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Kawai Y, Park J, Tsuda I, Asada M. Learning long-term motor timing/patterns on an orthogonal basis in random neural networks. Neural Netw 2023; 163:298-311. [PMID: 37087852 DOI: 10.1016/j.neunet.2023.04.006] [Citation(s) in RCA: 0] [Impact Index Per Article: 0] [Reference Citation Analysis] [What about the content of this article? (0)] [Affiliation(s)] [Abstract] [Key Words] [Track Full Text] [Journal Information] [Subscribe] [Scholar Register] [Received: 07/22/2022] [Revised: 03/15/2023] [Accepted: 04/05/2023] [Indexed: 04/25/2023]
Abstract
The ability of the brain to generate complex spatiotemporal patterns with specific timings is essential for motor learning and temporal processing. An approach that can model this function, using the spontaneous activity of a random neural network (RNN), is associated with orbital instability. We propose a simple system that learns an arbitrary time series as the linear sum of stable trajectories produced by several small network modules. New finding in computer experiments is that the trajectories of the module outputs are orthogonal to each other. They created a dynamic orthogonal basis acquiring a high representational capacity, which enabled the system to learn the timing of extremely long intervals, such as tens of seconds for a millisecond computation unit, and also the complex time series of Lorenz attractors. This self-sustained system satisfies the stability and orthogonality requirements and thus provides a new neurocomputing framework and perspective for the neural mechanisms of motor learning.
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Affiliation(s)
- Yuji Kawai
- Symbiotic Intelligent Systems Research Center, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, 1-1 Yamadaoka, Suita, Osaka 565-0871, Japan.
| | - Jihoon Park
- Symbiotic Intelligent Systems Research Center, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, 1-1 Yamadaoka, Suita, Osaka 565-0871, Japan; Center for Information and Neural Networks, National Institute of Information and Communications Technology, 1-4 Yamadaoka, Suita, Osaka 565-0871, Japan
| | - Ichiro Tsuda
- Chubu University Academy of Emerging Sciences/Center for Mathematical Science and Artificial Intelligence, Chubu University, 1200 Matsumoto-cho, Kasugai, Aichi 487-8501, Japan
| | - Minoru Asada
- Symbiotic Intelligent Systems Research Center, Institute for Open and Transdisciplinary Research Initiatives, Osaka University, 1-1 Yamadaoka, Suita, Osaka 565-0871, Japan; Center for Information and Neural Networks, National Institute of Information and Communications Technology, 1-4 Yamadaoka, Suita, Osaka 565-0871, Japan; Chubu University Academy of Emerging Sciences/Center for Mathematical Science and Artificial Intelligence, Chubu University, 1200 Matsumoto-cho, Kasugai, Aichi 487-8501, Japan; International Professional University of Technology in Osaka, 3-3-1 Umeda, Kita-ku, Osaka 530-0001, Japan
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Abstract
The fabric tensor is employed as a quantitative stereological measure of the structural anisotropy in the pore architecture of a porous medium. Earlier work showed that the fabric tensor can be used additionally to the porosity to describe the anisotropy in the elastic constants of the porous medium. This contribution presents a reformulation of the relationship between fabric tensor and anisotropic elastic constants that is approximation free and symmetry-invariant. From specific data on the elastic constants and the fabric, the parameters in the reformulated relationship can be evaluated individually and efficiently using a simplified method that works independent of the material symmetry. The well-behavedness of the parameters and the accuracy of the method was analyzed using the Mori-Tanaka model for aligned ellipsoidal inclusions and using Buckminster Fuller's octet-truss lattice. Application of the method to a cancellous bone data set revealed that employing the fabric tensor allowed explaining 75-90% of the total variance. An implementation of the proposed methods was made publicly available.
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Affiliation(s)
- Maarten Moesen
- Department of Metallurgy and Materials Engineering, Katholieke Universiteit Leuven, Kasteelpark Arenberg 44, PB 2450, 3001 Leuven, Belgium
- Prometheus, Division of Skeletal Tissue Engineering, Katholieke Universiteit Leuven, O&N 1, Herestraat 49, PB 813, 3000 Leuven, Belgium
| | - Luis Cardoso
- The New York Center for Biomedical Engineering, The Departments of Biomedical & Mechanical Engineering, The School of Engineering of The City College, and The Graduate School of The City University of New York, NY 10031, USA
| | - Stephen C. Cowin
- The New York Center for Biomedical Engineering, The Departments of Biomedical & Mechanical Engineering, The School of Engineering of The City College, and The Graduate School of The City University of New York, NY 10031, USA
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