent Oscillating State in the Inverse Function Delayed Neural Network" in IEICE TRANSACTIONS on Fundamentals,
vol. E90-A, no. 10, pp. 2101-2107, October 2007, doi: 10.1093/ietfec/e90-a.10.2101.
Abstract: Many researchers have attempted to solve the combinatorial optimization problems, that are NP-hard or NP-complete problems, by using neural networks. Though the method used in a neural network has some advantages, the local minimum problem is not solved yet. It has been shown that the Inverse Function Delayed (ID) model, which is a neuron model with a negative resistance on its dynamics and can destabilize an intended region, can be used as the powerful tool to avoid the local minima. In our previous paper, we have shown that the ID network can separate local minimum states from global minimum states in case that the energy function of the embed problem is zero. It can achieve 100% success rate in the N-Queen problem with the certain parameter region. However, for a wider parameter region, the ID network cannot reach a global minimum state while all of local minimum states are unstable. In this paper, we show that the ID network falls into a particular permanent oscillating state in this situation. Several neurons in the network keep spiking in the particular permanent oscillating state, and hence the state transition never proceed for global minima. However, we can also clarify that the oscillating state is controlled by the parameter α which affects the negative resistance region and the hysteresis property of the ID model. In consequence, there is a parameter region where combinatorial optimization problems are solved at the 100% success rate.
URL: https://global.ieice.org/en_transactions/fundamentals/10.1093/ietfec/e90-a.10.2101/_p
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@ARTICLE{e90-a_10_2101,
author={Akari SATO, Yoshihiro HAYAKAWA, Koji NAKAJIMA, },
journal={IEICE TRANSACTIONS on Fundamentals},
title={Avoidance of the Permanent Oscillating State in the Inverse Function Delayed Neural Network},
year={2007},
volume={E90-A},
number={10},
pages={2101-2107},
abstract={Many researchers have attempted to solve the combinatorial optimization problems, that are NP-hard or NP-complete problems, by using neural networks. Though the method used in a neural network has some advantages, the local minimum problem is not solved yet. It has been shown that the Inverse Function Delayed (ID) model, which is a neuron model with a negative resistance on its dynamics and can destabilize an intended region, can be used as the powerful tool to avoid the local minima. In our previous paper, we have shown that the ID network can separate local minimum states from global minimum states in case that the energy function of the embed problem is zero. It can achieve 100% success rate in the N-Queen problem with the certain parameter region. However, for a wider parameter region, the ID network cannot reach a global minimum state while all of local minimum states are unstable. In this paper, we show that the ID network falls into a particular permanent oscillating state in this situation. Several neurons in the network keep spiking in the particular permanent oscillating state, and hence the state transition never proceed for global minima. However, we can also clarify that the oscillating state is controlled by the parameter α which affects the negative resistance region and the hysteresis property of the ID model. In consequence, there is a parameter region where combinatorial optimization problems are solved at the 100% success rate.},
keywords={},
doi={10.1093/ietfec/e90-a.10.2101},
ISSN={1745-1337},
month={October},}
Copy
TY - JOUR
TI - Avoidance of the Permanent Oscillating State in the Inverse Function Delayed Neural Network
T2 - IEICE TRANSACTIONS on Fundamentals
SP - 2101
EP - 2107
AU - Akari SATO
AU - Yoshihiro HAYAKAWA
AU - Koji NAKAJIMA
PY - 2007
DO - 10.1093/ietfec/e90-a.10.2101
JO - IEICE TRANSACTIONS on Fundamentals
SN - 1745-1337
VL - E90-A
IS - 10
JA - IEICE TRANSACTIONS on Fundamentals
Y1 - October 2007
AB - Many researchers have attempted to solve the combinatorial optimization problems, that are NP-hard or NP-complete problems, by using neural networks. Though the method used in a neural network has some advantages, the local minimum problem is not solved yet. It has been shown that the Inverse Function Delayed (ID) model, which is a neuron model with a negative resistance on its dynamics and can destabilize an intended region, can be used as the powerful tool to avoid the local minima. In our previous paper, we have shown that the ID network can separate local minimum states from global minimum states in case that the energy function of the embed problem is zero. It can achieve 100% success rate in the N-Queen problem with the certain parameter region. However, for a wider parameter region, the ID network cannot reach a global minimum state while all of local minimum states are unstable. In this paper, we show that the ID network falls into a particular permanent oscillating state in this situation. Several neurons in the network keep spiking in the particular permanent oscillating state, and hence the state transition never proceed for global minima. However, we can also clarify that the oscillating state is controlled by the parameter α which affects the negative resistance region and the hysteresis property of the ID model. In consequence, there is a parameter region where combinatorial optimization problems are solved at the 100% success rate.
ER -
English
