Chaotic Boltzmann machines

Hideyuki Suzuki; Jun Ichi Imura; Yoshihiko Horio; Kazuyuki Aihara

doi:10.1038/srep01610

Chaotic Boltzmann machines

Hideyuki Suzuki, Jun Ichi Imura, Yoshihiko Horio, Kazuyuki Aihara

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

22 Citations (Scopus)

Abstract

The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented.

Original language	English
Article number	1610
Journal	Scientific reports
Volume	3
DOIs	https://doi.org/10.1038/srep01610
Publication status	Published - 2013 Apr 5
Externally published	Yes

ASJC Scopus subject areas

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10.1038/srep01610

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title = "Chaotic Boltzmann machines",

abstract = "The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented.",

author = "Hideyuki Suzuki and Imura, {Jun Ichi} and Yoshihiko Horio and Kazuyuki Aihara",

note = "Funding Information: This research is supported by the Aihara Innovative Mathematical Modelling Project, the Japan Society for the Promotion of Science (JSPS) through the {\textquoteleft}{\textquoteleft}Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program){\textquoteright}{\textquoteright}, initiated by the Council for Science and Technology Policy (CSTP).",

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T1 - Chaotic Boltzmann machines

AU - Suzuki, Hideyuki

AU - Imura, Jun Ichi

AU - Horio, Yoshihiko

AU - Aihara, Kazuyuki

N1 - Funding Information: This research is supported by the Aihara Innovative Mathematical Modelling Project, the Japan Society for the Promotion of Science (JSPS) through the ‘‘Funding Program for World-Leading Innovative R&D on Science and Technology (FIRST Program)’’, initiated by the Council for Science and Technology Policy (CSTP).

PY - 2013/4/5

Y1 - 2013/4/5

N2 - The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented.

AB - The chaotic Boltzmann machine proposed in this paper is a chaotic pseudo-billiard system that works as a Boltzmann machine. Chaotic Boltzmann machines are shown numerically to have computing abilities comparable to conventional (stochastic) Boltzmann machines. Since no randomness is required, efficient hardware implementation is expected. Moreover, the ferromagnetic phase transition of the Ising model is shown to be characterised by the largest Lyapunov exponent of the proposed system. In general, a method to relate probabilistic models to nonlinear dynamics by derandomising Gibbs sampling is presented.

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Chaotic Boltzmann machines

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