2006 Fiscal Year Final Research Report Summary
Constructive Research on Real-Number Computation with Large-Scale Chaotic Networks
| Project/Area Number |
16300072
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| Research Category |
Grant-in-Aid for Scientific Research (B)
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| Allocation Type | Single-year Grants |
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| Section | 一般 |
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| Research Field |
Sensitivity informatics/Soft computing
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| Research Institution | Tokyo Denki University |
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Principal Investigator |
HORIO Yoshihiko Tokyo Denki University, School of Engineering, Professor, 工学部, 教授 (60199544)
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| Co-Investigator(Kenkyū-buntansha) |
ADACHI Masaharu Tokyo Denki University, School of Engineering, Professor, 工学部, 教授 (20312035)
IKEGUCHI Tohru Saitama University, Information and Computer Science, Professor, 大学院理工学研究科, 教授 (30222863)
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| Project Period (FY) |
2004 – 2006
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| Keywords | Chaos / Real-Number Computation / Analog Nonlinear Circuits / Combinatorial Optimization / Complex Systems / Neural Network |
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| Research Abstract |
First, we constructed hardware systems with analog integrated circuits realizing large-scale physical chaotic networks. Here, we took two approaches ; 1) Top-down approach : In this approach, we observe the internal high-dimensional dynamics of the chaotic hardware system. Then, we construct a solution for a given problem according to the observed dynamics. 2) Bottom-up approach : A heuristic algorithm is driven by a high-dimensional physical chaotic dynamics. Through both approaches, we intended to make fusion of analog computation with physical dynamics and digital computation with numerical algorithm in order to device a novel computational system based on real-number. As a result, the proposed system has shown a superior computational performance over conventional digital computation, in particular, for combinatorial optimization problems. At the same time, we showed that spatial mutual information would be a good measure for information processing through high-dimensional chaotic
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dynamics even with noise.
Second, we proposed a method for analyzing the dynamics of associative chaotic neural networks. The method compares the original network with surrogate networks whose constituent neurons are replaced with the element preserving some statistics of the neurons in the original network. By the analysis with the method, it is found that the cross-correlation among neurons plays an important role for maintaining dynamical association. We also proposed a simple quantization method for chaotic dynamical systems, and apply the method to controlling chaos with a reinforcement learning. We confirmed that the proposed quantization method with a reinforcement learning is successful for controlling chaos of both discrete and continuous time systems with remarkably smaller computational costs than that of a conventional method.
Finally, we proposed a method for solving NP-hard combinatorial optimization problems by chaotic neurodynamics in order to demonstrate an applicability of our computational model to real-world problems. We applied the proposed methods to the packet routing problem (one of the stochastic and dynamic shortest path problems), the motif extraction problem (one of the most important issues in the genome information science), and the vehicle routing problems with time windows (one of the practical extended problems of Traveling Salesman Problem). Numerical simulation shows that the proposed method exhibits high solving ability for these problems. We also analyzed why the chaotic neuro dynamics is so effective for combinatorial optimization. Using the method of surrogate data, which is one of the techniques frequently used in the nonlinear time seriesanalysis, we investigated the refractory effect produced from the chaotic neurons and revealed that surrogate dynamics such as stochastic process Is not valid for solving these combinatorial optimization problems. Less
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